Metrics for 2cos (problem 3.3.5)

analyze43.0ms (0.2%)

Memory

-38.8MiB live, 51.7MiB allocated

Algorithm

1×

Search

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

Compiler

Compiled 27 to 19 computations (29.6% saved)

sample9.7s (53.6%)

Memory

-96.3MiB live, 11 470.3MiB allocated

Samples

4.0s	25 882×	0	invalid
3.4s	5 648×	2	valid
648.0ms	2 475×	1	valid
16.0ms	133×	0	valid

Precisions

Click to see histograms. Total time spent on operations: 6.3s

ival-cos: 2.7s (41.9% of total)

const: 1.0s (15.8% of total)

adjust: 533.0ms (8.4% of total)

ival-<=: 386.0ms (6.1% of total)

ival-sub: 373.0ms (5.9% of total)

ival-fabs: 347.0ms (5.5% of total)

ival-add: 319.0ms (5% of total)

ival-mult: 310.0ms (4.9% of total)

ival-<: 246.0ms (3.9% of total)

ival-and: 101.0ms (1.6% of total)

exact: 47.0ms (0.7% of total)

ival-assert: 14.0ms (0.2% of total)

Bogosity

preprocess94.0ms (0.5%)

Memory

16.3MiB live, 54.6MiB allocated

Algorithm

1×	egg-herbie

Rules

108×	`sub-neg`
80×	`lower-fma.f64`
80×	`lower-fma.f32`
80×	`associate--r+`
66×	`cancel-sign-sub-inv`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	41
1	38	37
2	81	35
3	152	35
4	278	35
5	370	35
6	448	35
7	485	35
8	531	35
9	546	35
10	554	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 (cos.f64 (+.f64 x eps)) (cos.f64 x))

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

explain258.0ms (1.4%)

Memory

7.8MiB live, 521.0MiB allocated

FPErrors

Click to see full error table

Ground Truth	Overpredictions	Example	Example	Subexpression
129	1	(1.189698924206829e-160 3.2066630412307237e-164)	-	`(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))`
2	0	-	-	`(cos.f64 (+.f64 x eps))`
0	0	-	-	`eps`
0	0	-	-	`(+.f64 x eps)`
0	0	-	-	`(cos.f64 x)`
0	0	-	-	`x`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`-.f64`	`(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))`	cancellation	130	0
`cos.f64`	`(cos.f64 (+.f64 x eps))`	sensitivity	2	0

Confusion

	Predicted +	Predicted -
+	131	0
-	1	124

Precision

0.9924242424242424

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	131	0	0
-	1	0	124

Precision?

0.9924242424242424

Recall?

1.0

Freqs

test

number	freq
0	124
1	132

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

151.0ms	366×	2	valid
25.0ms	136×	1	valid
1.0ms	10×	0	valid

Compiler

Compiled 58 to 28 computations (51.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 139.0ms

ival-cos: 105.0ms (75.4% of total)

adjust: 24.0ms (17.2% of total)

ival-sub: 6.0ms (4.3% of total)

ival-add: 3.0ms (2.2% of total)

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

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

eval0.0ms (0%)

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

prune1.0ms (0%)

Memory

2.0MiB live, 2.0MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	54.8%	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))

Compiler

Compiled 9 to 6 computations (33.3% saved)

simplify11.0ms (0.1%)

Memory

-19.8MiB live, 18.0MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

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

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

localize108.0ms (0.6%)

Memory

-23.1MiB live, 194.9MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(+.f64 x eps)
✓	accuracy	100.0%	(cos.f64 x)
✓	accuracy	99.9%	(cos.f64 (+.f64 x eps))
✓	accuracy	54.9%	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))

Samples

90.0ms	183×	2	valid
8.0ms	68×	1	valid
0.0ms	5×	0	valid

Compiler

Compiled 20 to 8 computations (60% saved)

Precisions

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

ival-cos: 70.0ms (83.2% of total)

adjust: 9.0ms (10.7% of total)

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

ival-add: 2.0ms (2.4% of total)

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

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

series4.0ms (0%)

Memory

9.8MiB live, 9.8MiB allocated

Counts

4 → 84

Calls

Call 1

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

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

Calls

21 calls:

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

rewrite337.0ms (1.9%)

Memory

13.1MiB live, 479.6MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

4 936×	`lower-fma.f64`
4 936×	`lower-fma.f32`
4 656×	`lower-*.f64`
4 656×	`lower-*.f32`
2 192×	`lower-/.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	16
0	10	16
1	54	16
2	380	16
3	4694	16
0	8209	16

Stop Event

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

Counts

4 → 228

Calls

Call 1

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

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

simplify386.0ms (2.1%)

Memory

25.7MiB live, 583.2MiB allocated

Algorithm

1×	egg-herbie

Rules

14 158×	`lower-fma.f64`
14 158×	`lower-fma.f32`
4 148×	`lower-*.f64`
4 148×	`lower-*.f32`
3 720×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	105	498
1	277	495
2	609	495
3	2398	494
4	7880	494
0	8026	474

Stop Event

1×	iter limit
1×	node limit

Counts

84 → 78

Calls

Call 1

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

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

eval39.0ms (0.2%)

Memory: -21.8MiB live, 90.1MiB allocated
Compiler: Compiled 7 945 to 876 computations (89% saved)

prune56.0ms (0.3%)

Memory

-30.7MiB live, 120.1MiB allocated

Pruning

15 alts after pruning (14 fresh and 1 done)

	Pruned	Kept	Total
New	292	14	306
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	292	15	307

Accuracy

99.8%

Counts

307 → 15

Alt Table

Click to see full alt table

Status	Accuracy	Program
	54.8%	(fma.f64 (pow.f64 (cos.f64 (+.f64 x eps)) #s(literal 3 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 (cos.f64 x) (+.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 (+.f64 x eps) #s(literal 2 binary64))) #s(literal 1/2 binary64)))) (neg.f64 (/.f64 (pow.f64 (cos.f64 x) #s(literal 3 binary64)) (fma.f64 (cos.f64 x) (+.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 (+.f64 x eps) #s(literal 2 binary64))) #s(literal 1/2 binary64))))))
	54.8%	(fma.f64 (cos.f64 x) (cos.f64 eps) (neg.f64 (fma.f64 (sin.f64 x) (sin.f64 eps) (cos.f64 x))))
▶	54.8%	(/.f64 (-.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 (+.f64 x eps) #s(literal 2 binary64))) #s(literal 1/2 binary64)) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (+.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)))
	54.8%	(/.f64 (-.f64 (pow.f64 (/.f64 (pow.f64 (cos.f64 (+.f64 x eps)) #s(literal 3 binary64)) (fma.f64 (cos.f64 x) (+.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 (+.f64 x eps) #s(literal 2 binary64))) #s(literal 1/2 binary64)))) #s(literal 2 binary64)) (pow.f64 (/.f64 (pow.f64 (cos.f64 x) #s(literal 3 binary64)) (fma.f64 (cos.f64 x) (+.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 (+.f64 x eps) #s(literal 2 binary64))) #s(literal 1/2 binary64)))) #s(literal 2 binary64))) (+.f64 (/.f64 (pow.f64 (cos.f64 (+.f64 x eps)) #s(literal 3 binary64)) (fma.f64 (cos.f64 x) (+.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 (+.f64 x eps) #s(literal 2 binary64))) #s(literal 1/2 binary64)))) (/.f64 (pow.f64 (cos.f64 x) #s(literal 3 binary64)) (fma.f64 (cos.f64 x) (+.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 (+.f64 x eps) #s(literal 2 binary64))) #s(literal 1/2 binary64))))))
	54.8%	(-.f64 (fma.f64 (cos.f64 x) (cos.f64 eps) (neg.f64 (*.f64 (sin.f64 x) (sin.f64 eps)))) (cos.f64 x))
	54.8%	(-.f64 (/.f64 (pow.f64 (cos.f64 (+.f64 x eps)) #s(literal 3 binary64)) (fma.f64 (cos.f64 x) (+.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 (+.f64 x eps) #s(literal 2 binary64))) #s(literal 1/2 binary64)))) (/.f64 (pow.f64 (cos.f64 x) #s(literal 3 binary64)) (fma.f64 (cos.f64 x) (+.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 (+.f64 x eps) #s(literal 2 binary64))) #s(literal 1/2 binary64)))))
▶	81.0%	(-.f64 (+.f64 (neg.f64 (cos.f64 x)) (.f64 (cos.f64 x) (cos.f64 eps))) (.f64 (sin.f64 x) (sin.f64 eps)))
▶	53.4%	(-.f64 (cos.f64 (+.f64 x eps)) (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)))
✓	54.8%	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
	53.1%	(-.f64 (cos.f64 (+.f64 x eps)) #s(literal 1 binary64))
▶	53.1%	(+.f64 (cos.f64 eps) #s(literal -1 binary64))
▶	99.6%	(.f64 (.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (sin.f64 (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)))) #s(literal -2 binary64))
	79.9%	(*.f64 (sin.f64 x) (neg.f64 eps))
	99.0%	(.f64 eps (fma.f64 eps (fma.f64 (cos.f64 x) (+.f64 #s(literal -1/2 binary64) (.f64 eps (.f64 eps #s(literal 1/24 binary64)))) (.f64 eps (*.f64 #s(literal 1/6 binary64) (sin.f64 x)))) (sin.f64 (neg.f64 x))))
	98.9%	(.f64 eps (-.f64 (.f64 eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x)))

Compiler

Compiled 775 to 348 computations (55.1% saved)

simplify356.0ms (2%)

Memory

45.5MiB live, 634.7MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 18 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(cos.f64 x)
✓	cost-diff	0	(neg.f64 (cos.f64 x))
✓	cost-diff	0	(-.f64 (+.f64 (neg.f64 (cos.f64 x)) (.f64 (cos.f64 x) (cos.f64 eps))) (.f64 (sin.f64 x) (sin.f64 eps)))
✓	cost-diff	6528	(+.f64 (neg.f64 (cos.f64 x)) (*.f64 (cos.f64 x) (cos.f64 eps)))
✓	cost-diff	0	(cos.f64 (*.f64 (+.f64 x eps) #s(literal 2 binary64)))
✓	cost-diff	0	(fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 (+.f64 x eps) #s(literal 2 binary64))) #s(literal 1/2 binary64))
✓	cost-diff	0	(/.f64 (-.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 (+.f64 x eps) #s(literal 2 binary64))) #s(literal 1/2 binary64)) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (+.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)))
✓	cost-diff	448	(-.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 (+.f64 x eps) #s(literal 2 binary64))) #s(literal 1/2 binary64)) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64)))
✓	cost-diff	0	(fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))
✓	cost-diff	0	(+.f64 x eps)
✓	cost-diff	0	(cos.f64 (+.f64 x eps))
✓	cost-diff	0	(-.f64 (cos.f64 (+.f64 x eps)) (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)))
✓	cost-diff	0	(cos.f64 eps)
✓	cost-diff	0	(+.f64 (cos.f64 eps) #s(literal -1 binary64))
✓	cost-diff	0	(.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (sin.f64 (*.f64 (+.f64 x (+.f64 x 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))) (sin.f64 (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)))) #s(literal -2 binary64))
✓	cost-diff	192	(+.f64 eps #s(literal 0 binary64))
✓	cost-diff	320	(*.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64))

Rules

14 364×	`lower-fma.f32`
14 358×	`lower-fma.f64`
3 168×	`lower-*.f32`
3 152×	`lower-*.f64`
2 688×	`lower-+.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	41	256
0	76	246
1	127	242
2	257	234
3	513	226
4	1116	226
5	3001	226
6	5569	226
0	8144	221

Stop Event

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

Calls

Call 1

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

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

localize540.0ms (3%)

Memory

-4.1MiB live, 741.3MiB allocated

Localize:

Found 18 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(*.f64 (cos.f64 x) (cos.f64 eps))
✓	accuracy	100.0%	(*.f64 (sin.f64 x) (sin.f64 eps))
✓	accuracy	99.8%	(-.f64 (+.f64 (neg.f64 (cos.f64 x)) (.f64 (cos.f64 x) (cos.f64 eps))) (.f64 (sin.f64 x) (sin.f64 eps)))
✓	accuracy	55.7%	(+.f64 (neg.f64 (cos.f64 x)) (*.f64 (cos.f64 x) (cos.f64 eps)))
✓	accuracy	100.0%	(/.f64 (-.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 (+.f64 x eps) #s(literal 2 binary64))) #s(literal 1/2 binary64)) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (+.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)))
✓	accuracy	99.9%	(cos.f64 (+.f64 x eps))
✓	accuracy	99.9%	(cos.f64 (*.f64 (+.f64 x eps) #s(literal 2 binary64)))
✓	accuracy	54.9%	(-.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 (+.f64 x eps) #s(literal 2 binary64))) #s(literal 1/2 binary64)) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64)))
✓	accuracy	100.0%	(+.f64 x eps)
✓	accuracy	100.0%	(*.f64 x #s(literal -1/2 binary64))
✓	accuracy	99.9%	(cos.f64 (+.f64 x eps))
✓	accuracy	55.8%	(-.f64 (cos.f64 (+.f64 x eps)) (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)))
✓	accuracy	100.0%	(cos.f64 eps)
✓	accuracy	55.7%	(+.f64 (cos.f64 eps) #s(literal -1 binary64))
✓	accuracy	100.0%	(.f64 (.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (sin.f64 (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)))) #s(literal -2 binary64))
✓	accuracy	99.8%	(sin.f64 (*.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)))
✓	accuracy	99.8%	(.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (sin.f64 (*.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64))))
✓	accuracy	99.6%	(+.f64 x (+.f64 x eps))

Samples

375.0ms	182×	2	valid
67.0ms	69×	1	valid
3.0ms	1×	3	valid
2.0ms	4×	0	valid

Compiler

Compiled 266 to 46 computations (82.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 339.0ms

ival-cos: 198.0ms (58.4% of total)

adjust: 46.0ms (13.6% of total)

ival-sin: 28.0ms (8.3% of total)

ival-mult: 27.0ms (8% of total)

ival-add: 24.0ms (7.1% of total)

ival-sub: 9.0ms (2.7% of total)

ival-div: 4.0ms (1.2% of total)

ival-neg: 3.0ms (0.9% of total)

exact: 1.0ms (0.3% of total)

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

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

series107.0ms (0.6%)

Memory

8.4MiB live, 109.4MiB allocated

Counts

23 → 468

Calls

Call 1

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

Outputs
#<alt (* 1/2 eps)>
#<alt (+ x (* 1/2 eps))>
#<alt (+ x (* 1/2 eps))>
#<alt (+ x (* 1/2 eps))>
#<alt x>
#<alt (* x (+ 1 (* 1/2 (/ eps x))))>
#<alt (* x (+ 1 (* 1/2 (/ eps x))))>
#<alt (* x (+ 1 (* 1/2 (/ eps x))))>
#<alt x>
#<alt (* -1 (* x (- (* -1/2 (/ eps x)) 1)))>
#<alt (* -1 (* x (- (* -1/2 (/ eps x)) 1)))>
#<alt (* -1 (* x (- (* -1/2 (/ eps x)) 1)))>
#<alt x>
#<alt (+ x (* 1/2 eps))>
#<alt (+ x (* 1/2 eps))>
#<alt (+ x (* 1/2 eps))>
#<alt (* 1/2 eps)>
#<alt (* eps (+ 1/2 (/ x eps)))>
#<alt (* eps (+ 1/2 (/ x eps)))>
#<alt (* eps (+ 1/2 (/ x eps)))>
#<alt (* 1/2 eps)>
#<alt (* -1 (* eps (- (* -1 (/ x eps)) 1/2)))>
#<alt (* -1 (* eps (- (* -1 (/ x eps)) 1/2)))>
#<alt (* -1 (* eps (- (* -1 (/ x eps)) 1/2)))>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt (* -1 (* eps (sin x)))>
#<alt (* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))>
#<alt (* eps (+ (* -1 (sin x)) (* eps (+ (* -2 (* eps (+ (* -1/16 (sin x)) (* -1/48 (sin x))))) (* -1/2 (cos x))))))>
#<alt (* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* eps (+ (* -2 (+ (* -1/16 (sin x)) (* -1/48 (sin x)))) (* 1/24 (* eps (cos x)))))))))>
#<alt (* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))>
#<alt (* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))>
#<alt (* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))>
#<alt (* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))>
#<alt (* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps))))))>
#<alt (* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps))))))>
#<alt (* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps))))))>
#<alt (* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps))))))>
#<alt (* -2 (pow (sin (* 1/2 eps)) 2))>
#<alt (+ (* -2 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (* -2 (pow (sin (* 1/2 eps)) 2)))>
#<alt (+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (pow (sin (* 1/2 eps)) 2)))))>
#<alt (+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* 1/3 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (pow (sin (* 1/2 eps)) 2))))))>
#<alt (* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))>
#<alt (* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))>
#<alt (* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))>
#<alt (* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))>
#<alt (* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x))))))>
#<alt (* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x))))))>
#<alt (* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x))))))>
#<alt (* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x))))))>
#<alt (* 1/2 (* eps (sin x)))>
#<alt (* eps (+ (* 1/4 (* eps (cos x))) (* 1/2 (sin x))))>
#<alt (* eps (+ (* 1/2 (sin x)) (* eps (+ (* 1/4 (cos x)) (* eps (+ (* -1/16 (sin x)) (* -1/48 (sin x))))))))>
#<alt (* eps (+ (* 1/2 (sin x)) (* eps (+ (* 1/4 (cos x)) (* eps (+ (* -1/16 (sin x)) (+ (* -1/48 (sin x)) (* -1/48 (* eps (cos x))))))))))>
#<alt (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))>
#<alt (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))>
#<alt (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))>
#<alt (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))>
#<alt (* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps)))))>
#<alt (* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps)))))>
#<alt (* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps)))))>
#<alt (* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps)))))>
#<alt (pow (sin (* 1/2 eps)) 2)>
#<alt (+ (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (pow (sin (* 1/2 eps)) 2))>
#<alt (+ (* x (+ (* -1/2 (* x (pow (sin (* 1/2 eps)) 2))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (pow (sin (* 1/2 eps)) 2))>
#<alt (+ (* x (+ (* x (+ (* -1/2 (pow (sin (* 1/2 eps)) 2)) (* -1/6 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (pow (sin (* 1/2 eps)) 2))>
#<alt (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))>
#<alt (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))>
#<alt (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))>
#<alt (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))>
#<alt (* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x)))))>
#<alt (* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x)))))>
#<alt (* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x)))))>
#<alt (* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x)))))>
#<alt (* -1/2 (pow eps 2))>
#<alt (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))>
#<alt (* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2))>
#<alt (* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* (pow eps 2) (- (* 1/40320 (pow eps 2)) 1/720)))) 1/2))>
#<alt (- (cos eps) 1)>
#<alt (- (cos eps) 1)>
#<alt (- (cos eps) 1)>
#<alt (- (cos eps) 1)>
#<alt (- (cos eps) 1)>
#<alt (- (cos eps) 1)>
#<alt (- (cos eps) 1)>
#<alt (- (cos eps) 1)>
#<alt 1>
#<alt (+ 1 (* -1/2 (pow eps 2)))>
#<alt (+ 1 (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))>
#<alt (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2)))>
#<alt (cos eps)>
#<alt (cos eps)>
#<alt (cos eps)>
#<alt (cos eps)>
#<alt (cos eps)>
#<alt (cos eps)>
#<alt (cos eps)>
#<alt (cos eps)>
#<alt (- (cos eps) 1)>
#<alt (- (+ (cos eps) (* -1 (* x (sin eps)))) 1)>
#<alt (- (+ (cos eps) (* x (- (* x (+ 1/2 (* -1/2 (cos eps)))) (sin eps)))) 1)>
#<alt (- (+ (cos eps) (* x (- (* x (+ 1/2 (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps)))))) (sin eps)))) 1)>
#<alt (* 1/2 (pow x 2))>
#<alt (* (pow x 2) (- (+ 1/2 (/ (cos (+ eps x)) (pow x 2))) (/ 1 (pow x 2))))>
#<alt (* (pow x 2) (- (+ 1/2 (/ (cos (+ eps x)) (pow x 2))) (/ 1 (pow x 2))))>
#<alt (* (pow x 2) (- (+ 1/2 (/ (cos (+ eps x)) (pow x 2))) (/ 1 (pow x 2))))>
#<alt (* 1/2 (pow x 2))>
#<alt (* (pow x 2) (- (+ 1/2 (/ (cos (- eps (* -1 x))) (pow x 2))) (/ 1 (pow x 2))))>
#<alt (* (pow x 2) (- (+ 1/2 (/ (cos (- eps (* -1 x))) (pow x 2))) (/ 1 (pow x 2))))>
#<alt (* (pow x 2) (- (+ 1/2 (/ (cos (- eps (* -1 x))) (pow x 2))) (/ 1 (pow x 2))))>
#<alt (- (cos x) (+ 1 (* -1/2 (pow x 2))))>
#<alt (- (+ (cos x) (* -1 (* eps (sin x)))) (+ 1 (* -1/2 (pow x 2))))>
#<alt (- (+ (cos x) (* eps (- (* -1/2 (* eps (cos x))) (sin x)))) (+ 1 (* -1/2 (pow x 2))))>
#<alt (- (+ (cos x) (* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x)))) (+ 1 (* -1/2 (pow x 2))))>
#<alt (- (cos (+ eps x)) (+ 1 (* -1/2 (pow x 2))))>
#<alt (- (cos (+ eps x)) (+ 1 (* -1/2 (pow x 2))))>
#<alt (- (cos (+ eps x)) (+ 1 (* -1/2 (pow x 2))))>
#<alt (- (cos (+ eps x)) (+ 1 (* -1/2 (pow x 2))))>
#<alt (- (cos (- x (* -1 eps))) (+ 1 (* -1/2 (pow x 2))))>
#<alt (- (cos (- x (* -1 eps))) (+ 1 (* -1/2 (pow x 2))))>
#<alt (- (cos (- x (* -1 eps))) (+ 1 (* -1/2 (pow x 2))))>
#<alt (- (cos (- x (* -1 eps))) (+ 1 (* -1/2 (pow x 2))))>
#<alt (cos eps)>
#<alt (+ (cos eps) (* -1 (* x (sin eps))))>
#<alt (+ (cos eps) (* x (- (* -1/2 (* x (cos eps))) (sin eps))))>
#<alt (+ (cos eps) (* x (- (* x (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps))))) (sin eps))))>
#<alt (cos (+ eps x))>
#<alt (cos (+ eps x))>
#<alt (cos (+ eps x))>
#<alt (cos (+ eps x))>
#<alt (cos (- eps (* -1 x)))>
#<alt (cos (- eps (* -1 x)))>
#<alt (cos (- eps (* -1 x)))>
#<alt (cos (- eps (* -1 x)))>
#<alt (cos x)>
#<alt (+ (cos x) (* -1 (* eps (sin x))))>
#<alt (+ (cos x) (* eps (- (* -1/2 (* eps (cos x))) (sin x))))>
#<alt (+ (cos x) (* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x))))>
#<alt (cos (+ eps x))>
#<alt (cos (+ eps x))>
#<alt (cos (+ eps x))>
#<alt (cos (+ eps x))>
#<alt (cos (- x (* -1 eps)))>
#<alt (cos (- x (* -1 eps)))>
#<alt (cos (- x (* -1 eps)))>
#<alt (cos (- 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 1>
#<alt (+ 1 (* -1/2 (pow x 2)))>
#<alt (+ 1 (* -1/2 (pow x 2)))>
#<alt (+ 1 (* -1/2 (pow x 2)))>
#<alt (* -1/2 (pow x 2))>
#<alt (* (pow x 2) (- (/ 1 (pow x 2)) 1/2))>
#<alt (* (pow x 2) (- (/ 1 (pow x 2)) 1/2))>
#<alt (* (pow x 2) (- (/ 1 (pow x 2)) 1/2))>
#<alt (* -1/2 (pow x 2))>
#<alt (* (pow x 2) (- (/ 1 (pow x 2)) 1/2))>
#<alt (* (pow x 2) (- (/ 1 (pow x 2)) 1/2))>
#<alt (* (pow x 2) (- (/ 1 (pow x 2)) 1/2))>
#<alt (- (* 1/2 (cos (* 2 eps))) 1/2)>
#<alt (- (+ (* -1 (* x (sin (* 2 eps)))) (* 1/2 (cos (* 2 eps)))) 1/2)>
#<alt (- (+ (* 1/2 (cos (* 2 eps))) (* x (+ (* -1 (sin (* 2 eps))) (* x (+ 1 (* -1 (cos (* 2 eps)))))))) 1/2)>
#<alt (- (+ (* 1/2 (cos (* 2 eps))) (* x (+ (* -1 (sin (* 2 eps))) (* x (+ 1 (+ (* -1 (cos (* 2 eps))) (* 2/3 (* x (sin (* 2 eps)))))))))) 1/2)>
#<alt (- (* 1/2 (cos (* 2 (+ eps x)))) (* 1/2 (cos (* 2 x))))>
#<alt (- (* 1/2 (cos (* 2 (+ eps x)))) (* 1/2 (cos (* 2 x))))>
#<alt (- (* 1/2 (cos (* 2 (+ eps x)))) (* 1/2 (cos (* 2 x))))>
#<alt (- (* 1/2 (cos (* 2 (+ eps x)))) (* 1/2 (cos (* 2 x))))>
#<alt (- (* 1/2 (cos (* 2 (- eps (* -1 x))))) (* 1/2 (cos (neg (* -2 x)))))>
#<alt (- (* 1/2 (cos (* 2 (- eps (* -1 x))))) (* 1/2 (cos (neg (* -2 x)))))>
#<alt (- (* 1/2 (cos (* 2 (- eps (* -1 x))))) (* 1/2 (cos (neg (* -2 x)))))>
#<alt (- (* 1/2 (cos (* 2 (- eps (* -1 x))))) (* 1/2 (cos (neg (* -2 x)))))>
#<alt (* -1 (* eps (sin (* 2 x))))>
#<alt (* eps (+ (* -1 (sin (* 2 x))) (* -1 (* eps (cos (* 2 x))))))>
#<alt (* eps (+ (* -1 (sin (* 2 x))) (* eps (+ (* -1 (cos (* 2 x))) (* 2/3 (* eps (sin (* 2 x))))))))>
#<alt (* eps (+ (* -1 (sin (* 2 x))) (* eps (+ (* -1 (cos (* 2 x))) (* eps (+ (* 1/3 (* eps (cos (* 2 x)))) (* 2/3 (sin (* 2 x)))))))))>
#<alt (- (* 1/2 (cos (* 2 (+ eps x)))) (* 1/2 (cos (* 2 x))))>
#<alt (- (* 1/2 (cos (* 2 (+ eps x)))) (* 1/2 (cos (* 2 x))))>
#<alt (- (* 1/2 (cos (* 2 (+ eps x)))) (* 1/2 (cos (* 2 x))))>
#<alt (- (* 1/2 (cos (* 2 (+ eps x)))) (* 1/2 (cos (* 2 x))))>
#<alt (- (* 1/2 (cos (* 2 (- x (* -1 eps))))) (* 1/2 (cos (* 2 x))))>
#<alt (- (* 1/2 (cos (* 2 (- x (* -1 eps))))) (* 1/2 (cos (* 2 x))))>
#<alt (- (* 1/2 (cos (* 2 (- x (* -1 eps))))) (* 1/2 (cos (* 2 x))))>
#<alt (- (* 1/2 (cos (* 2 (- x (* -1 eps))))) (* 1/2 (cos (* 2 x))))>
#<alt (/ (- (* 1/2 (cos (* 2 eps))) 1/2) (+ 1 (cos eps)))>
#<alt (- (+ (* 1/2 (/ (cos (* 2 eps)) (+ 1 (cos eps)))) (* x (- (* -1 (/ (sin (* 2 eps)) (+ 1 (cos eps)))) (* -1 (/ (* (sin eps) (- (* 1/2 (cos (* 2 eps))) 1/2)) (pow (+ 1 (cos eps)) 2)))))) (* 1/2 (/ 1 (+ 1 (cos eps)))))>
#<alt (- (+ (* 1/2 (/ (cos (* 2 eps)) (+ 1 (cos eps)))) (* x (- (+ (* -1 (/ (sin (* 2 eps)) (+ 1 (cos eps)))) (* x (- (+ (* -1 (/ (cos (* 2 eps)) (+ 1 (cos eps)))) (/ 1 (+ 1 (cos eps)))) (+ (* -1 (/ (* (sin eps) (- (* -1 (/ (sin (* 2 eps)) (+ 1 (cos eps)))) (* -1 (/ (* (sin eps) (- (* 1/2 (cos (* 2 eps))) 1/2)) (pow (+ 1 (cos eps)) 2))))) (+ 1 (cos eps)))) (/ (* (- (* -1/2 (cos eps)) 1/2) (- (* 1/2 (cos (* 2 eps))) 1/2)) (pow (+ 1 (cos eps)) 2)))))) (* -1 (/ (* (sin eps) (- (* 1/2 (cos (* 2 eps))) 1/2)) (pow (+ 1 (cos eps)) 2)))))) (* 1/2 (/ 1 (+ 1 (cos eps)))))>
#<alt (- (+ (* 1/2 (/ (cos (* 2 eps)) (+ 1 (cos eps)))) (* x (- (+ (* -1 (/ (sin (* 2 eps)) (+ 1 (cos eps)))) (* x (- (+ (* -1 (/ (cos (* 2 eps)) (+ 1 (cos eps)))) (+ (* x (- (* 2/3 (/ (sin (* 2 eps)) (+ 1 (cos eps)))) (+ (* -1 (/ (* (sin eps) (- (+ (* -1 (/ (cos (* 2 eps)) (+ 1 (cos eps)))) (/ 1 (+ 1 (cos eps)))) (+ (* -1 (/ (* (sin eps) (- (* -1 (/ (sin (* 2 eps)) (+ 1 (cos eps)))) (* -1 (/ (* (sin eps) (- (* 1/2 (cos (* 2 eps))) 1/2)) (pow (+ 1 (cos eps)) 2))))) (+ 1 (cos eps)))) (/ (* (- (* -1/2 (cos eps)) 1/2) (- (* 1/2 (cos (* 2 eps))) 1/2)) (pow (+ 1 (cos eps)) 2))))) (+ 1 (cos eps)))) (+ (* 1/6 (/ (* (sin eps) (- (* 1/2 (cos (* 2 eps))) 1/2)) (pow (+ 1 (cos eps)) 2))) (/ (* (- (* -1 (/ (sin (* 2 eps)) (+ 1 (cos eps)))) (* -1 (/ (* (sin eps) (- (* 1/2 (cos (* 2 eps))) 1/2)) (pow (+ 1 (cos eps)) 2)))) (- (* -1/2 (cos eps)) 1/2)) (+ 1 (cos eps))))))) (/ 1 (+ 1 (cos eps))))) (+ (* -1 (/ (* (sin eps) (- (* -1 (/ (sin (* 2 eps)) (+ 1 (cos eps)))) (* -1 (/ (* (sin eps) (- (* 1/2 (cos (* 2 eps))) 1/2)) (pow (+ 1 (cos eps)) 2))))) (+ 1 (cos eps)))) (/ (* (- (* -1/2 (cos eps)) 1/2) (- (* 1/2 (cos (* 2 eps))) 1/2)) (pow (+ 1 (cos eps)) 2)))))) (* -1 (/ (* (sin eps) (- (* 1/2 (cos (* 2 eps))) 1/2)) (pow (+ 1 (cos eps)) 2)))))) (* 1/2 (/ 1 (+ 1 (cos eps)))))>
#<alt (/ (- (* 1/2 (cos (* 2 (+ eps x)))) (* 1/2 (cos (* 2 x)))) (+ (cos x) (cos (+ eps x))))>
#<alt (/ (- (* 1/2 (cos (* 2 (+ eps x)))) (* 1/2 (cos (* 2 x)))) (+ (cos x) (cos (+ eps x))))>
#<alt (/ (- (* 1/2 (cos (* 2 (+ eps x)))) (* 1/2 (cos (* 2 x)))) (+ (cos x) (cos (+ eps x))))>
#<alt (/ (- (* 1/2 (cos (* 2 (+ eps x)))) (* 1/2 (cos (* 2 x)))) (+ (cos x) (cos (+ eps x))))>
#<alt (/ (- (* 1/2 (cos (* 2 (- eps (* -1 x))))) (* 1/2 (cos (neg (* -2 x))))) (+ (cos x) (cos (- eps (* -1 x)))))>
#<alt (/ (- (* 1/2 (cos (* 2 (- eps (* -1 x))))) (* 1/2 (cos (neg (* -2 x))))) (+ (cos x) (cos (- eps (* -1 x)))))>
#<alt (/ (- (* 1/2 (cos (* 2 (- eps (* -1 x))))) (* 1/2 (cos (neg (* -2 x))))) (+ (cos x) (cos (- eps (* -1 x)))))>
#<alt (/ (- (* 1/2 (cos (* 2 (- eps (* -1 x))))) (* 1/2 (cos (neg (* -2 x))))) (+ (cos x) (cos (- eps (* -1 x)))))>
#<alt (* -1/2 (/ (* eps (sin (* 2 x))) (cos x)))>
#<alt (* eps (+ (* -1/2 (/ (sin (* 2 x)) (cos x))) (* eps (- (* -1/2 (/ (cos (* 2 x)) (cos x))) (* 1/4 (/ (* (sin x) (sin (* 2 x))) (pow (cos x) 2)))))))>
#<alt (* eps (+ (* -1/2 (/ (sin (* 2 x)) (cos x))) (* eps (- (+ (* -1/2 (/ (cos (* 2 x)) (cos x))) (* eps (- (* 1/3 (/ (sin (* 2 x)) (cos x))) (+ (* -1/2 (/ (* (sin x) (- (* -1/2 (/ (cos (* 2 x)) (cos x))) (* 1/4 (/ (* (sin x) (sin (* 2 x))) (pow (cos x) 2))))) (cos x))) (* 1/8 (/ (sin (* 2 x)) (cos x))))))) (* 1/4 (/ (* (sin x) (sin (* 2 x))) (pow (cos x) 2)))))))>
#<alt (* eps (+ (* -1/2 (/ (sin (* 2 x)) (cos x))) (* eps (- (+ (* -1/2 (/ (cos (* 2 x)) (cos x))) (* eps (- (+ (* 1/3 (/ (sin (* 2 x)) (cos x))) (* eps (- (* 1/6 (/ (cos (* 2 x)) (cos x))) (+ (* -1/2 (/ (* (sin x) (- (* 1/3 (/ (sin (* 2 x)) (cos x))) (+ (* -1/2 (/ (* (sin x) (- (* -1/2 (/ (cos (* 2 x)) (cos x))) (* 1/4 (/ (* (sin x) (sin (* 2 x))) (pow (cos x) 2))))) (cos x))) (* 1/8 (/ (sin (* 2 x)) (cos x)))))) (cos x))) (+ (* -1/4 (- (* -1/2 (/ (cos (* 2 x)) (cos x))) (* 1/4 (/ (* (sin x) (sin (* 2 x))) (pow (cos x) 2))))) (* -1/24 (/ (* (sin x) (sin (* 2 x))) (pow (cos x) 2)))))))) (+ (* -1/2 (/ (* (sin x) (- (* -1/2 (/ (cos (* 2 x)) (cos x))) (* 1/4 (/ (* (sin x) (sin (* 2 x))) (pow (cos x) 2))))) (cos x))) (* 1/8 (/ (sin (* 2 x)) (cos x))))))) (* 1/4 (/ (* (sin x) (sin (* 2 x))) (pow (cos x) 2)))))))>
#<alt (/ (- (* 1/2 (cos (* 2 (+ eps x)))) (* 1/2 (cos (* 2 x)))) (+ (cos x) (cos (+ eps x))))>
#<alt (/ (- (* 1/2 (cos (* 2 (+ eps x)))) (* 1/2 (cos (* 2 x)))) (+ (cos x) (cos (+ eps x))))>
#<alt (/ (- (* 1/2 (cos (* 2 (+ eps x)))) (* 1/2 (cos (* 2 x)))) (+ (cos x) (cos (+ eps x))))>
#<alt (/ (- (* 1/2 (cos (* 2 (+ eps x)))) (* 1/2 (cos (* 2 x)))) (+ (cos x) (cos (+ eps x))))>
#<alt (/ (- (* 1/2 (cos (* 2 (- x (* -1 eps))))) (* 1/2 (cos (* 2 x)))) (+ (cos x) (cos (- x (* -1 eps)))))>
#<alt (/ (- (* 1/2 (cos (* 2 (- x (* -1 eps))))) (* 1/2 (cos (* 2 x)))) (+ (cos x) (cos (- x (* -1 eps)))))>
#<alt (/ (- (* 1/2 (cos (* 2 (- x (* -1 eps))))) (* 1/2 (cos (* 2 x)))) (+ (cos x) (cos (- x (* -1 eps)))))>
#<alt (/ (- (* 1/2 (cos (* 2 (- x (* -1 eps))))) (* 1/2 (cos (* 2 x)))) (+ (cos x) (cos (- x (* -1 eps)))))>
#<alt (+ 1/2 (* 1/2 (cos (* 2 eps))))>
#<alt (+ 1/2 (+ (* -1 (* x (sin (* 2 eps)))) (* 1/2 (cos (* 2 eps)))))>
#<alt (+ 1/2 (+ (* 1/2 (cos (* 2 eps))) (* x (+ (* -1 (sin (* 2 eps))) (* -1 (* x (cos (* 2 eps))))))))>
#<alt (+ 1/2 (+ (* 1/2 (cos (* 2 eps))) (* x (+ (* -1 (sin (* 2 eps))) (* x (+ (* -1 (cos (* 2 eps))) (* 2/3 (* x (sin (* 2 eps))))))))))>
#<alt (+ 1/2 (* 1/2 (cos (* 2 (+ eps x)))))>
#<alt (+ 1/2 (* 1/2 (cos (* 2 (+ eps x)))))>
#<alt (+ 1/2 (* 1/2 (cos (* 2 (+ eps x)))))>
#<alt (+ 1/2 (* 1/2 (cos (* 2 (+ eps x)))))>
#<alt (+ 1/2 (* 1/2 (cos (* 2 (- eps (* -1 x))))))>
#<alt (+ 1/2 (* 1/2 (cos (* 2 (- eps (* -1 x))))))>
#<alt (+ 1/2 (* 1/2 (cos (* 2 (- eps (* -1 x))))))>
#<alt (+ 1/2 (* 1/2 (cos (* 2 (- eps (* -1 x))))))>
#<alt (+ 1/2 (* 1/2 (cos (* 2 x))))>
#<alt (+ 1/2 (+ (* -1 (* eps (sin (* 2 x)))) (* 1/2 (cos (* 2 x)))))>
#<alt (+ 1/2 (+ (* 1/2 (cos (* 2 x))) (* eps (+ (* -1 (sin (* 2 x))) (* -1 (* eps (cos (* 2 x))))))))>
#<alt (+ 1/2 (+ (* 1/2 (cos (* 2 x))) (* eps (+ (* -1 (sin (* 2 x))) (* eps (+ (* -1 (cos (* 2 x))) (* 2/3 (* eps (sin (* 2 x))))))))))>
#<alt (+ 1/2 (* 1/2 (cos (* 2 (+ eps x)))))>
#<alt (+ 1/2 (* 1/2 (cos (* 2 (+ eps x)))))>
#<alt (+ 1/2 (* 1/2 (cos (* 2 (+ eps x)))))>
#<alt (+ 1/2 (* 1/2 (cos (* 2 (+ eps x)))))>
#<alt (+ 1/2 (* 1/2 (cos (* 2 (- x (* -1 eps))))))>
#<alt (+ 1/2 (* 1/2 (cos (* 2 (- x (* -1 eps))))))>
#<alt (+ 1/2 (* 1/2 (cos (* 2 (- x (* -1 eps))))))>
#<alt (+ 1/2 (* 1/2 (cos (* 2 (- x (* -1 eps))))))>
#<alt (cos (* 2 eps))>
#<alt (+ (cos (* 2 eps)) (* -2 (* x (sin (* 2 eps)))))>
#<alt (+ (cos (* 2 eps)) (* x (- (* -2 (* x (cos (* 2 eps)))) (* 2 (sin (* 2 eps))))))>
#<alt (+ (cos (* 2 eps)) (* x (- (* x (+ (* -2 (cos (* 2 eps))) (* 4/3 (* x (sin (* 2 eps)))))) (* 2 (sin (* 2 eps))))))>
#<alt (cos (* 2 (+ eps x)))>
#<alt (cos (* 2 (+ eps x)))>
#<alt (cos (* 2 (+ eps x)))>
#<alt (cos (* 2 (+ eps x)))>
#<alt (cos (* 2 (- eps (* -1 x))))>
#<alt (cos (* 2 (- eps (* -1 x))))>
#<alt (cos (* 2 (- eps (* -1 x))))>
#<alt (cos (* 2 (- eps (* -1 x))))>
#<alt (cos (* 2 x))>
#<alt (+ (cos (* 2 x)) (* -2 (* eps (sin (* 2 x)))))>
#<alt (+ (cos (* 2 x)) (* eps (- (* -2 (* eps (cos (* 2 x)))) (* 2 (sin (* 2 x))))))>
#<alt (+ (cos (* 2 x)) (* eps (- (* eps (+ (* -2 (cos (* 2 x))) (* 4/3 (* eps (sin (* 2 x)))))) (* 2 (sin (* 2 x))))))>
#<alt (cos (* 2 (+ eps x)))>
#<alt (cos (* 2 (+ eps x)))>
#<alt (cos (* 2 (+ eps x)))>
#<alt (cos (* 2 (+ eps x)))>
#<alt (cos (* 2 (- x (* -1 eps))))>
#<alt (cos (* 2 (- x (* -1 eps))))>
#<alt (cos (* 2 (- x (* -1 eps))))>
#<alt (cos (* 2 (- x (* -1 eps))))>
#<alt (- (cos eps) 1)>
#<alt (- (+ (cos eps) (* (pow x 2) (+ 1/2 (* -1/2 (cos eps))))) 1)>
#<alt (- (+ (cos eps) (* (pow x 2) (+ 1/2 (+ (* -1/2 (cos eps)) (* (pow x 2) (- (* 1/24 (cos eps)) 1/24)))))) 1)>
#<alt (- (+ (cos eps) (* (pow x 2) (+ 1/2 (+ (* -1/2 (cos eps)) (* (pow x 2) (- (+ (* 1/24 (cos eps)) (* (pow x 2) (+ 1/720 (* -1/720 (cos eps))))) 1/24)))))) 1)>
#<alt (- (* (cos eps) (cos x)) (cos x))>
#<alt (- (* (cos eps) (cos x)) (cos x))>
#<alt (- (* (cos eps) (cos x)) (cos x))>
#<alt (- (* (cos eps) (cos x)) (cos x))>
#<alt (- (* (cos eps) (cos x)) (cos x))>
#<alt (- (* (cos eps) (cos x)) (cos x))>
#<alt (- (* (cos eps) (cos x)) (cos x))>
#<alt (- (* (cos eps) (cos x)) (cos x))>
#<alt (* -1/2 (* (pow eps 2) (cos x)))>
#<alt (* (pow eps 2) (+ (* -1/2 (cos x)) (* 1/24 (* (pow eps 2) (cos x)))))>
#<alt (* (pow eps 2) (+ (* -1/2 (cos x)) (* (pow eps 2) (+ (* -1/720 (* (pow eps 2) (cos x))) (* 1/24 (cos x))))))>
#<alt (* (pow eps 2) (+ (* -1/2 (cos x)) (* (pow eps 2) (+ (* 1/24 (cos x)) (* (pow eps 2) (+ (* -1/720 (cos x)) (* 1/40320 (* (pow eps 2) (cos x)))))))))>
#<alt (- (* (cos eps) (cos x)) (cos x))>
#<alt (- (* (cos eps) (cos x)) (cos x))>
#<alt (- (* (cos eps) (cos x)) (cos x))>
#<alt (- (* (cos eps) (cos x)) (cos x))>
#<alt (- (* (cos eps) (cos x)) (cos x))>
#<alt (- (* (cos eps) (cos x)) (cos x))>
#<alt (- (* (cos eps) (cos x)) (cos x))>
#<alt (- (* (cos eps) (cos x)) (cos x))>
#<alt (- (cos eps) 1)>
#<alt (- (+ (cos eps) (* -1 (* x (sin eps)))) 1)>
#<alt (- (+ (cos eps) (* x (- (* x (+ 1/2 (* -1/2 (cos eps)))) (sin eps)))) 1)>
#<alt (- (+ (cos eps) (* x (- (* x (+ 1/2 (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps)))))) (sin eps)))) 1)>
#<alt (- (* (cos eps) (cos x)) (+ (cos x) (* (sin eps) (sin x))))>
#<alt (- (* (cos eps) (cos x)) (+ (cos x) (* (sin eps) (sin x))))>
#<alt (- (* (cos eps) (cos x)) (+ (cos x) (* (sin eps) (sin x))))>
#<alt (- (* (cos eps) (cos x)) (+ (cos x) (* (sin eps) (sin x))))>
#<alt (- (* (cos eps) (cos x)) (+ (cos x) (* (sin eps) (sin x))))>
#<alt (- (* (cos eps) (cos x)) (+ (cos x) (* (sin eps) (sin x))))>
#<alt (- (* (cos eps) (cos x)) (+ (cos x) (* (sin eps) (sin x))))>
#<alt (- (* (cos eps) (cos x)) (+ (cos x) (* (sin eps) (sin x))))>
#<alt (* -1 (* eps (sin x)))>
#<alt (* eps (- (* -1/2 (* eps (cos x))) (sin x)))>
#<alt (* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x)))>
#<alt (* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)))>
#<alt (- (* (cos eps) (cos x)) (+ (cos x) (* (sin eps) (sin x))))>
#<alt (- (* (cos eps) (cos x)) (+ (cos x) (* (sin eps) (sin x))))>
#<alt (- (* (cos eps) (cos x)) (+ (cos x) (* (sin eps) (sin x))))>
#<alt (- (* (cos eps) (cos x)) (+ (cos x) (* (sin eps) (sin x))))>
#<alt (- (* (cos eps) (cos x)) (+ (cos x) (* (sin eps) (sin x))))>
#<alt (- (* (cos eps) (cos x)) (+ (cos x) (* (sin eps) (sin x))))>
#<alt (- (* (cos eps) (cos x)) (+ (cos x) (* (sin eps) (sin x))))>
#<alt (- (* (cos eps) (cos x)) (+ (cos x) (* (sin eps) (sin x))))>
#<alt -1>
#<alt (- (* 1/2 (pow x 2)) 1)>
#<alt (- (* (pow x 2) (+ 1/2 (* -1/24 (pow x 2)))) 1)>
#<alt (- (* (pow x 2) (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24)))) 1)>
#<alt (* -1 (cos x))>
#<alt (* -1 (cos x))>
#<alt (* -1 (cos x))>
#<alt (* -1 (cos x))>
#<alt (* -1 (cos x))>
#<alt (* -1 (cos x))>
#<alt (* -1 (cos x))>
#<alt (* -1 (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>
#<alt (+ eps (* 2 x))>
#<alt (+ eps (* 2 x))>
#<alt (+ eps (* 2 x))>
#<alt (* 2 x)>
#<alt (* x (+ 2 (/ eps x)))>
#<alt (* x (+ 2 (/ eps x)))>
#<alt (* x (+ 2 (/ eps x)))>
#<alt (* 2 x)>
#<alt (* -1 (* x (- (* -1 (/ eps x)) 2)))>
#<alt (* -1 (* x (- (* -1 (/ eps x)) 2)))>
#<alt (* -1 (* x (- (* -1 (/ eps x)) 2)))>
#<alt (* 2 x)>
#<alt (+ eps (* 2 x))>
#<alt (+ eps (* 2 x))>
#<alt (+ eps (* 2 x))>
#<alt eps>
#<alt (* eps (+ 1 (* 2 (/ x eps))))>
#<alt (* eps (+ 1 (* 2 (/ x eps))))>
#<alt (* eps (+ 1 (* 2 (/ x eps))))>
#<alt eps>
#<alt (* -1 (* eps (- (* -2 (/ x eps)) 1)))>
#<alt (* -1 (* eps (- (* -2 (/ x eps)) 1)))>
#<alt (* -1 (* eps (- (* -2 (/ x eps)) 1)))>
#<alt (sin (* 1/2 eps))>
#<alt (+ (sin (* 1/2 eps)) (* x (cos (* 1/2 eps))))>
#<alt (+ (sin (* 1/2 eps)) (* x (+ (cos (* 1/2 eps)) (* -1/2 (* x (sin (* 1/2 eps)))))))>
#<alt (+ (sin (* 1/2 eps)) (* x (+ (cos (* 1/2 eps)) (* x (+ (* -1/2 (sin (* 1/2 eps))) (* -1/6 (* x (cos (* 1/2 eps)))))))))>
#<alt (sin (* 1/2 (+ eps (* 2 x))))>
#<alt (sin (* 1/2 (+ eps (* 2 x))))>
#<alt (sin (* 1/2 (+ eps (* 2 x))))>
#<alt (sin (* 1/2 (+ eps (* 2 x))))>
#<alt (sin (* 1/2 (- eps (* -2 x))))>
#<alt (sin (* 1/2 (- eps (* -2 x))))>
#<alt (sin (* 1/2 (- eps (* -2 x))))>
#<alt (sin (* 1/2 (- eps (* -2 x))))>
#<alt (sin x)>
#<alt (+ (sin x) (* 1/2 (* eps (cos x))))>
#<alt (+ (sin x) (* eps (+ (* -1/8 (* eps (sin x))) (* 1/2 (cos x)))))>
#<alt (+ (sin x) (* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/8 (sin x)) (* -1/48 (* eps (cos x))))))))>
#<alt (sin (* 1/2 (+ eps (* 2 x))))>
#<alt (sin (* 1/2 (+ eps (* 2 x))))>
#<alt (sin (* 1/2 (+ eps (* 2 x))))>
#<alt (sin (* 1/2 (+ eps (* 2 x))))>
#<alt (sin (* 1/2 (- (* 2 x) (* -1 eps))))>
#<alt (sin (* 1/2 (- (* 2 x) (* -1 eps))))>
#<alt (sin (* 1/2 (- (* 2 x) (* -1 eps))))>
#<alt (sin (* 1/2 (- (* 2 x) (* -1 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 (* x (sin eps))>
#<alt (* x (+ (sin eps) (* -1/6 (* (pow x 2) (sin eps)))))>
#<alt (* x (+ (sin eps) (* (pow x 2) (+ (* -1/6 (sin eps)) (* 1/120 (* (pow x 2) (sin eps)))))))>
#<alt (* x (+ (sin eps) (* (pow x 2) (+ (* -1/6 (sin eps)) (* (pow x 2) (+ (* -1/5040 (* (pow x 2) (sin eps))) (* 1/120 (sin eps))))))))>
#<alt (* (sin eps) (sin x))>
#<alt (* (sin eps) (sin x))>
#<alt (* (sin eps) (sin x))>
#<alt (* (sin eps) (sin x))>
#<alt (* (sin eps) (sin x))>
#<alt (* (sin eps) (sin x))>
#<alt (* (sin eps) (sin x))>
#<alt (* (sin eps) (sin x))>
#<alt (* eps (sin x))>
#<alt (* eps (+ (sin x) (* -1/6 (* (pow eps 2) (sin x)))))>
#<alt (* eps (+ (sin x) (* (pow eps 2) (+ (* -1/6 (sin x)) (* 1/120 (* (pow eps 2) (sin x)))))))>
#<alt (* eps (+ (sin x) (* (pow eps 2) (+ (* -1/6 (sin x)) (* (pow eps 2) (+ (* -1/5040 (* (pow eps 2) (sin x))) (* 1/120 (sin x))))))))>
#<alt (* (sin eps) (sin x))>
#<alt (* (sin eps) (sin x))>
#<alt (* (sin eps) (sin x))>
#<alt (* (sin eps) (sin x))>
#<alt (* (sin eps) (sin x))>
#<alt (* (sin eps) (sin x))>
#<alt (* (sin eps) (sin x))>
#<alt (* (sin eps) (sin x))>
#<alt (cos eps)>
#<alt (+ (cos eps) (* -1/2 (* (pow x 2) (cos eps))))>
#<alt (+ (cos eps) (* (pow x 2) (+ (* -1/2 (cos eps)) (* 1/24 (* (pow x 2) (cos eps))))))>
#<alt (+ (cos eps) (* (pow x 2) (+ (* -1/2 (cos eps)) (* (pow x 2) (+ (* -1/720 (* (pow x 2) (cos eps))) (* 1/24 (cos eps)))))))>
#<alt (* (cos eps) (cos x))>
#<alt (* (cos eps) (cos x))>
#<alt (* (cos eps) (cos x))>
#<alt (* (cos eps) (cos x))>
#<alt (* (cos eps) (cos x))>
#<alt (* (cos eps) (cos x))>
#<alt (* (cos eps) (cos x))>
#<alt (* (cos eps) (cos x))>
#<alt (cos x)>
#<alt (+ (cos x) (* -1/2 (* (pow eps 2) (cos x))))>
#<alt (+ (cos x) (* (pow eps 2) (+ (* -1/2 (cos x)) (* 1/24 (* (pow eps 2) (cos x))))))>
#<alt (+ (cos x) (* (pow eps 2) (+ (* -1/2 (cos x)) (* (pow eps 2) (+ (* -1/720 (* (pow eps 2) (cos x))) (* 1/24 (cos x)))))))>
#<alt (* (cos eps) (cos x))>
#<alt (* (cos eps) (cos x))>
#<alt (* (cos eps) (cos x))>
#<alt (* (cos eps) (cos x))>
#<alt (* (cos eps) (cos x))>
#<alt (* (cos eps) (cos x))>
#<alt (* (cos eps) (cos x))>
#<alt (* (cos eps) (cos x))>

Calls

117 calls:

Time	Variable		Point	Expression
29.0ms	eps	@	inf	(- (+ (* 1/2 (cos (* (+ x eps) 2))) 1/2) (+ (* 1/2 (cos (+ x x))) 1/2))
8.0ms	x	@	0	(+ (neg (cos x)) (* (cos x) (cos eps)))
2.0ms	eps	@	-inf	(/ (- (+ (* 1/2 (cos (* (+ x eps) 2))) 1/2) (+ (* 1/2 (cos (+ x x))) 1/2)) (+ (cos (+ x eps)) (cos x)))
2.0ms	eps	@	inf	(/ (- (+ (* 1/2 (cos (* (+ x eps) 2))) 1/2) (+ (* 1/2 (cos (+ x x))) 1/2)) (+ (cos (+ x eps)) (cos x)))
2.0ms	x	@	0	(/ (- (+ (* 1/2 (cos (* (+ x eps) 2))) 1/2) (+ (* 1/2 (cos (+ x x))) 1/2)) (+ (cos (+ x eps)) (cos x)))

rewrite257.0ms (1.4%)

Memory

8.9MiB live, 284.5MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

1 632×	`lower-fma.f32`
1 626×	`lower-fma.f64`
1 316×	`lower-*.f32`
1 302×	`lower-*.f64`
1 114×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	41	184
0	76	164
1	299	117
0	2736	116

Stop Event

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

Counts

23 → 574

Calls

Call 1

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

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

simplify725.0ms (4%)

Memory

-50.5MiB live, 715.1MiB allocated

Algorithm

1×	egg-herbie

Rules

12 352×	`lower-fma.f64`
12 352×	`lower-fma.f32`
5 782×	`lower-*.f64`
5 782×	`lower-*.f32`
4 612×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	621	5490
1	1946	5245
2	5534	5151
0	8293	4821

Stop Event

1×	iter limit
1×	node limit

Counts

468 → 444

Calls

Call 1

Inputs
(* 1/2 eps)
(+ x (* 1/2 eps))
(+ x (* 1/2 eps))
(+ x (* 1/2 eps))
x
(* x (+ 1 (* 1/2 (/ eps x))))
(* x (+ 1 (* 1/2 (/ eps x))))
(* x (+ 1 (* 1/2 (/ eps x))))
x
(* -1 (* x (- (* -1/2 (/ eps x)) 1)))
(* -1 (* x (- (* -1/2 (/ eps x)) 1)))
(* -1 (* x (- (* -1/2 (/ eps x)) 1)))
x
(+ x (* 1/2 eps))
(+ x (* 1/2 eps))
(+ x (* 1/2 eps))
(* 1/2 eps)
(* eps (+ 1/2 (/ x eps)))
(* eps (+ 1/2 (/ x eps)))
(* eps (+ 1/2 (/ x eps)))
(* 1/2 eps)
(* -1 (* eps (- (* -1 (/ x eps)) 1/2)))
(* -1 (* eps (- (* -1 (/ x eps)) 1/2)))
(* -1 (* eps (- (* -1 (/ x eps)) 1/2)))
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
(* -1 (* eps (sin x)))
(* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))
(* eps (+ (* -1 (sin x)) (* eps (+ (* -2 (* eps (+ (* -1/16 (sin x)) (* -1/48 (sin x))))) (* -1/2 (cos x))))))
(* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* eps (+ (* -2 (+ (* -1/16 (sin x)) (* -1/48 (sin x)))) (* 1/24 (* eps (cos x)))))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps))))))
(* -2 (pow (sin (* 1/2 eps)) 2))
(+ (* -2 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (* -2 (pow (sin (* 1/2 eps)) 2)))
(+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (pow (sin (* 1/2 eps)) 2)))))
(+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* 1/3 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (pow (sin (* 1/2 eps)) 2))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x))))))
(* 1/2 (* eps (sin x)))
(* eps (+ (* 1/4 (* eps (cos x))) (* 1/2 (sin x))))
(* eps (+ (* 1/2 (sin x)) (* eps (+ (* 1/4 (cos x)) (* eps (+ (* -1/16 (sin x)) (* -1/48 (sin x))))))))
(* eps (+ (* 1/2 (sin x)) (* eps (+ (* 1/4 (cos x)) (* eps (+ (* -1/16 (sin x)) (+ (* -1/48 (sin x)) (* -1/48 (* eps (cos x))))))))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps)))))
(pow (sin (* 1/2 eps)) 2)
(+ (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (pow (sin (* 1/2 eps)) 2))
(+ (* x (+ (* -1/2 (* x (pow (sin (* 1/2 eps)) 2))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (pow (sin (* 1/2 eps)) 2))
(+ (* x (+ (* x (+ (* -1/2 (pow (sin (* 1/2 eps)) 2)) (* -1/6 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (pow (sin (* 1/2 eps)) 2))
(* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x)))))
(* -1/2 (pow eps 2))
(* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))
(* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2))
(* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* (pow eps 2) (- (* 1/40320 (pow eps 2)) 1/720)))) 1/2))
(- (cos eps) 1)
(- (cos eps) 1)
(- (cos eps) 1)
(- (cos eps) 1)
(- (cos eps) 1)
(- (cos eps) 1)
(- (cos eps) 1)
(- (cos eps) 1)
1
(+ 1 (* -1/2 (pow eps 2)))
(+ 1 (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))
(+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2)))
(cos eps)
(cos eps)
(cos eps)
(cos eps)
(cos eps)
(cos eps)
(cos eps)
(cos eps)
(- (cos eps) 1)
(- (+ (cos eps) (* -1 (* x (sin eps)))) 1)
(- (+ (cos eps) (* x (- (* x (+ 1/2 (* -1/2 (cos eps)))) (sin eps)))) 1)
(- (+ (cos eps) (* x (- (* x (+ 1/2 (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps)))))) (sin eps)))) 1)
(* 1/2 (pow x 2))
(* (pow x 2) (- (+ 1/2 (/ (cos (+ eps x)) (pow x 2))) (/ 1 (pow x 2))))
(* (pow x 2) (- (+ 1/2 (/ (cos (+ eps x)) (pow x 2))) (/ 1 (pow x 2))))
(* (pow x 2) (- (+ 1/2 (/ (cos (+ eps x)) (pow x 2))) (/ 1 (pow x 2))))
(* 1/2 (pow x 2))
(* (pow x 2) (- (+ 1/2 (/ (cos (- eps (* -1 x))) (pow x 2))) (/ 1 (pow x 2))))
(* (pow x 2) (- (+ 1/2 (/ (cos (- eps (* -1 x))) (pow x 2))) (/ 1 (pow x 2))))
(* (pow x 2) (- (+ 1/2 (/ (cos (- eps (* -1 x))) (pow x 2))) (/ 1 (pow x 2))))
(- (cos x) (+ 1 (* -1/2 (pow x 2))))
(- (+ (cos x) (* -1 (* eps (sin x)))) (+ 1 (* -1/2 (pow x 2))))
(- (+ (cos x) (* eps (- (* -1/2 (* eps (cos x))) (sin x)))) (+ 1 (* -1/2 (pow x 2))))
(- (+ (cos x) (* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x)))) (+ 1 (* -1/2 (pow x 2))))
(- (cos (+ eps x)) (+ 1 (* -1/2 (pow x 2))))
(- (cos (+ eps x)) (+ 1 (* -1/2 (pow x 2))))
(- (cos (+ eps x)) (+ 1 (* -1/2 (pow x 2))))
(- (cos (+ eps x)) (+ 1 (* -1/2 (pow x 2))))
(- (cos (- x (* -1 eps))) (+ 1 (* -1/2 (pow x 2))))
(- (cos (- x (* -1 eps))) (+ 1 (* -1/2 (pow x 2))))
(- (cos (- x (* -1 eps))) (+ 1 (* -1/2 (pow x 2))))
(- (cos (- x (* -1 eps))) (+ 1 (* -1/2 (pow x 2))))
(cos eps)
(+ (cos eps) (* -1 (* x (sin eps))))
(+ (cos eps) (* x (- (* -1/2 (* x (cos eps))) (sin eps))))
(+ (cos eps) (* x (- (* x (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps))))) (sin eps))))
(cos (+ eps x))
(cos (+ eps x))
(cos (+ eps x))
(cos (+ eps x))
(cos (- eps (* -1 x)))
(cos (- eps (* -1 x)))
(cos (- eps (* -1 x)))
(cos (- eps (* -1 x)))
(cos x)
(+ (cos x) (* -1 (* eps (sin x))))
(+ (cos x) (* eps (- (* -1/2 (* eps (cos x))) (sin x))))
(+ (cos x) (* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x))))
(cos (+ eps x))
(cos (+ eps x))
(cos (+ eps x))
(cos (+ eps x))
(cos (- x (* -1 eps)))
(cos (- x (* -1 eps)))
(cos (- x (* -1 eps)))
(cos (- 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)))
1
(+ 1 (* -1/2 (pow x 2)))
(+ 1 (* -1/2 (pow x 2)))
(+ 1 (* -1/2 (pow x 2)))
(* -1/2 (pow x 2))
(* (pow x 2) (- (/ 1 (pow x 2)) 1/2))
(* (pow x 2) (- (/ 1 (pow x 2)) 1/2))
(* (pow x 2) (- (/ 1 (pow x 2)) 1/2))
(* -1/2 (pow x 2))
(* (pow x 2) (- (/ 1 (pow x 2)) 1/2))
(* (pow x 2) (- (/ 1 (pow x 2)) 1/2))
(* (pow x 2) (- (/ 1 (pow x 2)) 1/2))
(- (* 1/2 (cos (* 2 eps))) 1/2)
(- (+ (* -1 (* x (sin (* 2 eps)))) (* 1/2 (cos (* 2 eps)))) 1/2)
(- (+ (* 1/2 (cos (* 2 eps))) (* x (+ (* -1 (sin (* 2 eps))) (* x (+ 1 (* -1 (cos (* 2 eps)))))))) 1/2)
(- (+ (* 1/2 (cos (* 2 eps))) (* x (+ (* -1 (sin (* 2 eps))) (* x (+ 1 (+ (* -1 (cos (* 2 eps))) (* 2/3 (* x (sin (* 2 eps)))))))))) 1/2)
(- (* 1/2 (cos (* 2 (+ eps x)))) (* 1/2 (cos (* 2 x))))
(- (* 1/2 (cos (* 2 (+ eps x)))) (* 1/2 (cos (* 2 x))))
(- (* 1/2 (cos (* 2 (+ eps x)))) (* 1/2 (cos (* 2 x))))
(- (* 1/2 (cos (* 2 (+ eps x)))) (* 1/2 (cos (* 2 x))))
(- (* 1/2 (cos (* 2 (- eps (* -1 x))))) (* 1/2 (cos (neg (* -2 x)))))
(- (* 1/2 (cos (* 2 (- eps (* -1 x))))) (* 1/2 (cos (neg (* -2 x)))))
(- (* 1/2 (cos (* 2 (- eps (* -1 x))))) (* 1/2 (cos (neg (* -2 x)))))
(- (* 1/2 (cos (* 2 (- eps (* -1 x))))) (* 1/2 (cos (neg (* -2 x)))))
(* -1 (* eps (sin (* 2 x))))
(* eps (+ (* -1 (sin (* 2 x))) (* -1 (* eps (cos (* 2 x))))))
(* eps (+ (* -1 (sin (* 2 x))) (* eps (+ (* -1 (cos (* 2 x))) (* 2/3 (* eps (sin (* 2 x))))))))
(* eps (+ (* -1 (sin (* 2 x))) (* eps (+ (* -1 (cos (* 2 x))) (* eps (+ (* 1/3 (* eps (cos (* 2 x)))) (* 2/3 (sin (* 2 x)))))))))
(- (* 1/2 (cos (* 2 (+ eps x)))) (* 1/2 (cos (* 2 x))))
(- (* 1/2 (cos (* 2 (+ eps x)))) (* 1/2 (cos (* 2 x))))
(- (* 1/2 (cos (* 2 (+ eps x)))) (* 1/2 (cos (* 2 x))))
(- (* 1/2 (cos (* 2 (+ eps x)))) (* 1/2 (cos (* 2 x))))
(- (* 1/2 (cos (* 2 (- x (* -1 eps))))) (* 1/2 (cos (* 2 x))))
(- (* 1/2 (cos (* 2 (- x (* -1 eps))))) (* 1/2 (cos (* 2 x))))
(- (* 1/2 (cos (* 2 (- x (* -1 eps))))) (* 1/2 (cos (* 2 x))))
(- (* 1/2 (cos (* 2 (- x (* -1 eps))))) (* 1/2 (cos (* 2 x))))
(/ (- (* 1/2 (cos (* 2 eps))) 1/2) (+ 1 (cos eps)))
(- (+ (* 1/2 (/ (cos (* 2 eps)) (+ 1 (cos eps)))) (* x (- (* -1 (/ (sin (* 2 eps)) (+ 1 (cos eps)))) (* -1 (/ (* (sin eps) (- (* 1/2 (cos (* 2 eps))) 1/2)) (pow (+ 1 (cos eps)) 2)))))) (* 1/2 (/ 1 (+ 1 (cos eps)))))
(- (+ (* 1/2 (/ (cos (* 2 eps)) (+ 1 (cos eps)))) (* x (- (+ (* -1 (/ (sin (* 2 eps)) (+ 1 (cos eps)))) (* x (- (+ (* -1 (/ (cos (* 2 eps)) (+ 1 (cos eps)))) (/ 1 (+ 1 (cos eps)))) (+ (* -1 (/ (* (sin eps) (- (* -1 (/ (sin (* 2 eps)) (+ 1 (cos eps)))) (* -1 (/ (* (sin eps) (- (* 1/2 (cos (* 2 eps))) 1/2)) (pow (+ 1 (cos eps)) 2))))) (+ 1 (cos eps)))) (/ (* (- (* -1/2 (cos eps)) 1/2) (- (* 1/2 (cos (* 2 eps))) 1/2)) (pow (+ 1 (cos eps)) 2)))))) (* -1 (/ (* (sin eps) (- (* 1/2 (cos (* 2 eps))) 1/2)) (pow (+ 1 (cos eps)) 2)))))) (* 1/2 (/ 1 (+ 1 (cos eps)))))
(- (+ (* 1/2 (/ (cos (* 2 eps)) (+ 1 (cos eps)))) (* x (- (+ (* -1 (/ (sin (* 2 eps)) (+ 1 (cos eps)))) (* x (- (+ (* -1 (/ (cos (* 2 eps)) (+ 1 (cos eps)))) (+ (* x (- (* 2/3 (/ (sin (* 2 eps)) (+ 1 (cos eps)))) (+ (* -1 (/ (* (sin eps) (- (+ (* -1 (/ (cos (* 2 eps)) (+ 1 (cos eps)))) (/ 1 (+ 1 (cos eps)))) (+ (* -1 (/ (* (sin eps) (- (* -1 (/ (sin (* 2 eps)) (+ 1 (cos eps)))) (* -1 (/ (* (sin eps) (- (* 1/2 (cos (* 2 eps))) 1/2)) (pow (+ 1 (cos eps)) 2))))) (+ 1 (cos eps)))) (/ (* (- (* -1/2 (cos eps)) 1/2) (- (* 1/2 (cos (* 2 eps))) 1/2)) (pow (+ 1 (cos eps)) 2))))) (+ 1 (cos eps)))) (+ (* 1/6 (/ (* (sin eps) (- (* 1/2 (cos (* 2 eps))) 1/2)) (pow (+ 1 (cos eps)) 2))) (/ (* (- (* -1 (/ (sin (* 2 eps)) (+ 1 (cos eps)))) (* -1 (/ (* (sin eps) (- (* 1/2 (cos (* 2 eps))) 1/2)) (pow (+ 1 (cos eps)) 2)))) (- (* -1/2 (cos eps)) 1/2)) (+ 1 (cos eps))))))) (/ 1 (+ 1 (cos eps))))) (+ (* -1 (/ (* (sin eps) (- (* -1 (/ (sin (* 2 eps)) (+ 1 (cos eps)))) (* -1 (/ (* (sin eps) (- (* 1/2 (cos (* 2 eps))) 1/2)) (pow (+ 1 (cos eps)) 2))))) (+ 1 (cos eps)))) (/ (* (- (* -1/2 (cos eps)) 1/2) (- (* 1/2 (cos (* 2 eps))) 1/2)) (pow (+ 1 (cos eps)) 2)))))) (* -1 (/ (* (sin eps) (- (* 1/2 (cos (* 2 eps))) 1/2)) (pow (+ 1 (cos eps)) 2)))))) (* 1/2 (/ 1 (+ 1 (cos eps)))))
(/ (- (* 1/2 (cos (* 2 (+ eps x)))) (* 1/2 (cos (* 2 x)))) (+ (cos x) (cos (+ eps x))))
(/ (- (* 1/2 (cos (* 2 (+ eps x)))) (* 1/2 (cos (* 2 x)))) (+ (cos x) (cos (+ eps x))))
(/ (- (* 1/2 (cos (* 2 (+ eps x)))) (* 1/2 (cos (* 2 x)))) (+ (cos x) (cos (+ eps x))))
(/ (- (* 1/2 (cos (* 2 (+ eps x)))) (* 1/2 (cos (* 2 x)))) (+ (cos x) (cos (+ eps x))))
(/ (- (* 1/2 (cos (* 2 (- eps (* -1 x))))) (* 1/2 (cos (neg (* -2 x))))) (+ (cos x) (cos (- eps (* -1 x)))))
(/ (- (* 1/2 (cos (* 2 (- eps (* -1 x))))) (* 1/2 (cos (neg (* -2 x))))) (+ (cos x) (cos (- eps (* -1 x)))))
(/ (- (* 1/2 (cos (* 2 (- eps (* -1 x))))) (* 1/2 (cos (neg (* -2 x))))) (+ (cos x) (cos (- eps (* -1 x)))))
(/ (- (* 1/2 (cos (* 2 (- eps (* -1 x))))) (* 1/2 (cos (neg (* -2 x))))) (+ (cos x) (cos (- eps (* -1 x)))))
(* -1/2 (/ (* eps (sin (* 2 x))) (cos x)))
(* eps (+ (* -1/2 (/ (sin (* 2 x)) (cos x))) (* eps (- (* -1/2 (/ (cos (* 2 x)) (cos x))) (* 1/4 (/ (* (sin x) (sin (* 2 x))) (pow (cos x) 2)))))))
(* eps (+ (* -1/2 (/ (sin (* 2 x)) (cos x))) (* eps (- (+ (* -1/2 (/ (cos (* 2 x)) (cos x))) (* eps (- (* 1/3 (/ (sin (* 2 x)) (cos x))) (+ (* -1/2 (/ (* (sin x) (- (* -1/2 (/ (cos (* 2 x)) (cos x))) (* 1/4 (/ (* (sin x) (sin (* 2 x))) (pow (cos x) 2))))) (cos x))) (* 1/8 (/ (sin (* 2 x)) (cos x))))))) (* 1/4 (/ (* (sin x) (sin (* 2 x))) (pow (cos x) 2)))))))
(* eps (+ (* -1/2 (/ (sin (* 2 x)) (cos x))) (* eps (- (+ (* -1/2 (/ (cos (* 2 x)) (cos x))) (* eps (- (+ (* 1/3 (/ (sin (* 2 x)) (cos x))) (* eps (- (* 1/6 (/ (cos (* 2 x)) (cos x))) (+ (* -1/2 (/ (* (sin x) (- (* 1/3 (/ (sin (* 2 x)) (cos x))) (+ (* -1/2 (/ (* (sin x) (- (* -1/2 (/ (cos (* 2 x)) (cos x))) (* 1/4 (/ (* (sin x) (sin (* 2 x))) (pow (cos x) 2))))) (cos x))) (* 1/8 (/ (sin (* 2 x)) (cos x)))))) (cos x))) (+ (* -1/4 (- (* -1/2 (/ (cos (* 2 x)) (cos x))) (* 1/4 (/ (* (sin x) (sin (* 2 x))) (pow (cos x) 2))))) (* -1/24 (/ (* (sin x) (sin (* 2 x))) (pow (cos x) 2)))))))) (+ (* -1/2 (/ (* (sin x) (- (* -1/2 (/ (cos (* 2 x)) (cos x))) (* 1/4 (/ (* (sin x) (sin (* 2 x))) (pow (cos x) 2))))) (cos x))) (* 1/8 (/ (sin (* 2 x)) (cos x))))))) (* 1/4 (/ (* (sin x) (sin (* 2 x))) (pow (cos x) 2)))))))
(/ (- (* 1/2 (cos (* 2 (+ eps x)))) (* 1/2 (cos (* 2 x)))) (+ (cos x) (cos (+ eps x))))
(/ (- (* 1/2 (cos (* 2 (+ eps x)))) (* 1/2 (cos (* 2 x)))) (+ (cos x) (cos (+ eps x))))
(/ (- (* 1/2 (cos (* 2 (+ eps x)))) (* 1/2 (cos (* 2 x)))) (+ (cos x) (cos (+ eps x))))
(/ (- (* 1/2 (cos (* 2 (+ eps x)))) (* 1/2 (cos (* 2 x)))) (+ (cos x) (cos (+ eps x))))
(/ (- (* 1/2 (cos (* 2 (- x (* -1 eps))))) (* 1/2 (cos (* 2 x)))) (+ (cos x) (cos (- x (* -1 eps)))))
(/ (- (* 1/2 (cos (* 2 (- x (* -1 eps))))) (* 1/2 (cos (* 2 x)))) (+ (cos x) (cos (- x (* -1 eps)))))
(/ (- (* 1/2 (cos (* 2 (- x (* -1 eps))))) (* 1/2 (cos (* 2 x)))) (+ (cos x) (cos (- x (* -1 eps)))))
(/ (- (* 1/2 (cos (* 2 (- x (* -1 eps))))) (* 1/2 (cos (* 2 x)))) (+ (cos x) (cos (- x (* -1 eps)))))
(+ 1/2 (* 1/2 (cos (* 2 eps))))
(+ 1/2 (+ (* -1 (* x (sin (* 2 eps)))) (* 1/2 (cos (* 2 eps)))))
(+ 1/2 (+ (* 1/2 (cos (* 2 eps))) (* x (+ (* -1 (sin (* 2 eps))) (* -1 (* x (cos (* 2 eps))))))))
(+ 1/2 (+ (* 1/2 (cos (* 2 eps))) (* x (+ (* -1 (sin (* 2 eps))) (* x (+ (* -1 (cos (* 2 eps))) (* 2/3 (* x (sin (* 2 eps))))))))))
(+ 1/2 (* 1/2 (cos (* 2 (+ eps x)))))
(+ 1/2 (* 1/2 (cos (* 2 (+ eps x)))))
(+ 1/2 (* 1/2 (cos (* 2 (+ eps x)))))
(+ 1/2 (* 1/2 (cos (* 2 (+ eps x)))))
(+ 1/2 (* 1/2 (cos (* 2 (- eps (* -1 x))))))
(+ 1/2 (* 1/2 (cos (* 2 (- eps (* -1 x))))))
(+ 1/2 (* 1/2 (cos (* 2 (- eps (* -1 x))))))
(+ 1/2 (* 1/2 (cos (* 2 (- eps (* -1 x))))))
(+ 1/2 (* 1/2 (cos (* 2 x))))
(+ 1/2 (+ (* -1 (* eps (sin (* 2 x)))) (* 1/2 (cos (* 2 x)))))
(+ 1/2 (+ (* 1/2 (cos (* 2 x))) (* eps (+ (* -1 (sin (* 2 x))) (* -1 (* eps (cos (* 2 x))))))))
(+ 1/2 (+ (* 1/2 (cos (* 2 x))) (* eps (+ (* -1 (sin (* 2 x))) (* eps (+ (* -1 (cos (* 2 x))) (* 2/3 (* eps (sin (* 2 x))))))))))
(+ 1/2 (* 1/2 (cos (* 2 (+ eps x)))))
(+ 1/2 (* 1/2 (cos (* 2 (+ eps x)))))
(+ 1/2 (* 1/2 (cos (* 2 (+ eps x)))))
(+ 1/2 (* 1/2 (cos (* 2 (+ eps x)))))
(+ 1/2 (* 1/2 (cos (* 2 (- x (* -1 eps))))))
(+ 1/2 (* 1/2 (cos (* 2 (- x (* -1 eps))))))
(+ 1/2 (* 1/2 (cos (* 2 (- x (* -1 eps))))))
(+ 1/2 (* 1/2 (cos (* 2 (- x (* -1 eps))))))
(cos (* 2 eps))
(+ (cos (* 2 eps)) (* -2 (* x (sin (* 2 eps)))))
(+ (cos (* 2 eps)) (* x (- (* -2 (* x (cos (* 2 eps)))) (* 2 (sin (* 2 eps))))))
(+ (cos (* 2 eps)) (* x (- (* x (+ (* -2 (cos (* 2 eps))) (* 4/3 (* x (sin (* 2 eps)))))) (* 2 (sin (* 2 eps))))))
(cos (* 2 (+ eps x)))
(cos (* 2 (+ eps x)))
(cos (* 2 (+ eps x)))
(cos (* 2 (+ eps x)))
(cos (* 2 (- eps (* -1 x))))
(cos (* 2 (- eps (* -1 x))))
(cos (* 2 (- eps (* -1 x))))
(cos (* 2 (- eps (* -1 x))))
(cos (* 2 x))
(+ (cos (* 2 x)) (* -2 (* eps (sin (* 2 x)))))
(+ (cos (* 2 x)) (* eps (- (* -2 (* eps (cos (* 2 x)))) (* 2 (sin (* 2 x))))))
(+ (cos (* 2 x)) (* eps (- (* eps (+ (* -2 (cos (* 2 x))) (* 4/3 (* eps (sin (* 2 x)))))) (* 2 (sin (* 2 x))))))
(cos (* 2 (+ eps x)))
(cos (* 2 (+ eps x)))
(cos (* 2 (+ eps x)))
(cos (* 2 (+ eps x)))
(cos (* 2 (- x (* -1 eps))))
(cos (* 2 (- x (* -1 eps))))
(cos (* 2 (- x (* -1 eps))))
(cos (* 2 (- x (* -1 eps))))
(- (cos eps) 1)
(- (+ (cos eps) (* (pow x 2) (+ 1/2 (* -1/2 (cos eps))))) 1)
(- (+ (cos eps) (* (pow x 2) (+ 1/2 (+ (* -1/2 (cos eps)) (* (pow x 2) (- (* 1/24 (cos eps)) 1/24)))))) 1)
(- (+ (cos eps) (* (pow x 2) (+ 1/2 (+ (* -1/2 (cos eps)) (* (pow x 2) (- (+ (* 1/24 (cos eps)) (* (pow x 2) (+ 1/720 (* -1/720 (cos eps))))) 1/24)))))) 1)
(- (* (cos eps) (cos x)) (cos x))
(- (* (cos eps) (cos x)) (cos x))
(- (* (cos eps) (cos x)) (cos x))
(- (* (cos eps) (cos x)) (cos x))
(- (* (cos eps) (cos x)) (cos x))
(- (* (cos eps) (cos x)) (cos x))
(- (* (cos eps) (cos x)) (cos x))
(- (* (cos eps) (cos x)) (cos x))
(* -1/2 (* (pow eps 2) (cos x)))
(* (pow eps 2) (+ (* -1/2 (cos x)) (* 1/24 (* (pow eps 2) (cos x)))))
(* (pow eps 2) (+ (* -1/2 (cos x)) (* (pow eps 2) (+ (* -1/720 (* (pow eps 2) (cos x))) (* 1/24 (cos x))))))
(* (pow eps 2) (+ (* -1/2 (cos x)) (* (pow eps 2) (+ (* 1/24 (cos x)) (* (pow eps 2) (+ (* -1/720 (cos x)) (* 1/40320 (* (pow eps 2) (cos x)))))))))
(- (* (cos eps) (cos x)) (cos x))
(- (* (cos eps) (cos x)) (cos x))
(- (* (cos eps) (cos x)) (cos x))
(- (* (cos eps) (cos x)) (cos x))
(- (* (cos eps) (cos x)) (cos x))
(- (* (cos eps) (cos x)) (cos x))
(- (* (cos eps) (cos x)) (cos x))
(- (* (cos eps) (cos x)) (cos x))
(- (cos eps) 1)
(- (+ (cos eps) (* -1 (* x (sin eps)))) 1)
(- (+ (cos eps) (* x (- (* x (+ 1/2 (* -1/2 (cos eps)))) (sin eps)))) 1)
(- (+ (cos eps) (* x (- (* x (+ 1/2 (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps)))))) (sin eps)))) 1)
(- (* (cos eps) (cos x)) (+ (cos x) (* (sin eps) (sin x))))
(- (* (cos eps) (cos x)) (+ (cos x) (* (sin eps) (sin x))))
(- (* (cos eps) (cos x)) (+ (cos x) (* (sin eps) (sin x))))
(- (* (cos eps) (cos x)) (+ (cos x) (* (sin eps) (sin x))))
(- (* (cos eps) (cos x)) (+ (cos x) (* (sin eps) (sin x))))
(- (* (cos eps) (cos x)) (+ (cos x) (* (sin eps) (sin x))))
(- (* (cos eps) (cos x)) (+ (cos x) (* (sin eps) (sin x))))
(- (* (cos eps) (cos x)) (+ (cos x) (* (sin eps) (sin x))))
(* -1 (* eps (sin x)))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x)))
(* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)))
(- (* (cos eps) (cos x)) (+ (cos x) (* (sin eps) (sin x))))
(- (* (cos eps) (cos x)) (+ (cos x) (* (sin eps) (sin x))))
(- (* (cos eps) (cos x)) (+ (cos x) (* (sin eps) (sin x))))
(- (* (cos eps) (cos x)) (+ (cos x) (* (sin eps) (sin x))))
(- (* (cos eps) (cos x)) (+ (cos x) (* (sin eps) (sin x))))
(- (* (cos eps) (cos x)) (+ (cos x) (* (sin eps) (sin x))))
(- (* (cos eps) (cos x)) (+ (cos x) (* (sin eps) (sin x))))
(- (* (cos eps) (cos x)) (+ (cos x) (* (sin eps) (sin x))))
-1
(- (* 1/2 (pow x 2)) 1)
(- (* (pow x 2) (+ 1/2 (* -1/24 (pow x 2)))) 1)
(- (* (pow x 2) (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24)))) 1)
(* -1 (cos x))
(* -1 (cos x))
(* -1 (cos x))
(* -1 (cos x))
(* -1 (cos x))
(* -1 (cos x))
(* -1 (cos x))
(* -1 (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
(+ eps (* 2 x))
(+ eps (* 2 x))
(+ eps (* 2 x))
(* 2 x)
(* x (+ 2 (/ eps x)))
(* x (+ 2 (/ eps x)))
(* x (+ 2 (/ eps x)))
(* 2 x)
(* -1 (* x (- (* -1 (/ eps x)) 2)))
(* -1 (* x (- (* -1 (/ eps x)) 2)))
(* -1 (* x (- (* -1 (/ eps x)) 2)))
(* 2 x)
(+ eps (* 2 x))
(+ eps (* 2 x))
(+ eps (* 2 x))
eps
(* eps (+ 1 (* 2 (/ x eps))))
(* eps (+ 1 (* 2 (/ x eps))))
(* eps (+ 1 (* 2 (/ x eps))))
eps
(* -1 (* eps (- (* -2 (/ x eps)) 1)))
(* -1 (* eps (- (* -2 (/ x eps)) 1)))
(* -1 (* eps (- (* -2 (/ x eps)) 1)))
(sin (* 1/2 eps))
(+ (sin (* 1/2 eps)) (* x (cos (* 1/2 eps))))
(+ (sin (* 1/2 eps)) (* x (+ (cos (* 1/2 eps)) (* -1/2 (* x (sin (* 1/2 eps)))))))
(+ (sin (* 1/2 eps)) (* x (+ (cos (* 1/2 eps)) (* x (+ (* -1/2 (sin (* 1/2 eps))) (* -1/6 (* x (cos (* 1/2 eps)))))))))
(sin (* 1/2 (+ eps (* 2 x))))
(sin (* 1/2 (+ eps (* 2 x))))
(sin (* 1/2 (+ eps (* 2 x))))
(sin (* 1/2 (+ eps (* 2 x))))
(sin (* 1/2 (- eps (* -2 x))))
(sin (* 1/2 (- eps (* -2 x))))
(sin (* 1/2 (- eps (* -2 x))))
(sin (* 1/2 (- eps (* -2 x))))
(sin x)
(+ (sin x) (* 1/2 (* eps (cos x))))
(+ (sin x) (* eps (+ (* -1/8 (* eps (sin x))) (* 1/2 (cos x)))))
(+ (sin x) (* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/8 (sin x)) (* -1/48 (* eps (cos x))))))))
(sin (* 1/2 (+ eps (* 2 x))))
(sin (* 1/2 (+ eps (* 2 x))))
(sin (* 1/2 (+ eps (* 2 x))))
(sin (* 1/2 (+ eps (* 2 x))))
(sin (* 1/2 (- (* 2 x) (* -1 eps))))
(sin (* 1/2 (- (* 2 x) (* -1 eps))))
(sin (* 1/2 (- (* 2 x) (* -1 eps))))
(sin (* 1/2 (- (* 2 x) (* -1 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)
(* x (sin eps))
(* x (+ (sin eps) (* -1/6 (* (pow x 2) (sin eps)))))
(* x (+ (sin eps) (* (pow x 2) (+ (* -1/6 (sin eps)) (* 1/120 (* (pow x 2) (sin eps)))))))
(* x (+ (sin eps) (* (pow x 2) (+ (* -1/6 (sin eps)) (* (pow x 2) (+ (* -1/5040 (* (pow x 2) (sin eps))) (* 1/120 (sin eps))))))))
(* (sin eps) (sin x))
(* (sin eps) (sin x))
(* (sin eps) (sin x))
(* (sin eps) (sin x))
(* (sin eps) (sin x))
(* (sin eps) (sin x))
(* (sin eps) (sin x))
(* (sin eps) (sin x))
(* eps (sin x))
(* eps (+ (sin x) (* -1/6 (* (pow eps 2) (sin x)))))
(* eps (+ (sin x) (* (pow eps 2) (+ (* -1/6 (sin x)) (* 1/120 (* (pow eps 2) (sin x)))))))
(* eps (+ (sin x) (* (pow eps 2) (+ (* -1/6 (sin x)) (* (pow eps 2) (+ (* -1/5040 (* (pow eps 2) (sin x))) (* 1/120 (sin x))))))))
(* (sin eps) (sin x))
(* (sin eps) (sin x))
(* (sin eps) (sin x))
(* (sin eps) (sin x))
(* (sin eps) (sin x))
(* (sin eps) (sin x))
(* (sin eps) (sin x))
(* (sin eps) (sin x))
(cos eps)
(+ (cos eps) (* -1/2 (* (pow x 2) (cos eps))))
(+ (cos eps) (* (pow x 2) (+ (* -1/2 (cos eps)) (* 1/24 (* (pow x 2) (cos eps))))))
(+ (cos eps) (* (pow x 2) (+ (* -1/2 (cos eps)) (* (pow x 2) (+ (* -1/720 (* (pow x 2) (cos eps))) (* 1/24 (cos eps)))))))
(* (cos eps) (cos x))
(* (cos eps) (cos x))
(* (cos eps) (cos x))
(* (cos eps) (cos x))
(* (cos eps) (cos x))
(* (cos eps) (cos x))
(* (cos eps) (cos x))
(* (cos eps) (cos x))
(cos x)
(+ (cos x) (* -1/2 (* (pow eps 2) (cos x))))
(+ (cos x) (* (pow eps 2) (+ (* -1/2 (cos x)) (* 1/24 (* (pow eps 2) (cos x))))))
(+ (cos x) (* (pow eps 2) (+ (* -1/2 (cos x)) (* (pow eps 2) (+ (* -1/720 (* (pow eps 2) (cos x))) (* 1/24 (cos x)))))))
(* (cos eps) (cos x))
(* (cos eps) (cos x))
(* (cos eps) (cos x))
(* (cos eps) (cos x))
(* (cos eps) (cos x))
(* (cos eps) (cos x))
(* (cos eps) (cos x))
(* (cos eps) (cos x))

Outputs
(* 1/2 eps)
(*.f64 #s(literal 1/2 binary64) eps)
(+ x (* 1/2 eps))
(fma.f64 #s(literal 1/2 binary64) eps x)
(+ x (* 1/2 eps))
(fma.f64 #s(literal 1/2 binary64) eps x)
(+ x (* 1/2 eps))
(fma.f64 #s(literal 1/2 binary64) eps x)
x
(* x (+ 1 (* 1/2 (/ eps x))))
(fma.f64 x (/.f64 (*.f64 #s(literal 1/2 binary64) eps) x) x)
(* x (+ 1 (* 1/2 (/ eps x))))
(fma.f64 x (/.f64 (*.f64 #s(literal 1/2 binary64) eps) x) x)
(* x (+ 1 (* 1/2 (/ eps x))))
(fma.f64 x (/.f64 (*.f64 #s(literal 1/2 binary64) eps) x) x)
x
(* -1 (* x (- (* -1/2 (/ eps x)) 1)))
(fma.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) (neg.f64 x) x)
(* -1 (* x (- (* -1/2 (/ eps x)) 1)))
(fma.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) (neg.f64 x) x)
(* -1 (* x (- (* -1/2 (/ eps x)) 1)))
(fma.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) (neg.f64 x) x)
x
(+ x (* 1/2 eps))
(fma.f64 #s(literal 1/2 binary64) eps x)
(+ x (* 1/2 eps))
(fma.f64 #s(literal 1/2 binary64) eps x)
(+ x (* 1/2 eps))
(fma.f64 #s(literal 1/2 binary64) eps x)
(* 1/2 eps)
(*.f64 #s(literal 1/2 binary64) eps)
(* eps (+ 1/2 (/ x eps)))
(*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)))
(* eps (+ 1/2 (/ x eps)))
(*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)))
(* eps (+ 1/2 (/ x eps)))
(*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)))
(* 1/2 eps)
(*.f64 #s(literal 1/2 binary64) eps)
(* -1 (* eps (- (* -1 (/ x eps)) 1/2)))
(*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)))
(* -1 (* eps (- (* -1 (/ x eps)) 1/2)))
(*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)))
(* -1 (* eps (- (* -1 (/ x eps)) 1/2)))
(*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)))
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
(* -1 (* eps (sin x)))
(neg.f64 (*.f64 eps (sin.f64 x)))
(* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))
(.f64 eps (-.f64 (.f64 #s(literal -1/2 binary64) (*.f64 eps (cos.f64 x))) (sin.f64 x)))
(* eps (+ (* -1 (sin x)) (* eps (+ (* -2 (* eps (+ (* -1/16 (sin x)) (* -1/48 (sin x))))) (* -1/2 (cos x))))))
(.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x)) (.f64 (sin.f64 x) (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)))))
(* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* eps (+ (* -2 (+ (* -1/16 (sin x)) (* -1/48 (sin x)))) (* 1/24 (* eps (cos x)))))))))
(.f64 eps (fma.f64 eps (fma.f64 (cos.f64 x) (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) (.f64 eps (.f64 (sin.f64 x) #s(literal 1/6 binary64)))) (neg.f64 (sin.f64 x))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))
(.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (.f64 #s(literal -2 binary64) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))
(.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (.f64 #s(literal -2 binary64) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))
(.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (.f64 #s(literal -2 binary64) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))
(.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (.f64 #s(literal -2 binary64) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps))))))
(.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (.f64 #s(literal -2 binary64) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps))))))
(.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (.f64 #s(literal -2 binary64) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps))))))
(.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (.f64 #s(literal -2 binary64) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps))))))
(.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (.f64 #s(literal -2 binary64) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))))
(* -2 (pow (sin (* 1/2 eps)) 2))
(.f64 #s(literal -2 binary64) (pow.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)))
(+ (* -2 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (* -2 (pow (sin (* 1/2 eps)) 2)))
(.f64 (.f64 #s(literal -2 binary64) (sin.f64 (.f64 #s(literal 1/2 binary64) eps))) (fma.f64 x (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))))
(+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (pow (sin (* 1/2 eps)) 2)))))
(fma.f64 x (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (.f64 #s(literal -2 binary64) (sin.f64 (.f64 #s(literal 1/2 binary64) eps)))) (.f64 (pow.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (fma.f64 x x #s(literal -2 binary64))))
(+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* 1/3 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (pow (sin (* 1/2 eps)) 2))))))
(fma.f64 x (fma.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (.f64 #s(literal 1/2 binary64) eps))) (+.f64 #s(literal -2 binary64) (.f64 x (.f64 x #s(literal 1/3 binary64)))) (.f64 x (pow.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)))) (.f64 #s(literal -2 binary64) (pow.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))
(.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (.f64 #s(literal -2 binary64) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))
(.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (.f64 #s(literal -2 binary64) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))
(.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (.f64 #s(literal -2 binary64) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))
(.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (.f64 #s(literal -2 binary64) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x))))))
(.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (.f64 #s(literal -2 binary64) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x))))))
(.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (.f64 #s(literal -2 binary64) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x))))))
(.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (.f64 #s(literal -2 binary64) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x))))))
(.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (.f64 #s(literal -2 binary64) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))))
(* 1/2 (* eps (sin x)))
(.f64 #s(literal 1/2 binary64) (.f64 eps (sin.f64 x)))
(* eps (+ (* 1/4 (* eps (cos x))) (* 1/2 (sin x))))
(.f64 eps (fma.f64 eps (.f64 (cos.f64 x) #s(literal 1/4 binary64)) (*.f64 #s(literal 1/2 binary64) (sin.f64 x))))
(* eps (+ (* 1/2 (sin x)) (* eps (+ (* 1/4 (cos x)) (* eps (+ (* -1/16 (sin x)) (* -1/48 (sin x))))))))
(.f64 eps (fma.f64 eps (fma.f64 eps (.f64 (sin.f64 x) #s(literal -1/12 binary64)) (.f64 (cos.f64 x) #s(literal 1/4 binary64))) (.f64 #s(literal 1/2 binary64) (sin.f64 x))))
(* eps (+ (* 1/2 (sin x)) (* eps (+ (* 1/4 (cos x)) (* eps (+ (* -1/16 (sin x)) (+ (* -1/48 (sin x)) (* -1/48 (* eps (cos x))))))))))
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(* eps (+ (* -1/2 (/ (sin (* 2 x)) (cos x))) (* eps (- (+ (* -1/2 (/ (cos (* 2 x)) (cos x))) (* eps (- (* 1/3 (/ (sin (* 2 x)) (cos x))) (+ (* -1/2 (/ (* (sin x) (- (* -1/2 (/ (cos (* 2 x)) (cos x))) (* 1/4 (/ (* (sin x) (sin (* 2 x))) (pow (cos x) 2))))) (cos x))) (* 1/8 (/ (sin (* 2 x)) (cos x))))))) (* 1/4 (/ (* (sin x) (sin (* 2 x))) (pow (cos x) 2)))))))
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(* eps (+ (* -1/2 (/ (sin (* 2 x)) (cos x))) (* eps (- (+ (* -1/2 (/ (cos (* 2 x)) (cos x))) (* eps (- (+ (* 1/3 (/ (sin (* 2 x)) (cos x))) (* eps (- (* 1/6 (/ (cos (* 2 x)) (cos x))) (+ (* -1/2 (/ (* (sin x) (- (* 1/3 (/ (sin (* 2 x)) (cos x))) (+ (* -1/2 (/ (* (sin x) (- (* -1/2 (/ (cos (* 2 x)) (cos x))) (* 1/4 (/ (* (sin x) (sin (* 2 x))) (pow (cos x) 2))))) (cos x))) (* 1/8 (/ (sin (* 2 x)) (cos x)))))) (cos x))) (+ (* -1/4 (- (* -1/2 (/ (cos (* 2 x)) (cos x))) (* 1/4 (/ (* (sin x) (sin (* 2 x))) (pow (cos x) 2))))) (* -1/24 (/ (* (sin x) (sin (* 2 x))) (pow (cos x) 2)))))))) (+ (* -1/2 (/ (* (sin x) (- (* -1/2 (/ (cos (* 2 x)) (cos x))) (* 1/4 (/ (* (sin x) (sin (* 2 x))) (pow (cos x) 2))))) (cos x))) (* 1/8 (/ (sin (* 2 x)) (cos x))))))) (* 1/4 (/ (* (sin x) (sin (* 2 x))) (pow (cos x) 2)))))))
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(fma.f64 (cos.f64 x) (+.f64 #s(literal -1 binary64) (cos.f64 eps)) (*.f64 (sin.f64 x) (neg.f64 (sin.f64 eps))))
(- (* (cos eps) (cos x)) (+ (cos x) (* (sin eps) (sin x))))
(fma.f64 (cos.f64 x) (+.f64 #s(literal -1 binary64) (cos.f64 eps)) (*.f64 (sin.f64 x) (neg.f64 (sin.f64 eps))))
(- (* (cos eps) (cos x)) (+ (cos x) (* (sin eps) (sin x))))
(fma.f64 (cos.f64 x) (+.f64 #s(literal -1 binary64) (cos.f64 eps)) (*.f64 (sin.f64 x) (neg.f64 (sin.f64 eps))))
(- (* (cos eps) (cos x)) (+ (cos x) (* (sin eps) (sin x))))
(fma.f64 (cos.f64 x) (+.f64 #s(literal -1 binary64) (cos.f64 eps)) (*.f64 (sin.f64 x) (neg.f64 (sin.f64 eps))))
(- (* (cos eps) (cos x)) (+ (cos x) (* (sin eps) (sin x))))
(fma.f64 (cos.f64 x) (+.f64 #s(literal -1 binary64) (cos.f64 eps)) (*.f64 (sin.f64 x) (neg.f64 (sin.f64 eps))))
(- (* (cos eps) (cos x)) (+ (cos x) (* (sin eps) (sin x))))
(fma.f64 (cos.f64 x) (+.f64 #s(literal -1 binary64) (cos.f64 eps)) (*.f64 (sin.f64 x) (neg.f64 (sin.f64 eps))))
-1
#s(literal -1 binary64)
(- (* 1/2 (pow x 2)) 1)
(fma.f64 #s(literal 1/2 binary64) (*.f64 x x) #s(literal -1 binary64))
(- (* (pow x 2) (+ 1/2 (* -1/24 (pow x 2)))) 1)
(fma.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal -1/24 binary64)) #s(literal 1/2 binary64))) #s(literal -1 binary64))
(- (* (pow x 2) (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24)))) 1)
(fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 x (*.f64 x #s(literal 1/720 binary64)) #s(literal -1/24 binary64)) #s(literal 1/2 binary64)) #s(literal -1 binary64))
(* -1 (cos x))
(neg.f64 (cos.f64 x))
(* -1 (cos x))
(neg.f64 (cos.f64 x))
(* -1 (cos x))
(neg.f64 (cos.f64 x))
(* -1 (cos x))
(neg.f64 (cos.f64 x))
(* -1 (cos x))
(neg.f64 (cos.f64 x))
(* -1 (cos x))
(neg.f64 (cos.f64 x))
(* -1 (cos x))
(neg.f64 (cos.f64 x))
(* -1 (cos x))
(neg.f64 (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 #s(literal 1/24 binary64) (.f64 x x) #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 x (.f64 x (fma.f64 (.f64 x x) (fma.f64 #s(literal -1/720 binary64) (*.f64 x x) #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
(+ eps (* 2 x))
(fma.f64 x #s(literal 2 binary64) eps)
(+ eps (* 2 x))
(fma.f64 x #s(literal 2 binary64) eps)
(+ eps (* 2 x))
(fma.f64 x #s(literal 2 binary64) eps)
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* x (+ 2 (/ eps x)))
(*.f64 x (+.f64 (/.f64 eps x) #s(literal 2 binary64)))
(* x (+ 2 (/ eps x)))
(*.f64 x (+.f64 (/.f64 eps x) #s(literal 2 binary64)))
(* x (+ 2 (/ eps x)))
(*.f64 x (+.f64 (/.f64 eps x) #s(literal 2 binary64)))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* -1 (* x (- (* -1 (/ eps x)) 2)))
(*.f64 x (+.f64 (/.f64 eps x) #s(literal 2 binary64)))
(* -1 (* x (- (* -1 (/ eps x)) 2)))
(*.f64 x (+.f64 (/.f64 eps x) #s(literal 2 binary64)))
(* -1 (* x (- (* -1 (/ eps x)) 2)))
(*.f64 x (+.f64 (/.f64 eps x) #s(literal 2 binary64)))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(+ eps (* 2 x))
(fma.f64 x #s(literal 2 binary64) eps)
(+ eps (* 2 x))
(fma.f64 x #s(literal 2 binary64) eps)
(+ eps (* 2 x))
(fma.f64 x #s(literal 2 binary64) eps)
eps
(* eps (+ 1 (* 2 (/ x eps))))
(fma.f64 eps (/.f64 (*.f64 x #s(literal 2 binary64)) eps) eps)
(* eps (+ 1 (* 2 (/ x eps))))
(fma.f64 eps (/.f64 (*.f64 x #s(literal 2 binary64)) eps) eps)
(* eps (+ 1 (* 2 (/ x eps))))
(fma.f64 eps (/.f64 (*.f64 x #s(literal 2 binary64)) eps) eps)
eps
(* -1 (* eps (- (* -2 (/ x eps)) 1)))
(fma.f64 eps (/.f64 (*.f64 x #s(literal 2 binary64)) eps) eps)
(* -1 (* eps (- (* -2 (/ x eps)) 1)))
(fma.f64 eps (/.f64 (*.f64 x #s(literal 2 binary64)) eps) eps)
(* -1 (* eps (- (* -2 (/ x eps)) 1)))
(fma.f64 eps (/.f64 (*.f64 x #s(literal 2 binary64)) eps) eps)
(sin (* 1/2 eps))
(sin.f64 (*.f64 #s(literal 1/2 binary64) eps))
(+ (sin (* 1/2 eps)) (* x (cos (* 1/2 eps))))
(fma.f64 x (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (.f64 #s(literal 1/2 binary64) eps)))
(+ (sin (* 1/2 eps)) (* x (+ (cos (* 1/2 eps)) (* -1/2 (* x (sin (* 1/2 eps)))))))
(fma.f64 x (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (.f64 (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) (sin.f64 (.f64 #s(literal 1/2 binary64) eps))))
(+ (sin (* 1/2 eps)) (* x (+ (cos (* 1/2 eps)) (* x (+ (* -1/2 (sin (* 1/2 eps))) (* -1/6 (* x (cos (* 1/2 eps)))))))))
(fma.f64 x (fma.f64 #s(literal -1/2 binary64) (.f64 x (sin.f64 (.f64 #s(literal 1/2 binary64) eps))) (.f64 (fma.f64 x (.f64 x #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 (.f64 #s(literal 1/2 binary64) eps)))) (sin.f64 (.f64 #s(literal 1/2 binary64) eps)))
(sin (* 1/2 (+ eps (* 2 x))))
(sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(sin (* 1/2 (+ eps (* 2 x))))
(sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(sin (* 1/2 (+ eps (* 2 x))))
(sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(sin (* 1/2 (+ eps (* 2 x))))
(sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(sin (* 1/2 (- eps (* -2 x))))
(sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(sin (* 1/2 (- eps (* -2 x))))
(sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(sin (* 1/2 (- eps (* -2 x))))
(sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(sin (* 1/2 (- eps (* -2 x))))
(sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(sin x)
(sin.f64 x)
(+ (sin x) (* 1/2 (* eps (cos x))))
(fma.f64 #s(literal 1/2 binary64) (*.f64 eps (cos.f64 x)) (sin.f64 x))
(+ (sin x) (* eps (+ (* -1/8 (* eps (sin x))) (* 1/2 (cos x)))))
(fma.f64 (fma.f64 eps (.f64 eps #s(literal -1/8 binary64)) #s(literal 1 binary64)) (sin.f64 x) (.f64 #s(literal 1/2 binary64) (*.f64 eps (cos.f64 x))))
(+ (sin x) (* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/8 (sin x)) (* -1/48 (* eps (cos x))))))))
(fma.f64 eps (fma.f64 eps (.f64 (sin.f64 x) #s(literal -1/8 binary64)) (.f64 (cos.f64 x) (fma.f64 eps (*.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (sin.f64 x))
(sin (* 1/2 (+ eps (* 2 x))))
(sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(sin (* 1/2 (+ eps (* 2 x))))
(sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(sin (* 1/2 (+ eps (* 2 x))))
(sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(sin (* 1/2 (+ eps (* 2 x))))
(sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(sin (* 1/2 (- (* 2 x) (* -1 eps))))
(sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(sin (* 1/2 (- (* 2 x) (* -1 eps))))
(sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(sin (* 1/2 (- (* 2 x) (* -1 eps))))
(sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(sin (* 1/2 (- (* 2 x) (* -1 eps))))
(sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(* -1/2 x)
(*.f64 x #s(literal -1/2 binary64))
(* -1/2 x)
(*.f64 x #s(literal -1/2 binary64))
(* -1/2 x)
(*.f64 x #s(literal -1/2 binary64))
(* -1/2 x)
(*.f64 x #s(literal -1/2 binary64))
(* -1/2 x)
(*.f64 x #s(literal -1/2 binary64))
(* -1/2 x)
(*.f64 x #s(literal -1/2 binary64))
(* -1/2 x)
(*.f64 x #s(literal -1/2 binary64))
(* -1/2 x)
(*.f64 x #s(literal -1/2 binary64))
(* -1/2 x)
(*.f64 x #s(literal -1/2 binary64))
(* -1/2 x)
(*.f64 x #s(literal -1/2 binary64))
(* -1/2 x)
(*.f64 x #s(literal -1/2 binary64))
(* -1/2 x)
(*.f64 x #s(literal -1/2 binary64))
(* x (sin eps))
(*.f64 x (sin.f64 eps))
(* x (+ (sin eps) (* -1/6 (* (pow x 2) (sin eps)))))
(.f64 (sin.f64 eps) (fma.f64 x (.f64 #s(literal -1/6 binary64) (*.f64 x x)) x))
(* x (+ (sin eps) (* (pow x 2) (+ (* -1/6 (sin eps)) (* 1/120 (* (pow x 2) (sin eps)))))))
(.f64 x (.f64 (sin.f64 eps) (+.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 x x) #s(literal 1 binary64)) (.f64 (.f64 x x) (.f64 (*.f64 x x) #s(literal 1/120 binary64))))))
(* x (+ (sin eps) (* (pow x 2) (+ (* -1/6 (sin eps)) (* (pow x 2) (+ (* -1/5040 (* (pow x 2) (sin eps))) (* 1/120 (sin eps))))))))
(.f64 x (fma.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 x x) #s(literal 1 binary64)) (sin.f64 eps) (.f64 (.f64 x x) (.f64 (.f64 (sin.f64 eps) (.f64 x x)) (fma.f64 (.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64))))))
(* (sin eps) (sin x))
(*.f64 (sin.f64 x) (sin.f64 eps))
(* (sin eps) (sin x))
(*.f64 (sin.f64 x) (sin.f64 eps))
(* (sin eps) (sin x))
(*.f64 (sin.f64 x) (sin.f64 eps))
(* (sin eps) (sin x))
(*.f64 (sin.f64 x) (sin.f64 eps))
(* (sin eps) (sin x))
(*.f64 (sin.f64 x) (sin.f64 eps))
(* (sin eps) (sin x))
(*.f64 (sin.f64 x) (sin.f64 eps))
(* (sin eps) (sin x))
(*.f64 (sin.f64 x) (sin.f64 eps))
(* (sin eps) (sin x))
(*.f64 (sin.f64 x) (sin.f64 eps))
(* eps (sin x))
(*.f64 eps (sin.f64 x))
(* eps (+ (sin x) (* -1/6 (* (pow eps 2) (sin x)))))
(.f64 (sin.f64 x) (fma.f64 eps (.f64 #s(literal -1/6 binary64) (*.f64 eps eps)) eps))
(* eps (+ (sin x) (* (pow eps 2) (+ (* -1/6 (sin x)) (* 1/120 (* (pow eps 2) (sin x)))))))
(.f64 eps (.f64 (sin.f64 x) (+.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 eps eps) #s(literal 1 binary64)) (.f64 (.f64 eps eps) (.f64 (*.f64 eps eps) #s(literal 1/120 binary64))))))
(* eps (+ (sin x) (* (pow eps 2) (+ (* -1/6 (sin x)) (* (pow eps 2) (+ (* -1/5040 (* (pow eps 2) (sin x))) (* 1/120 (sin x))))))))
(.f64 eps (fma.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 eps eps) #s(literal 1 binary64)) (sin.f64 x) (.f64 (.f64 eps eps) (.f64 (.f64 eps (.f64 eps (sin.f64 x))) (fma.f64 (.f64 eps eps) #s(literal -1/5040 binary64) #s(literal 1/120 binary64))))))
(* (sin eps) (sin x))
(*.f64 (sin.f64 x) (sin.f64 eps))
(* (sin eps) (sin x))
(*.f64 (sin.f64 x) (sin.f64 eps))
(* (sin eps) (sin x))
(*.f64 (sin.f64 x) (sin.f64 eps))
(* (sin eps) (sin x))
(*.f64 (sin.f64 x) (sin.f64 eps))
(* (sin eps) (sin x))
(*.f64 (sin.f64 x) (sin.f64 eps))
(* (sin eps) (sin x))
(*.f64 (sin.f64 x) (sin.f64 eps))
(* (sin eps) (sin x))
(*.f64 (sin.f64 x) (sin.f64 eps))
(* (sin eps) (sin x))
(*.f64 (sin.f64 x) (sin.f64 eps))
(cos eps)
(cos.f64 eps)
(+ (cos eps) (* -1/2 (* (pow x 2) (cos eps))))
(.f64 (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) (cos.f64 eps))
(+ (cos eps) (* (pow x 2) (+ (* -1/2 (cos eps)) (* 1/24 (* (pow x 2) (cos eps))))))
(.f64 (cos.f64 eps) (+.f64 (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) (.f64 (.f64 x x) (.f64 #s(literal 1/24 binary64) (.f64 x x)))))
(+ (cos eps) (* (pow x 2) (+ (* -1/2 (cos eps)) (* (pow x 2) (+ (* -1/720 (* (pow x 2) (cos eps))) (* 1/24 (cos eps)))))))
(fma.f64 (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) (cos.f64 eps) (.f64 (.f64 x x) (.f64 (.f64 x (.f64 x (cos.f64 eps))) (fma.f64 #s(literal -1/720 binary64) (*.f64 x x) #s(literal 1/24 binary64)))))
(* (cos eps) (cos x))
(*.f64 (cos.f64 x) (cos.f64 eps))
(* (cos eps) (cos x))
(*.f64 (cos.f64 x) (cos.f64 eps))
(* (cos eps) (cos x))
(*.f64 (cos.f64 x) (cos.f64 eps))
(* (cos eps) (cos x))
(*.f64 (cos.f64 x) (cos.f64 eps))
(* (cos eps) (cos x))
(*.f64 (cos.f64 x) (cos.f64 eps))
(* (cos eps) (cos x))
(*.f64 (cos.f64 x) (cos.f64 eps))
(* (cos eps) (cos x))
(*.f64 (cos.f64 x) (cos.f64 eps))
(* (cos eps) (cos x))
(*.f64 (cos.f64 x) (cos.f64 eps))
(cos x)
(cos.f64 x)
(+ (cos x) (* -1/2 (* (pow eps 2) (cos x))))
(.f64 (fma.f64 eps (.f64 eps #s(literal -1/2 binary64)) #s(literal 1 binary64)) (cos.f64 x))
(+ (cos x) (* (pow eps 2) (+ (* -1/2 (cos x)) (* 1/24 (* (pow eps 2) (cos x))))))
(.f64 (cos.f64 x) (+.f64 (fma.f64 eps (.f64 eps #s(literal -1/2 binary64)) #s(literal 1 binary64)) (.f64 (.f64 eps eps) (.f64 eps (.f64 eps #s(literal 1/24 binary64))))))
(+ (cos x) (* (pow eps 2) (+ (* -1/2 (cos x)) (* (pow eps 2) (+ (* -1/720 (* (pow eps 2) (cos x))) (* 1/24 (cos x)))))))
(fma.f64 (fma.f64 eps (.f64 eps #s(literal -1/2 binary64)) #s(literal 1 binary64)) (cos.f64 x) (.f64 (.f64 eps eps) (.f64 (.f64 eps (.f64 eps (cos.f64 x))) (fma.f64 eps (*.f64 eps #s(literal -1/720 binary64)) #s(literal 1/24 binary64)))))
(* (cos eps) (cos x))
(*.f64 (cos.f64 x) (cos.f64 eps))
(* (cos eps) (cos x))
(*.f64 (cos.f64 x) (cos.f64 eps))
(* (cos eps) (cos x))
(*.f64 (cos.f64 x) (cos.f64 eps))
(* (cos eps) (cos x))
(*.f64 (cos.f64 x) (cos.f64 eps))
(* (cos eps) (cos x))
(*.f64 (cos.f64 x) (cos.f64 eps))
(* (cos eps) (cos x))
(*.f64 (cos.f64 x) (cos.f64 eps))
(* (cos eps) (cos x))
(*.f64 (cos.f64 x) (cos.f64 eps))
(* (cos eps) (cos x))
(*.f64 (cos.f64 x) (cos.f64 eps))

eval253.0ms (1.4%)

Memory: 15.1MiB live, 165.8MiB allocated
Compiler: Compiled 29 622 to 2 369 computations (92% saved)

prune195.0ms (1.1%)

Memory

21.5MiB live, 185.7MiB allocated

Pruning

27 alts after pruning (24 fresh and 3 done)

	Pruned	Kept	Total
New	1 207	21	1 228
Fresh	6	3	9
Picked	3	2	5
Done	0	1	1
Total	1 216	27	1 243

Accuracy

100.0%

Counts

1 243 → 27

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	80.9%	(fma.f64 (sin.f64 x) (neg.f64 (sin.f64 eps)) (*.f64 (cos.f64 x) (+.f64 (cos.f64 eps) #s(literal -1 binary64))))
	97.2%	(fma.f64 x (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (.f64 #s(literal -2 binary64) (sin.f64 (.f64 #s(literal 1/2 binary64) eps)))) (.f64 (pow.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (fma.f64 x x #s(literal -2 binary64))))
	81.0%	(-.f64 (-.f64 (.f64 (cos.f64 eps) (cos.f64 x)) (cos.f64 x)) (.f64 (sin.f64 x) (sin.f64 eps)))
	52.5%	(-.f64 (-.f64 (cos.f64 (+.f64 x eps)) #s(literal 1 binary64)) (.f64 x (.f64 x #s(literal -1/2 binary64))))
	99.3%	(-.f64 (.f64 (.f64 eps eps) (fma.f64 (.f64 eps (.f64 eps (cos.f64 x))) (fma.f64 eps (.f64 eps #s(literal -1/720 binary64)) #s(literal 1/24 binary64)) (.f64 #s(literal -1/2 binary64) (cos.f64 x)))) (*.f64 (sin.f64 x) (sin.f64 eps)))
	99.3%	(-.f64 (.f64 (.f64 eps eps) (fma.f64 (cos.f64 x) (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) (.f64 (.f64 eps eps) (.f64 (cos.f64 x) (.f64 eps (.f64 eps (fma.f64 (.f64 eps eps) #s(literal 1/40320 binary64) #s(literal -1/720 binary64)))))))) (.f64 (sin.f64 x) (sin.f64 eps)))
	99.0%	(-.f64 (.f64 eps (.f64 #s(literal -1/2 binary64) (.f64 eps (cos.f64 x)))) (.f64 (sin.f64 x) (sin.f64 eps)))
✓	53.4%	(-.f64 (cos.f64 (+.f64 x eps)) (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)))
✓	54.8%	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
	53.1%	(-.f64 (cos.f64 (+.f64 x eps)) #s(literal 1 binary64))
✓	53.1%	(+.f64 (cos.f64 eps) #s(literal -1 binary64))
▶	53.0%	(+.f64 #s(literal 1 binary64) #s(literal -1 binary64))
	22.0%	(.f64 (.f64 (sin.f64 (.f64 (fma.f64 (fma.f64 x (.f64 x x) (.f64 eps (.f64 eps eps))) (/.f64 #s(literal 1 binary64) (fma.f64 eps (-.f64 eps x) (.f64 x x))) (neg.f64 x)) #s(literal 1/2 binary64))) (sin.f64 (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)))) #s(literal -2 binary64))
	81.4%	(.f64 (.f64 (sin.f64 (.f64 (fma.f64 (.f64 (+.f64 x eps) (-.f64 x eps)) (/.f64 #s(literal 1 binary64) (-.f64 x eps)) (neg.f64 x)) #s(literal 1/2 binary64))) (sin.f64 (*.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)))) #s(literal -2 binary64))
	37.6%	(.f64 (.f64 (sin.f64 (.f64 (/.f64 (.f64 (fma.f64 (+.f64 x eps) eps (.f64 x x)) eps) (fma.f64 (+.f64 x eps) (+.f64 x eps) (-.f64 (.f64 x x) (.f64 x (+.f64 x eps))))) #s(literal 1/2 binary64))) (sin.f64 (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)))) #s(literal -2 binary64))
	31.6%	(.f64 (.f64 (sin.f64 (.f64 (/.f64 (.f64 eps (.f64 eps eps)) (.f64 eps eps)) #s(literal 1/2 binary64))) (sin.f64 (*.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)))) #s(literal -2 binary64))
	31.5%	(.f64 (.f64 (sin.f64 (.f64 (/.f64 #s(literal 1 binary64) (/.f64 (.f64 eps eps) (.f64 eps (.f64 eps eps)))) #s(literal 1/2 binary64))) (sin.f64 (*.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)))) #s(literal -2 binary64))
▶	98.2%	(.f64 (.f64 (sin.f64 (.f64 (/.f64 #s(literal 1 binary64) (/.f64 eps (.f64 eps eps))) #s(literal 1/2 binary64))) (sin.f64 (*.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)))) #s(literal -2 binary64))
	99.6%	(.f64 (.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (sin.f64 (.f64 (*.f64 x (+.f64 (/.f64 eps x) #s(literal 2 binary64))) #s(literal 1/2 binary64)))) #s(literal -2 binary64))
	99.6%	(.f64 (.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (sin.f64 (.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps))))) #s(literal -2 binary64))
	98.2%	(.f64 (.f64 (sin.f64 (.f64 (.f64 (.f64 eps eps) (/.f64 #s(literal 1 binary64) eps)) #s(literal 1/2 binary64))) (sin.f64 (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)))) #s(literal -2 binary64))
	99.6%	(.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)))) #s(literal -2 binary64))
▶	99.7%	(.f64 (.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) #s(literal -2 binary64))
	79.9%	(*.f64 (sin.f64 x) (neg.f64 eps))
▶	98.9%	(.f64 eps (-.f64 (.f64 eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x)))
	54.4%	(.f64 eps (.f64 eps #s(literal -1/2 binary64)))
	52.3%	(.f64 #s(literal 1/2 binary64) (.f64 x x))

Compiler

Compiled 994 to 630 computations (36.6% saved)

simplify321.0ms (1.8%)

Memory

-34.7MiB live, 202.0MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 17 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(sin.f64 eps)
✓	cost-diff	0	(neg.f64 (sin.f64 eps))
✓	cost-diff	0	(sin.f64 x)
✓	cost-diff	0	(fma.f64 (sin.f64 x) (neg.f64 (sin.f64 eps)) (*.f64 (cos.f64 x) (+.f64 (cos.f64 eps) #s(literal -1 binary64))))
✓	cost-diff	0	(.f64 (.f64 (sin.f64 (.f64 (/.f64 #s(literal 1 binary64) (/.f64 eps (.f64 eps eps))) #s(literal 1/2 binary64))) (sin.f64 (*.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)))) #s(literal -2 binary64))
✓	cost-diff	320	(*.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64))
✓	cost-diff	320	(/.f64 eps (*.f64 eps eps))
✓	cost-diff	1408	(/.f64 #s(literal 1 binary64) (/.f64 eps (*.f64 eps eps)))
✓	cost-diff	0	(*.f64 #s(literal -1/2 binary64) (cos.f64 x))
✓	cost-diff	0	(.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x)))
✓	cost-diff	0	(-.f64 (.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x))
✓	cost-diff	0	(.f64 eps (-.f64 (.f64 eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x)))
✓	cost-diff	192	(+.f64 #s(literal 1 binary64) #s(literal -1 binary64))
✓	cost-diff	0	(*.f64 #s(literal 1/2 binary64) eps)
✓	cost-diff	0	(sin.f64 (*.f64 #s(literal 1/2 binary64) eps))
✓	cost-diff	0	(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))
✓	cost-diff	0	(.f64 (.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) #s(literal -2 binary64))

Rules

5 334×	`lower-*.f32`
5 314×	`lower-*.f64`
4 702×	`lower-fma.f32`
4 698×	`lower-fma.f64`
2 456×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	37	222
0	69	180
1	113	178
2	206	178
3	322	178
4	807	178
5	3206	178
6	6038	178
0	8351	177

Stop Event

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

Calls

Call 1

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

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

localize139.0ms (0.8%)

Memory

9.7MiB live, 96.8MiB allocated

Localize:

Found 17 expressions of interest:

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

Samples

99.0ms	252×	1	exit
2.0ms	4×	0	valid

Compiler

Compiled 231 to 40 computations (82.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 76.0ms

ival-mult: 34.0ms (44.9% of total)

adjust: 17.0ms (22.5% of total)

ival-sin: 10.0ms (13.2% of total)

ival-add: 6.0ms (7.9% of total)

ival-div: 3.0ms (4% of total)

ival-cos: 3.0ms (4% of total)

ival-sub: 1.0ms (1.3% of total)

exact: 1.0ms (1.3% of total)

ival-neg: 1.0ms (1.3% of total)

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

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

series69.0ms (0.4%)

Memory

-9.7MiB live, 28.0MiB allocated

Counts

25 → 444

Calls

Call 1

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

Outputs
#<alt (* -1 (* eps (sin x)))>
#<alt (* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))>
#<alt (* eps (+ (* -1 (sin x)) (* eps (+ (* -2 (* eps (+ (* -1/16 (sin x)) (* -1/48 (sin x))))) (* -1/2 (cos x))))))>
#<alt (* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* eps (+ (* -2 (+ (* -1/16 (sin x)) (* -1/48 (sin x)))) (* 1/24 (* eps (cos x)))))))))>
#<alt (* -2 (* (sin (* 1/2 eps)) (sin (+ x (* 1/2 eps)))))>
#<alt (* -2 (* (sin (* 1/2 eps)) (sin (+ x (* 1/2 eps)))))>
#<alt (* -2 (* (sin (* 1/2 eps)) (sin (+ x (* 1/2 eps)))))>
#<alt (* -2 (* (sin (* 1/2 eps)) (sin (+ x (* 1/2 eps)))))>
#<alt (* -2 (* (sin (* 1/2 eps)) (sin (- x (* -1/2 eps)))))>
#<alt (* -2 (* (sin (* 1/2 eps)) (sin (- x (* -1/2 eps)))))>
#<alt (* -2 (* (sin (* 1/2 eps)) (sin (- x (* -1/2 eps)))))>
#<alt (* -2 (* (sin (* 1/2 eps)) (sin (- x (* -1/2 eps)))))>
#<alt (* -2 (pow (sin (* 1/2 eps)) 2))>
#<alt (+ (* -2 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (* -2 (pow (sin (* 1/2 eps)) 2)))>
#<alt (+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (pow (sin (* 1/2 eps)) 2)))))>
#<alt (+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* 1/3 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (pow (sin (* 1/2 eps)) 2))))))>
#<alt (* -2 (* (sin (* 1/2 eps)) (sin (+ x (* 1/2 eps)))))>
#<alt (* -2 (* (sin (* 1/2 eps)) (sin (+ x (* 1/2 eps)))))>
#<alt (* -2 (* (sin (* 1/2 eps)) (sin (+ x (* 1/2 eps)))))>
#<alt (* -2 (* (sin (* 1/2 eps)) (sin (+ x (* 1/2 eps)))))>
#<alt (* -2 (* (sin (* 1/2 eps)) (sin (- (* 1/2 eps) (* -1 x)))))>
#<alt (* -2 (* (sin (* 1/2 eps)) (sin (- (* 1/2 eps) (* -1 x)))))>
#<alt (* -2 (* (sin (* 1/2 eps)) (sin (- (* 1/2 eps) (* -1 x)))))>
#<alt (* -2 (* (sin (* 1/2 eps)) (sin (- (* 1/2 eps) (* -1 x)))))>
#<alt (* 1/2 (* eps (sin x)))>
#<alt (* eps (+ (* 1/4 (* eps (cos x))) (* 1/2 (sin x))))>
#<alt (* eps (+ (* 1/2 (sin x)) (* eps (+ (* 1/4 (cos x)) (* eps (+ (* -1/16 (sin x)) (* -1/48 (sin x))))))))>
#<alt (* eps (+ (* 1/2 (sin x)) (* eps (+ (* 1/4 (cos x)) (* eps (+ (* -1/16 (sin x)) (+ (* -1/48 (sin x)) (* -1/48 (* eps (cos x))))))))))>
#<alt (* (sin (* 1/2 eps)) (sin (+ x (* 1/2 eps))))>
#<alt (* (sin (* 1/2 eps)) (sin (+ x (* 1/2 eps))))>
#<alt (* (sin (* 1/2 eps)) (sin (+ x (* 1/2 eps))))>
#<alt (* (sin (* 1/2 eps)) (sin (+ x (* 1/2 eps))))>
#<alt (* (sin (* 1/2 eps)) (sin (- x (* -1/2 eps))))>
#<alt (* (sin (* 1/2 eps)) (sin (- x (* -1/2 eps))))>
#<alt (* (sin (* 1/2 eps)) (sin (- x (* -1/2 eps))))>
#<alt (* (sin (* 1/2 eps)) (sin (- x (* -1/2 eps))))>
#<alt (pow (sin (* 1/2 eps)) 2)>
#<alt (+ (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (pow (sin (* 1/2 eps)) 2))>
#<alt (+ (* x (+ (* -1/2 (* x (pow (sin (* 1/2 eps)) 2))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (pow (sin (* 1/2 eps)) 2))>
#<alt (+ (* x (+ (* x (+ (* -1/2 (pow (sin (* 1/2 eps)) 2)) (* -1/6 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (pow (sin (* 1/2 eps)) 2))>
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#<alt (* eps (+ 1 (* 2 (/ x eps))))>
#<alt (* eps (+ 1 (* 2 (/ x eps))))>
#<alt (* eps (+ 1 (* 2 (/ x eps))))>
#<alt eps>
#<alt (* -1 (* eps (- (* -2 (/ x eps)) 1)))>
#<alt (* -1 (* eps (- (* -2 (/ x eps)) 1)))>
#<alt (* -1 (* eps (- (* -2 (/ x eps)) 1)))>
#<alt (* -1/2 (pow eps 2))>
#<alt (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))>
#<alt (* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2))>
#<alt (* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* (pow eps 2) (- (* 1/40320 (pow eps 2)) 1/720)))) 1/2))>
#<alt (- (cos eps) 1)>
#<alt (- (cos eps) 1)>
#<alt (- (cos eps) 1)>
#<alt (- (cos eps) 1)>
#<alt (- (cos eps) 1)>
#<alt (- (cos eps) 1)>
#<alt (- (cos eps) 1)>
#<alt (- (cos eps) 1)>
#<alt (- (cos eps) 1)>
#<alt (- (+ (cos eps) (* -1/2 (* (pow x 2) (- (cos eps) 1)))) 1)>
#<alt (- (+ (cos eps) (* (pow x 2) (+ (* -1/2 (- (cos eps) 1)) (* 1/24 (* (pow x 2) (- (cos eps) 1)))))) 1)>
#<alt (- (+ (cos eps) (* (pow x 2) (+ (* -1/2 (- (cos eps) 1)) (* (pow x 2) (+ (* -1/720 (* (pow x 2) (- (cos eps) 1))) (* 1/24 (- (cos eps) 1))))))) 1)>
#<alt (* (cos x) (- (cos eps) 1))>
#<alt (* (cos x) (- (cos eps) 1))>
#<alt (* (cos x) (- (cos eps) 1))>
#<alt (* (cos x) (- (cos eps) 1))>
#<alt (* (cos x) (- (cos eps) 1))>
#<alt (* (cos x) (- (cos eps) 1))>
#<alt (* (cos x) (- (cos eps) 1))>
#<alt (* (cos x) (- (cos eps) 1))>
#<alt (* -1/2 (* (pow eps 2) (cos x)))>
#<alt (* (pow eps 2) (+ (* -1/2 (cos x)) (* 1/24 (* (pow eps 2) (cos x)))))>
#<alt (* (pow eps 2) (+ (* -1/2 (cos x)) (* (pow eps 2) (+ (* -1/720 (* (pow eps 2) (cos x))) (* 1/24 (cos x))))))>
#<alt (* (pow eps 2) (+ (* -1/2 (cos x)) (* (pow eps 2) (+ (* 1/24 (cos x)) (* (pow eps 2) (+ (* -1/720 (cos x)) (* 1/40320 (* (pow eps 2) (cos x)))))))))>
#<alt (* (cos x) (- (cos eps) 1))>
#<alt (* (cos x) (- (cos eps) 1))>
#<alt (* (cos x) (- (cos eps) 1))>
#<alt (* (cos x) (- (cos eps) 1))>
#<alt (* (cos x) (- (cos eps) 1))>
#<alt (* (cos x) (- (cos eps) 1))>
#<alt (* (cos x) (- (cos eps) 1))>
#<alt (* (cos x) (- (cos eps) 1))>
#<alt 1>
#<alt (+ 1 (* -1/2 (pow eps 2)))>
#<alt (+ 1 (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))>
#<alt (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2)))>
#<alt (cos eps)>
#<alt (cos eps)>
#<alt (cos eps)>
#<alt (cos eps)>
#<alt (cos eps)>
#<alt (cos eps)>
#<alt (cos eps)>
#<alt (cos eps)>

Calls

111 calls:

Time	Variable		Point	Expression
6.0ms	x	@	inf	(* eps (- (* eps (* -1/2 (cos x))) (sin x)))
1.0ms	x	@	inf	(+ (* (sin x) (neg (sin eps))) (* (cos x) (+ (cos eps) -1)))
1.0ms	eps	@	-inf	(+ (* (sin x) (neg (sin eps))) (* (cos x) (+ (cos eps) -1)))
1.0ms	eps	@	inf	(+ (* (sin x) (neg (sin eps))) (* (cos x) (+ (cos eps) -1)))
1.0ms	x	@	-inf	(+ (* (sin x) (neg (sin eps))) (* (cos x) (+ (cos eps) -1)))

rewrite370.0ms (2%)

Memory

27.3MiB live, 696.4MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

6 134×	`lower-*.f32`
6 110×	`lower-*.f64`
4 740×	`lower-/.f32`
4 736×	`lower-/.f64`
3 842×	`lower-fma.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	37	172
0	69	168
1	213	154
2	1486	152
0	8942	147

Stop Event

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

Counts

25 → 422

Calls

Call 1

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

Outputs
(/.f64 (.f64 #s(literal -2 binary64) (-.f64 (cos.f64 (-.f64 (.f64 #s(literal 1/2 binary64) eps) (fma.f64 #s(literal 1/2 binary64) eps x))) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps (fma.f64 #s(literal 1/2 binary64) eps x))))) #s(literal 2 binary64))
(/.f64 (.f64 (-.f64 (cos.f64 (-.f64 (.f64 #s(literal 1/2 binary64) eps) (fma.f64 #s(literal 1/2 binary64) eps x))) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal -2 binary64)) #s(literal 2 binary64))
(/.f64 (neg.f64 (.f64 #s(literal -2 binary64) (-.f64 (cos.f64 (-.f64 (.f64 #s(literal 1/2 binary64) eps) (fma.f64 #s(literal 1/2 binary64) eps x))) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps (fma.f64 #s(literal 1/2 binary64) eps x)))))) #s(literal -2 binary64))
(/.f64 (neg.f64 (.f64 (-.f64 (cos.f64 (-.f64 (.f64 #s(literal 1/2 binary64) eps) (fma.f64 #s(literal 1/2 binary64) eps x))) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal -2 binary64))) #s(literal -2 binary64))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (*.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal -2 binary64)))
(.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal -2 binary64)))
(.f64 (.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) #s(literal -2 binary64))
(.f64 #s(literal -2 binary64) (.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))))
(.f64 (.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal -2 binary64)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))
(.f64 (.f64 #s(literal -2 binary64) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))
(+.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x))) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (.f64 (sin.f64 x) (cos.f64 (.f64 #s(literal 1/2 binary64) eps)))))
(+.f64 (.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x)) (sin.f64 (.f64 #s(literal 1/2 binary64) eps))) (.f64 (.f64 (sin.f64 x) (cos.f64 (.f64 #s(literal 1/2 binary64) eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) eps))))
(-.f64 (/.f64 (cos.f64 (-.f64 (*.f64 #s(literal 1/2 binary64) eps) (fma.f64 #s(literal 1/2 binary64) eps x))) #s(literal 2 binary64)) (/.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps (fma.f64 #s(literal 1/2 binary64) eps x))) #s(literal 2 binary64)))
(-.f64 (/.f64 (cos.f64 (-.f64 (fma.f64 #s(literal 1/2 binary64) eps x) (*.f64 #s(literal 1/2 binary64) eps))) #s(literal 2 binary64)) (/.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps (fma.f64 #s(literal 1/2 binary64) eps x))) #s(literal 2 binary64)))
(fma.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x)) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (.f64 (sin.f64 x) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)))))
(fma.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x)) (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (.f64 (.f64 (sin.f64 x) (cos.f64 (.f64 #s(literal 1/2 binary64) eps))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) (-.f64 (cos.f64 (-.f64 (*.f64 #s(literal 1/2 binary64) eps) (fma.f64 #s(literal 1/2 binary64) eps x))) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps (fma.f64 #s(literal 1/2 binary64) eps x))))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal 2 binary64) (-.f64 (cos.f64 (-.f64 (*.f64 #s(literal 1/2 binary64) eps) (fma.f64 #s(literal 1/2 binary64) eps x))) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps (fma.f64 #s(literal 1/2 binary64) eps x)))))))
(/.f64 (-.f64 (cos.f64 (-.f64 (*.f64 #s(literal 1/2 binary64) eps) (fma.f64 #s(literal 1/2 binary64) eps x))) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal 2 binary64))
(/.f64 (-.f64 (cos.f64 (-.f64 (fma.f64 #s(literal 1/2 binary64) eps x) (*.f64 #s(literal 1/2 binary64) eps))) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal 2 binary64))
(/.f64 (neg.f64 (-.f64 (cos.f64 (-.f64 (*.f64 #s(literal 1/2 binary64) eps) (fma.f64 #s(literal 1/2 binary64) eps x))) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps (fma.f64 #s(literal 1/2 binary64) eps x))))) #s(literal -2 binary64))
(/.f64 (-.f64 (.f64 (cos.f64 (-.f64 (.f64 #s(literal 1/2 binary64) eps) (fma.f64 #s(literal 1/2 binary64) eps x))) #s(literal 2 binary64)) (*.f64 #s(literal 2 binary64) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps (fma.f64 #s(literal 1/2 binary64) eps x))))) #s(literal 4 binary64))
(/.f64 (neg.f64 (-.f64 (cos.f64 (-.f64 (fma.f64 #s(literal 1/2 binary64) eps x) (*.f64 #s(literal 1/2 binary64) eps))) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps (fma.f64 #s(literal 1/2 binary64) eps x))))) #s(literal -2 binary64))
(/.f64 (neg.f64 (neg.f64 (-.f64 (cos.f64 (-.f64 (*.f64 #s(literal 1/2 binary64) eps) (fma.f64 #s(literal 1/2 binary64) eps x))) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps (fma.f64 #s(literal 1/2 binary64) eps x)))))) #s(literal 2 binary64))
(/.f64 (+.f64 (pow.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x))) #s(literal 3 binary64)) (pow.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (.f64 (sin.f64 x) (cos.f64 (.f64 #s(literal 1/2 binary64) eps)))) #s(literal 3 binary64))) (fma.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x))) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x))) (-.f64 (.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (.f64 (sin.f64 x) (cos.f64 (.f64 #s(literal 1/2 binary64) eps)))) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (.f64 (sin.f64 x) (cos.f64 (.f64 #s(literal 1/2 binary64) eps))))) (.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x))) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (.f64 (sin.f64 x) (cos.f64 (.f64 #s(literal 1/2 binary64) eps))))))))
(/.f64 (+.f64 (pow.f64 (.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x)) (sin.f64 (.f64 #s(literal 1/2 binary64) eps))) #s(literal 3 binary64)) (pow.f64 (.f64 (.f64 (sin.f64 x) (cos.f64 (.f64 #s(literal 1/2 binary64) eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) eps))) #s(literal 3 binary64))) (fma.f64 (.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x)) (sin.f64 (.f64 #s(literal 1/2 binary64) eps))) (.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x)) (sin.f64 (.f64 #s(literal 1/2 binary64) eps))) (-.f64 (.f64 (.f64 (.f64 (sin.f64 x) (cos.f64 (.f64 #s(literal 1/2 binary64) eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) eps))) (.f64 (.f64 (sin.f64 x) (cos.f64 (.f64 #s(literal 1/2 binary64) eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) eps)))) (.f64 (.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x)) (sin.f64 (.f64 #s(literal 1/2 binary64) eps))) (.f64 (.f64 (sin.f64 x) (cos.f64 (.f64 #s(literal 1/2 binary64) eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) eps)))))))
(pow.f64 (/.f64 #s(literal 2 binary64) (-.f64 (cos.f64 (-.f64 (*.f64 #s(literal 1/2 binary64) eps) (fma.f64 #s(literal 1/2 binary64) eps x))) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps (fma.f64 #s(literal 1/2 binary64) eps x))))) #s(literal -1 binary64))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))
(.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (sin.f64 (.f64 #s(literal 1/2 binary64) eps)))
(.f64 (-.f64 (cos.f64 (-.f64 (.f64 #s(literal 1/2 binary64) eps) (fma.f64 #s(literal 1/2 binary64) eps x))) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal 1/2 binary64))
(sin.f64 (*.f64 #s(literal 1/2 binary64) eps))
(/.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) eps))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1/2 binary64)))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1/2 binary64))))
(/.f64 #s(literal -1/2 binary64) (/.f64 #s(literal -1 binary64) eps))
(/.f64 (/.f64 #s(literal 1/2 binary64) eps) (/.f64 #s(literal 1 binary64) (*.f64 eps eps)))
(/.f64 (neg.f64 (/.f64 #s(literal 1/2 binary64) eps)) (neg.f64 (/.f64 #s(literal 1 binary64) (*.f64 eps eps))))
(pow.f64 (/.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1/2 binary64)) #s(literal -1 binary64))
(*.f64 #s(literal 1/2 binary64) eps)
(*.f64 eps #s(literal 1/2 binary64))
(.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) eps))
(.f64 (/.f64 #s(literal 1 binary64) eps) (.f64 (*.f64 eps eps) #s(literal 1/2 binary64)))
(.f64 (.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) eps)) (*.f64 eps eps))
(.f64 (/.f64 #s(literal 1/2 binary64) eps) (.f64 eps eps))
(.f64 (/.f64 #s(literal 1/2 binary64) (neg.f64 eps)) (.f64 eps (neg.f64 eps)))
#s(literal 0 binary64)
(+.f64 (.f64 eps (.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x)))) (.f64 eps (neg.f64 (sin.f64 x))))
(+.f64 (.f64 (.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) (.f64 (neg.f64 (sin.f64 x)) eps))
(fma.f64 eps (.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (*.f64 eps (neg.f64 (sin.f64 x))))
(fma.f64 (.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps (*.f64 (neg.f64 (sin.f64 x)) eps))
(/.f64 (.f64 eps (-.f64 (pow.f64 (.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) #s(literal 3 binary64)) (pow.f64 (sin.f64 x) #s(literal 3 binary64)))) (fma.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 eps #s(literal -1/2 binary64))) (.f64 (sin.f64 x) (fma.f64 eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) (sin.f64 x)))))
(/.f64 (.f64 eps (-.f64 (.f64 (+.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 eps #s(literal -1/2 binary64)))) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))))) (fma.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x)) (sin.f64 x)))
(/.f64 (.f64 (-.f64 (pow.f64 (.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) #s(literal 3 binary64)) (pow.f64 (sin.f64 x) #s(literal 3 binary64))) eps) (fma.f64 (+.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 eps #s(literal -1/2 binary64))) (.f64 (sin.f64 x) (fma.f64 eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) (sin.f64 x)))))
(/.f64 (.f64 (-.f64 (.f64 (+.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 eps #s(literal -1/2 binary64)))) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))) eps) (fma.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x)) (sin.f64 x)))
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(/.f64 (fma.f64 x (.f64 x x) (.f64 (+.f64 eps x) (.f64 (+.f64 eps x) (+.f64 eps x)))) (fma.f64 (+.f64 eps x) (+.f64 eps x) (-.f64 (.f64 x x) (*.f64 x (+.f64 eps x)))))
(/.f64 (*.f64 (+.f64 eps (+.f64 x x)) (-.f64 x (+.f64 eps x))) (-.f64 x (+.f64 eps x)))
(/.f64 (neg.f64 (fma.f64 x (.f64 x x) (.f64 (+.f64 eps x) (.f64 (+.f64 eps x) (+.f64 eps x))))) (neg.f64 (fma.f64 (+.f64 eps x) (-.f64 (+.f64 eps x) x) (.f64 x x))))
(/.f64 (neg.f64 (fma.f64 x (.f64 x x) (.f64 (+.f64 eps x) (.f64 (+.f64 eps x) (+.f64 eps x))))) (neg.f64 (fma.f64 (+.f64 eps x) (+.f64 eps x) (-.f64 (.f64 x x) (*.f64 x (+.f64 eps x))))))
(/.f64 (neg.f64 (*.f64 (+.f64 eps (+.f64 x x)) (-.f64 x (+.f64 eps x)))) (neg.f64 (-.f64 x (+.f64 eps x))))
(/.f64 (fma.f64 #s(literal 8 binary64) (.f64 x (.f64 x x)) (.f64 eps (.f64 eps eps))) (fma.f64 (+.f64 x x) (+.f64 x x) (-.f64 (.f64 eps eps) (.f64 (+.f64 x x) eps))))
(/.f64 (-.f64 (.f64 (+.f64 eps x) (+.f64 eps x)) (.f64 x x)) (-.f64 (+.f64 eps x) x))
(/.f64 (-.f64 (.f64 (+.f64 x x) (+.f64 x x)) (.f64 eps eps)) (-.f64 (+.f64 x x) eps))
(/.f64 (-.f64 (.f64 (.f64 x x) (-.f64 x (+.f64 eps x))) (.f64 (-.f64 x (+.f64 eps x)) (.f64 (+.f64 eps x) (+.f64 eps x)))) (*.f64 (-.f64 x (+.f64 eps x)) (-.f64 x (+.f64 eps x))))
(/.f64 (.f64 (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) (.f64 (.f64 (+.f64 eps x) (.f64 (+.f64 eps x) (+.f64 eps x))) (.f64 (.f64 (+.f64 eps x) (.f64 (+.f64 eps x) (+.f64 eps x))) (.f64 (+.f64 eps x) (.f64 (+.f64 eps x) (+.f64 eps x)))))) #s(literal 1 binary64)) (.f64 (fma.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)) (-.f64 (.f64 (.f64 (+.f64 eps x) (.f64 (+.f64 eps x) (+.f64 eps x))) (.f64 (+.f64 eps x) (.f64 (+.f64 eps x) (+.f64 eps x)))) (.f64 (.f64 x (.f64 x x)) (.f64 (+.f64 eps x) (.f64 (+.f64 eps x) (+.f64 eps x)))))) (fma.f64 (+.f64 eps x) (-.f64 (+.f64 eps x) x) (.f64 x x))))
(/.f64 (.f64 (-.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) (.f64 (.f64 (+.f64 eps x) (.f64 (+.f64 eps x) (+.f64 eps x))) (.f64 (+.f64 eps x) (.f64 (+.f64 eps x) (+.f64 eps x))))) #s(literal 1 binary64)) (.f64 (-.f64 (.f64 x (.f64 x x)) (.f64 (+.f64 eps x) (.f64 (+.f64 eps x) (+.f64 eps x)))) (fma.f64 (+.f64 eps x) (-.f64 (+.f64 eps x) x) (*.f64 x x))))
(/.f64 (.f64 (-.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) (.f64 (.f64 (+.f64 eps x) (.f64 (+.f64 eps x) (+.f64 eps x))) (.f64 (+.f64 eps x) (.f64 (+.f64 eps x) (+.f64 eps x))))) #s(literal 1 binary64)) (.f64 (fma.f64 (.f64 x x) (.f64 x x) (fma.f64 (.f64 (+.f64 eps x) (+.f64 eps x)) (.f64 (+.f64 eps x) (+.f64 eps x)) (.f64 (.f64 x x) (*.f64 (+.f64 eps x) (+.f64 eps x))))) (-.f64 x (+.f64 eps x))))
(/.f64 (.f64 (-.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 (.f64 (+.f64 eps x) (+.f64 eps x)) (.f64 (+.f64 eps x) (+.f64 eps x)))) #s(literal 1 binary64)) (.f64 (fma.f64 x x (*.f64 (+.f64 eps x) (+.f64 eps x))) (-.f64 x (+.f64 eps x))))
(/.f64 (neg.f64 (neg.f64 (fma.f64 x (.f64 x x) (.f64 (+.f64 eps x) (.f64 (+.f64 eps x) (+.f64 eps x)))))) (neg.f64 (neg.f64 (fma.f64 (+.f64 eps x) (-.f64 (+.f64 eps x) x) (.f64 x x)))))
(/.f64 (neg.f64 (neg.f64 (*.f64 (+.f64 eps (+.f64 x x)) (-.f64 x (+.f64 eps x))))) (neg.f64 (neg.f64 (-.f64 x (+.f64 eps x)))))
(/.f64 (neg.f64 (fma.f64 #s(literal 8 binary64) (.f64 x (.f64 x x)) (.f64 eps (.f64 eps eps)))) (neg.f64 (fma.f64 (+.f64 x x) (+.f64 x x) (-.f64 (.f64 eps eps) (.f64 (+.f64 x x) eps)))))
(/.f64 (neg.f64 (-.f64 (.f64 (+.f64 eps x) (+.f64 eps x)) (.f64 x x))) (neg.f64 (-.f64 (+.f64 eps x) x)))
(/.f64 (neg.f64 (-.f64 (.f64 (+.f64 x x) (+.f64 x x)) (.f64 eps eps))) (neg.f64 (-.f64 (+.f64 x x) eps)))
(/.f64 (fma.f64 eps (.f64 eps eps) (.f64 #s(literal 8 binary64) (.f64 x (.f64 x x)))) (fma.f64 eps eps (-.f64 (.f64 (+.f64 x x) (+.f64 x x)) (.f64 eps (+.f64 x x)))))
(pow.f64 (/.f64 (fma.f64 (+.f64 eps x) (-.f64 (+.f64 eps x) x) (.f64 x x)) (fma.f64 x (.f64 x x) (.f64 (+.f64 eps x) (.f64 (+.f64 eps x) (+.f64 eps x))))) #s(literal -1 binary64))
(pow.f64 (/.f64 (-.f64 x (+.f64 eps x)) (*.f64 (+.f64 eps (+.f64 x x)) (-.f64 x (+.f64 eps x)))) #s(literal -1 binary64))
(.f64 (fma.f64 x (.f64 x x) (.f64 (+.f64 eps x) (.f64 (+.f64 eps x) (+.f64 eps x)))) (/.f64 #s(literal 1 binary64) (fma.f64 (+.f64 eps x) (-.f64 (+.f64 eps x) x) (*.f64 x x))))
(.f64 (.f64 (+.f64 eps (+.f64 x x)) (-.f64 x (+.f64 eps x))) (/.f64 #s(literal 1 binary64) (-.f64 x (+.f64 eps x))))
(+.f64 #s(literal -1 binary64) (cos.f64 eps))
(+.f64 (cos.f64 eps) #s(literal -1 binary64))
(-.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 eps eps)))) (+.f64 (cos.f64 eps) #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (cos.f64 eps) #s(literal 1 binary64))))
(-.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal -1 binary64) (cos.f64 eps))) (/.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 eps eps)))) (-.f64 #s(literal -1 binary64) (cos.f64 eps))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 eps eps)))) (-.f64 #s(literal 1 binary64) (.f64 #s(literal -1 binary64) (cos.f64 eps)))) (+.f64 #s(literal -1 binary64) (pow.f64 (cos.f64 eps) #s(literal 3 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (cos.f64 eps) #s(literal 1 binary64)) (neg.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 eps eps)))))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (+.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 eps eps)))) (-.f64 #s(literal 1 binary64) (.f64 #s(literal -1 binary64) (cos.f64 eps)))) (+.f64 #s(literal -1 binary64) (pow.f64 (cos.f64 eps) #s(literal 3 binary64))))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (+.f64 (cos.f64 eps) #s(literal 1 binary64)) (neg.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 eps eps))))))))
(/.f64 (+.f64 #s(literal -1 binary64) (pow.f64 (cos.f64 eps) #s(literal 3 binary64))) (+.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 eps eps)))) (-.f64 #s(literal 1 binary64) (.f64 #s(literal -1 binary64) (cos.f64 eps)))))
(/.f64 (+.f64 #s(literal -1 binary64) (pow.f64 (cos.f64 eps) #s(literal 3 binary64))) (+.f64 #s(literal 1 binary64) (-.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 eps eps)))) (.f64 #s(literal -1 binary64) (cos.f64 eps)))))
(/.f64 (neg.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 eps eps))))) (+.f64 (cos.f64 eps) #s(literal 1 binary64)))
(/.f64 (neg.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 eps eps))))) (neg.f64 (-.f64 #s(literal -1 binary64) (cos.f64 eps))))
(/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 eps eps)))) (-.f64 #s(literal -1 binary64) (cos.f64 eps)))
(/.f64 (neg.f64 (+.f64 #s(literal -1 binary64) (pow.f64 (cos.f64 eps) #s(literal 3 binary64)))) (neg.f64 (+.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 eps eps)))) (-.f64 #s(literal 1 binary64) (.f64 #s(literal -1 binary64) (cos.f64 eps))))))
(/.f64 (neg.f64 (+.f64 #s(literal -1 binary64) (pow.f64 (cos.f64 eps) #s(literal 3 binary64)))) (neg.f64 (+.f64 #s(literal 1 binary64) (-.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 eps eps)))) (.f64 #s(literal -1 binary64) (cos.f64 eps))))))
(/.f64 (neg.f64 (neg.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 eps eps)))))) (neg.f64 (+.f64 (cos.f64 eps) #s(literal 1 binary64))))
(/.f64 (-.f64 (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 eps eps)))) (+.f64 (cos.f64 eps) #s(literal 1 binary64))) (.f64 (+.f64 (cos.f64 eps) #s(literal 1 binary64)) #s(literal 1 binary64))) (.f64 (+.f64 (cos.f64 eps) #s(literal 1 binary64)) (+.f64 (cos.f64 eps) #s(literal 1 binary64))))
(/.f64 (.f64 (+.f64 (pow.f64 (cos.f64 eps) #s(literal 9 binary64)) #s(literal -1 binary64)) #s(literal 1 binary64)) (.f64 (+.f64 (pow.f64 (cos.f64 eps) #s(literal 6 binary64)) (-.f64 #s(literal 1 binary64) (.f64 #s(literal -1 binary64) (pow.f64 (cos.f64 eps) #s(literal 3 binary64))))) (+.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 eps eps)))) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -1 binary64) (cos.f64 eps))))))
(/.f64 (.f64 (-.f64 (pow.f64 (cos.f64 eps) #s(literal 6 binary64)) #s(literal 1 binary64)) #s(literal 1 binary64)) (.f64 (-.f64 (pow.f64 (cos.f64 eps) #s(literal 3 binary64)) #s(literal -1 binary64)) (+.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 eps eps)))) (-.f64 #s(literal 1 binary64) (.f64 #s(literal -1 binary64) (cos.f64 eps))))))
(/.f64 (.f64 (-.f64 (pow.f64 (cos.f64 eps) #s(literal 6 binary64)) #s(literal 1 binary64)) #s(literal 1 binary64)) (.f64 (+.f64 (pow.f64 (cos.f64 eps) #s(literal 4 binary64)) (+.f64 #s(literal 1 binary64) (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 eps eps)))) #s(literal 1 binary64)))) (+.f64 (cos.f64 eps) #s(literal 1 binary64))))
(/.f64 (.f64 (-.f64 (pow.f64 (cos.f64 eps) #s(literal 4 binary64)) #s(literal 1 binary64)) #s(literal 1 binary64)) (.f64 (+.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 eps eps)))) #s(literal 1 binary64)) (+.f64 (cos.f64 eps) #s(literal 1 binary64))))
(/.f64 (neg.f64 (neg.f64 (+.f64 #s(literal -1 binary64) (pow.f64 (cos.f64 eps) #s(literal 3 binary64))))) (neg.f64 (neg.f64 (+.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 eps eps)))) (-.f64 #s(literal 1 binary64) (.f64 #s(literal -1 binary64) (cos.f64 eps)))))))
(/.f64 (neg.f64 (neg.f64 (neg.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 eps eps))))))) (neg.f64 (neg.f64 (+.f64 (cos.f64 eps) #s(literal 1 binary64)))))
(pow.f64 (/.f64 (+.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 eps eps)))) (-.f64 #s(literal 1 binary64) (.f64 #s(literal -1 binary64) (cos.f64 eps)))) (+.f64 #s(literal -1 binary64) (pow.f64 (cos.f64 eps) #s(literal 3 binary64)))) #s(literal -1 binary64))
(pow.f64 (/.f64 (+.f64 (cos.f64 eps) #s(literal 1 binary64)) (neg.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 eps eps)))))) #s(literal -1 binary64))
(.f64 (+.f64 #s(literal -1 binary64) (pow.f64 (cos.f64 eps) #s(literal 3 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 eps eps)))) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -1 binary64) (cos.f64 eps))))))
(.f64 (neg.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 eps eps))))) (/.f64 #s(literal 1 binary64) (+.f64 (cos.f64 eps) #s(literal 1 binary64))))
(+.f64 (*.f64 (cos.f64 x) (cos.f64 eps)) (neg.f64 (cos.f64 x)))
(+.f64 (neg.f64 (cos.f64 x)) (*.f64 (cos.f64 x) (cos.f64 eps)))
(-.f64 (/.f64 (pow.f64 (.f64 (cos.f64 x) (cos.f64 eps)) #s(literal 2 binary64)) (-.f64 (.f64 (cos.f64 x) (cos.f64 eps)) (neg.f64 (cos.f64 x)))) (/.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (-.f64 (.f64 (cos.f64 x) (cos.f64 eps)) (neg.f64 (cos.f64 x)))))
(fma.f64 #s(literal -1 binary64) (cos.f64 x) (*.f64 (cos.f64 x) (cos.f64 eps)))
(fma.f64 (cos.f64 x) #s(literal -1 binary64) (*.f64 (cos.f64 x) (cos.f64 eps)))
(fma.f64 (cos.f64 x) (cos.f64 eps) (neg.f64 (cos.f64 x)))
(fma.f64 (cos.f64 eps) (cos.f64 x) (neg.f64 (cos.f64 x)))
(/.f64 (+.f64 (pow.f64 (.f64 (cos.f64 x) (cos.f64 eps)) #s(literal 3 binary64)) (neg.f64 (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) (+.f64 (pow.f64 (.f64 (cos.f64 x) (cos.f64 eps)) #s(literal 2 binary64)) (-.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (.f64 (*.f64 (cos.f64 x) (cos.f64 eps)) (neg.f64 (cos.f64 x))))))
(/.f64 (-.f64 (pow.f64 (.f64 (cos.f64 x) (cos.f64 eps)) #s(literal 2 binary64)) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))) (-.f64 (*.f64 (cos.f64 x) (cos.f64 eps)) (neg.f64 (cos.f64 x))))
(/.f64 (.f64 (cos.f64 x) (+.f64 #s(literal -1 binary64) (pow.f64 (cos.f64 eps) #s(literal 3 binary64)))) (+.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 eps eps)))) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -1 binary64) (cos.f64 eps)))))
(/.f64 (.f64 (cos.f64 x) (neg.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 eps eps)))))) (+.f64 (cos.f64 eps) #s(literal 1 binary64)))
(/.f64 (.f64 (+.f64 #s(literal -1 binary64) (pow.f64 (cos.f64 eps) #s(literal 3 binary64))) (cos.f64 x)) (+.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 eps eps)))) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -1 binary64) (cos.f64 eps)))))
(/.f64 (.f64 (neg.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 eps eps))))) (cos.f64 x)) (+.f64 (cos.f64 eps) #s(literal 1 binary64)))
(/.f64 (neg.f64 (+.f64 (pow.f64 (.f64 (cos.f64 x) (cos.f64 eps)) #s(literal 3 binary64)) (neg.f64 (pow.f64 (cos.f64 x) #s(literal 3 binary64))))) (neg.f64 (+.f64 (pow.f64 (.f64 (cos.f64 x) (cos.f64 eps)) #s(literal 2 binary64)) (-.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (.f64 (*.f64 (cos.f64 x) (cos.f64 eps)) (neg.f64 (cos.f64 x)))))))
(/.f64 (neg.f64 (-.f64 (pow.f64 (.f64 (cos.f64 x) (cos.f64 eps)) #s(literal 2 binary64)) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))))) (neg.f64 (-.f64 (*.f64 (cos.f64 x) (cos.f64 eps)) (neg.f64 (cos.f64 x)))))
(/.f64 (neg.f64 (.f64 (cos.f64 x) (+.f64 #s(literal -1 binary64) (pow.f64 (cos.f64 eps) #s(literal 3 binary64))))) (neg.f64 (+.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 eps eps)))) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -1 binary64) (cos.f64 eps))))))
(/.f64 (neg.f64 (.f64 (cos.f64 x) (neg.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 eps eps))))))) (neg.f64 (+.f64 (cos.f64 eps) #s(literal 1 binary64))))
(/.f64 (neg.f64 (.f64 (+.f64 #s(literal -1 binary64) (pow.f64 (cos.f64 eps) #s(literal 3 binary64))) (cos.f64 x))) (neg.f64 (+.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 eps eps)))) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -1 binary64) (cos.f64 eps))))))
(/.f64 (neg.f64 (.f64 (neg.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 eps eps))))) (cos.f64 x))) (neg.f64 (+.f64 (cos.f64 eps) #s(literal 1 binary64))))
(/.f64 (+.f64 (neg.f64 (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (pow.f64 (.f64 (cos.f64 x) (cos.f64 eps)) #s(literal 3 binary64))) (+.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (-.f64 (pow.f64 (.f64 (cos.f64 x) (cos.f64 eps)) #s(literal 2 binary64)) (.f64 (neg.f64 (cos.f64 x)) (*.f64 (cos.f64 x) (cos.f64 eps))))))
(*.f64 (cos.f64 x) (+.f64 #s(literal -1 binary64) (cos.f64 eps)))
(*.f64 (+.f64 #s(literal -1 binary64) (cos.f64 eps)) (cos.f64 x))
(cos.f64 eps)

simplify446.0ms (2.5%)

Memory

0.8MiB live, 914.7MiB allocated

Algorithm

1×	egg-herbie

Rules

13 614×	`lower-fma.f64`
13 614×	`lower-fma.f32`
6 396×	`lower-*.f64`
6 396×	`lower-*.f32`
4 696×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	422	4073
1	1298	3982
2	3586	3906
0	8100	3640

Stop Event

1×	iter limit
1×	node limit

Counts

444 → 424

Calls

Call 1

Inputs
(* -1 (* eps (sin x)))
(* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))
(* eps (+ (* -1 (sin x)) (* eps (+ (* -2 (* eps (+ (* -1/16 (sin x)) (* -1/48 (sin x))))) (* -1/2 (cos x))))))
(* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* eps (+ (* -2 (+ (* -1/16 (sin x)) (* -1/48 (sin x)))) (* 1/24 (* eps (cos x)))))))))
(* -2 (* (sin (* 1/2 eps)) (sin (+ x (* 1/2 eps)))))
(* -2 (* (sin (* 1/2 eps)) (sin (+ x (* 1/2 eps)))))
(* -2 (* (sin (* 1/2 eps)) (sin (+ x (* 1/2 eps)))))
(* -2 (* (sin (* 1/2 eps)) (sin (+ x (* 1/2 eps)))))
(* -2 (* (sin (* 1/2 eps)) (sin (- x (* -1/2 eps)))))
(* -2 (* (sin (* 1/2 eps)) (sin (- x (* -1/2 eps)))))
(* -2 (* (sin (* 1/2 eps)) (sin (- x (* -1/2 eps)))))
(* -2 (* (sin (* 1/2 eps)) (sin (- x (* -1/2 eps)))))
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eps
eps
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x
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1
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eps
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(- (cos eps) 1)
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(- (cos eps) 1)
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(* (cos x) (- (cos eps) 1))
(* (cos x) (- (cos eps) 1))
(* (cos x) (- (cos eps) 1))
(* (cos x) (- (cos eps) 1))
(* (cos x) (- (cos eps) 1))
(* (cos x) (- (cos eps) 1))
(* (cos x) (- (cos eps) 1))
(* (cos x) (- (cos eps) 1))
(* -1/2 (* (pow eps 2) (cos x)))
(* (pow eps 2) (+ (* -1/2 (cos x)) (* 1/24 (* (pow eps 2) (cos x)))))
(* (pow eps 2) (+ (* -1/2 (cos x)) (* (pow eps 2) (+ (* -1/720 (* (pow eps 2) (cos x))) (* 1/24 (cos x))))))
(* (pow eps 2) (+ (* -1/2 (cos x)) (* (pow eps 2) (+ (* 1/24 (cos x)) (* (pow eps 2) (+ (* -1/720 (cos x)) (* 1/40320 (* (pow eps 2) (cos x)))))))))
(* (cos x) (- (cos eps) 1))
(* (cos x) (- (cos eps) 1))
(* (cos x) (- (cos eps) 1))
(* (cos x) (- (cos eps) 1))
(* (cos x) (- (cos eps) 1))
(* (cos x) (- (cos eps) 1))
(* (cos x) (- (cos eps) 1))
(* (cos x) (- (cos eps) 1))
1
(+ 1 (* -1/2 (pow eps 2)))
(+ 1 (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))
(+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2)))
(cos eps)
(cos eps)
(cos eps)
(cos eps)
(cos eps)
(cos eps)
(cos eps)
(cos eps)

Outputs
(* -1 (* eps (sin x)))
(neg.f64 (*.f64 eps (sin.f64 x)))
(* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))
(.f64 eps (-.f64 (.f64 #s(literal -1/2 binary64) (*.f64 eps (cos.f64 x))) (sin.f64 x)))
(* eps (+ (* -1 (sin x)) (* eps (+ (* -2 (* eps (+ (* -1/16 (sin x)) (* -1/48 (sin x))))) (* -1/2 (cos x))))))
(.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x)) (.f64 (sin.f64 x) (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)))))
(* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* eps (+ (* -2 (+ (* -1/16 (sin x)) (* -1/48 (sin x)))) (* 1/24 (* eps (cos x)))))))))
(.f64 eps (fma.f64 eps (fma.f64 eps (.f64 (sin.f64 x) #s(literal 1/6 binary64)) (.f64 (cos.f64 x) (fma.f64 #s(literal 1/24 binary64) (.f64 eps eps) #s(literal -1/2 binary64)))) (neg.f64 (sin.f64 x))))
(* -2 (* (sin (* 1/2 eps)) (sin (+ x (* 1/2 eps)))))
(.f64 (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (.f64 #s(literal -2 binary64) (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))))
(* -2 (* (sin (* 1/2 eps)) (sin (+ x (* 1/2 eps)))))
(.f64 (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (.f64 #s(literal -2 binary64) (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))))
(* -2 (* (sin (* 1/2 eps)) (sin (+ x (* 1/2 eps)))))
(.f64 (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (.f64 #s(literal -2 binary64) (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))))
(* -2 (* (sin (* 1/2 eps)) (sin (+ x (* 1/2 eps)))))
(.f64 (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (.f64 #s(literal -2 binary64) (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))))
(* -2 (* (sin (* 1/2 eps)) (sin (- x (* -1/2 eps)))))
(.f64 (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (.f64 #s(literal -2 binary64) (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))))
(* -2 (* (sin (* 1/2 eps)) (sin (- x (* -1/2 eps)))))
(.f64 (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (.f64 #s(literal -2 binary64) (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))))
(* -2 (* (sin (* 1/2 eps)) (sin (- x (* -1/2 eps)))))
(.f64 (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (.f64 #s(literal -2 binary64) (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))))
(* -2 (* (sin (* 1/2 eps)) (sin (- x (* -1/2 eps)))))
(.f64 (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (.f64 #s(literal -2 binary64) (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))))
(* -2 (pow (sin (* 1/2 eps)) 2))
(.f64 #s(literal -2 binary64) (pow.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64)))
(+ (* -2 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (* -2 (pow (sin (* 1/2 eps)) 2)))
(.f64 (.f64 #s(literal -2 binary64) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))) (fma.f64 x (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))))
(+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (pow (sin (* 1/2 eps)) 2)))))
(fma.f64 x (.f64 #s(literal -2 binary64) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 (.f64 eps #s(literal 1/2 binary64))))) (.f64 (pow.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64)) (fma.f64 x x #s(literal -2 binary64))))
(+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* 1/3 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (pow (sin (* 1/2 eps)) 2))))))
(fma.f64 x (fma.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 (.f64 eps #s(literal 1/2 binary64)))) (+.f64 #s(literal -2 binary64) (.f64 x (.f64 x #s(literal 1/3 binary64)))) (.f64 x (pow.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64)))) (.f64 #s(literal -2 binary64) (pow.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64))))
(* -2 (* (sin (* 1/2 eps)) (sin (+ x (* 1/2 eps)))))
(.f64 (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (.f64 #s(literal -2 binary64) (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))))
(* -2 (* (sin (* 1/2 eps)) (sin (+ x (* 1/2 eps)))))
(.f64 (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (.f64 #s(literal -2 binary64) (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))))
(* -2 (* (sin (* 1/2 eps)) (sin (+ x (* 1/2 eps)))))
(.f64 (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (.f64 #s(literal -2 binary64) (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))))
(* -2 (* (sin (* 1/2 eps)) (sin (+ x (* 1/2 eps)))))
(.f64 (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (.f64 #s(literal -2 binary64) (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))))
(* -2 (* (sin (* 1/2 eps)) (sin (- (* 1/2 eps) (* -1 x)))))
(.f64 (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (.f64 #s(literal -2 binary64) (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))))
(* -2 (* (sin (* 1/2 eps)) (sin (- (* 1/2 eps) (* -1 x)))))
(.f64 (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (.f64 #s(literal -2 binary64) (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))))
(* -2 (* (sin (* 1/2 eps)) (sin (- (* 1/2 eps) (* -1 x)))))
(.f64 (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (.f64 #s(literal -2 binary64) (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))))
(* -2 (* (sin (* 1/2 eps)) (sin (- (* 1/2 eps) (* -1 x)))))
(.f64 (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (.f64 #s(literal -2 binary64) (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))))
(* 1/2 (* eps (sin x)))
(.f64 (.f64 eps (sin.f64 x)) #s(literal 1/2 binary64))
(* eps (+ (* 1/4 (* eps (cos x))) (* 1/2 (sin x))))
(.f64 eps (fma.f64 eps (.f64 (cos.f64 x) #s(literal 1/4 binary64)) (*.f64 (sin.f64 x) #s(literal 1/2 binary64))))
(* eps (+ (* 1/2 (sin x)) (* eps (+ (* 1/4 (cos x)) (* eps (+ (* -1/16 (sin x)) (* -1/48 (sin x))))))))
(.f64 eps (fma.f64 eps (fma.f64 eps (.f64 (sin.f64 x) #s(literal -1/12 binary64)) (.f64 (cos.f64 x) #s(literal 1/4 binary64))) (.f64 (sin.f64 x) #s(literal 1/2 binary64))))
(* eps (+ (* 1/2 (sin x)) (* eps (+ (* 1/4 (cos x)) (* eps (+ (* -1/16 (sin x)) (+ (* -1/48 (sin x)) (* -1/48 (* eps (cos x))))))))))
(.f64 eps (fma.f64 eps (fma.f64 eps (fma.f64 eps (.f64 #s(literal -1/48 binary64) (cos.f64 x)) (.f64 (sin.f64 x) #s(literal -1/12 binary64))) (.f64 (cos.f64 x) #s(literal 1/4 binary64))) (*.f64 (sin.f64 x) #s(literal 1/2 binary64))))
(* (sin (* 1/2 eps)) (sin (+ x (* 1/2 eps))))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))
(* (sin (* 1/2 eps)) (sin (+ x (* 1/2 eps))))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))
(* (sin (* 1/2 eps)) (sin (+ x (* 1/2 eps))))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))
(* (sin (* 1/2 eps)) (sin (+ x (* 1/2 eps))))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))
(* (sin (* 1/2 eps)) (sin (- x (* -1/2 eps))))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))
(* (sin (* 1/2 eps)) (sin (- x (* -1/2 eps))))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))
(* (sin (* 1/2 eps)) (sin (- x (* -1/2 eps))))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))
(* (sin (* 1/2 eps)) (sin (- x (* -1/2 eps))))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))
(pow (sin (* 1/2 eps)) 2)
(pow.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64))
(+ (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (pow (sin (* 1/2 eps)) 2))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (fma.f64 x (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))))
(+ (* x (+ (* -1/2 (* x (pow (sin (* 1/2 eps)) 2))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (pow (sin (* 1/2 eps)) 2))
(fma.f64 (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) (pow.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64)) (.f64 x (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 (.f64 eps #s(literal 1/2 binary64))))))
(+ (* x (+ (* x (+ (* -1/2 (pow (sin (* 1/2 eps)) 2)) (* -1/6 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (pow (sin (* 1/2 eps)) 2))
(fma.f64 x (fma.f64 x (.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64))) (.f64 (fma.f64 x (.f64 x #s(literal -1/6 binary64)) #s(literal 1 binary64)) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 (.f64 eps #s(literal 1/2 binary64)))))) (pow.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64)))
(* (sin (* 1/2 eps)) (sin (+ x (* 1/2 eps))))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))
(* (sin (* 1/2 eps)) (sin (+ x (* 1/2 eps))))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))
(* (sin (* 1/2 eps)) (sin (+ x (* 1/2 eps))))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))
(* (sin (* 1/2 eps)) (sin (+ x (* 1/2 eps))))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))
(* (sin (* 1/2 eps)) (sin (- (* 1/2 eps) (* -1 x))))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))
(* (sin (* 1/2 eps)) (sin (- (* 1/2 eps) (* -1 x))))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))
(* (sin (* 1/2 eps)) (sin (- (* 1/2 eps) (* -1 x))))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))
(* (sin (* 1/2 eps)) (sin (- (* 1/2 eps) (* -1 x))))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))
(* 1/2 eps)
(*.f64 eps #s(literal 1/2 binary64))
(* eps (+ 1/2 (* -1/48 (pow eps 2))))
(.f64 eps (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)))
(* eps (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))
(.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 eps (*.f64 eps #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))
(* eps (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))
(.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))
(sin (* 1/2 eps))
(sin.f64 (*.f64 eps #s(literal 1/2 binary64)))
(sin (* 1/2 eps))
(sin.f64 (*.f64 eps #s(literal 1/2 binary64)))
(sin (* 1/2 eps))
(sin.f64 (*.f64 eps #s(literal 1/2 binary64)))
(sin (* 1/2 eps))
(sin.f64 (*.f64 eps #s(literal 1/2 binary64)))
(sin (* 1/2 eps))
(sin.f64 (*.f64 eps #s(literal 1/2 binary64)))
(sin (* 1/2 eps))
(sin.f64 (*.f64 eps #s(literal 1/2 binary64)))
(sin (* 1/2 eps))
(sin.f64 (*.f64 eps #s(literal 1/2 binary64)))
(sin (* 1/2 eps))
(sin.f64 (*.f64 eps #s(literal 1/2 binary64)))
(* 1/2 eps)
(*.f64 eps #s(literal 1/2 binary64))
(* 1/2 eps)
(*.f64 eps #s(literal 1/2 binary64))
(* 1/2 eps)
(*.f64 eps #s(literal 1/2 binary64))
(* 1/2 eps)
(*.f64 eps #s(literal 1/2 binary64))
(* 1/2 eps)
(*.f64 eps #s(literal 1/2 binary64))
(* 1/2 eps)
(*.f64 eps #s(literal 1/2 binary64))
(* 1/2 eps)
(*.f64 eps #s(literal 1/2 binary64))
(* 1/2 eps)
(*.f64 eps #s(literal 1/2 binary64))
(* 1/2 eps)
(*.f64 eps #s(literal 1/2 binary64))
(* 1/2 eps)
(*.f64 eps #s(literal 1/2 binary64))
(* 1/2 eps)
(*.f64 eps #s(literal 1/2 binary64))
(* 1/2 eps)
(*.f64 eps #s(literal 1/2 binary64))
(* -1 (* eps (sin x)))
(neg.f64 (*.f64 eps (sin.f64 x)))
(* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))
(.f64 eps (-.f64 (.f64 #s(literal -1/2 binary64) (*.f64 eps (cos.f64 x))) (sin.f64 x)))
(* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))
(.f64 eps (-.f64 (.f64 #s(literal -1/2 binary64) (*.f64 eps (cos.f64 x))) (sin.f64 x)))
(* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))
(.f64 eps (-.f64 (.f64 #s(literal -1/2 binary64) (*.f64 eps (cos.f64 x))) (sin.f64 x)))
(* -1/2 (* (pow eps 2) (cos x)))
(.f64 (cos.f64 x) (.f64 eps (*.f64 eps #s(literal -1/2 binary64))))
(* (pow eps 2) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))
(.f64 eps (neg.f64 (.f64 eps (fma.f64 (cos.f64 x) #s(literal 1/2 binary64) (/.f64 (sin.f64 x) eps)))))
(* (pow eps 2) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))
(.f64 eps (neg.f64 (.f64 eps (fma.f64 (cos.f64 x) #s(literal 1/2 binary64) (/.f64 (sin.f64 x) eps)))))
(* (pow eps 2) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))
(.f64 eps (neg.f64 (.f64 eps (fma.f64 (cos.f64 x) #s(literal 1/2 binary64) (/.f64 (sin.f64 x) eps)))))
(* -1/2 (* (pow eps 2) (cos x)))
(.f64 (cos.f64 x) (.f64 eps (*.f64 eps #s(literal -1/2 binary64))))
(* (pow eps 2) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))
(.f64 eps (neg.f64 (.f64 eps (fma.f64 (cos.f64 x) #s(literal 1/2 binary64) (/.f64 (sin.f64 x) eps)))))
(* (pow eps 2) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))
(.f64 eps (neg.f64 (.f64 eps (fma.f64 (cos.f64 x) #s(literal 1/2 binary64) (/.f64 (sin.f64 x) eps)))))
(* (pow eps 2) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))
(.f64 eps (neg.f64 (.f64 eps (fma.f64 (cos.f64 x) #s(literal 1/2 binary64) (/.f64 (sin.f64 x) eps)))))
(* -1/2 (pow eps 2))
(.f64 eps (.f64 eps #s(literal -1/2 binary64)))
(+ (* -1 (* eps x)) (* -1/2 (pow eps 2)))
(.f64 eps (-.f64 (.f64 eps #s(literal -1/2 binary64)) x))
(+ (* -1/2 (pow eps 2)) (* x (+ (* -1 eps) (* 1/4 (* (pow eps 2) x)))))
(fma.f64 x (fma.f64 x (.f64 #s(literal 1/4 binary64) (.f64 eps eps)) (neg.f64 eps)) (.f64 eps (.f64 eps #s(literal -1/2 binary64))))
(+ (* -1/2 (pow eps 2)) (* x (+ (* -1 eps) (* x (+ (* 1/6 (* eps x)) (* 1/4 (pow eps 2)))))))
(fma.f64 eps (-.f64 (.f64 eps #s(literal -1/2 binary64)) x) (.f64 x (.f64 x (.f64 eps (fma.f64 eps #s(literal 1/4 binary64) (*.f64 x #s(literal 1/6 binary64)))))))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(.f64 eps (-.f64 (.f64 #s(literal -1/2 binary64) (*.f64 eps (cos.f64 x))) (sin.f64 x)))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(.f64 eps (-.f64 (.f64 #s(literal -1/2 binary64) (*.f64 eps (cos.f64 x))) (sin.f64 x)))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(.f64 eps (-.f64 (.f64 #s(literal -1/2 binary64) (*.f64 eps (cos.f64 x))) (sin.f64 x)))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(.f64 eps (-.f64 (.f64 #s(literal -1/2 binary64) (*.f64 eps (cos.f64 x))) (sin.f64 x)))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(.f64 eps (-.f64 (.f64 #s(literal -1/2 binary64) (*.f64 eps (cos.f64 x))) (sin.f64 x)))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(.f64 eps (-.f64 (.f64 #s(literal -1/2 binary64) (*.f64 eps (cos.f64 x))) (sin.f64 x)))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(.f64 eps (-.f64 (.f64 #s(literal -1/2 binary64) (*.f64 eps (cos.f64 x))) (sin.f64 x)))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(.f64 eps (-.f64 (.f64 #s(literal -1/2 binary64) (*.f64 eps (cos.f64 x))) (sin.f64 x)))
(* -1 (sin x))
(neg.f64 (sin.f64 x))
(- (* -1/2 (* eps (cos x))) (sin x))
(-.f64 (.f64 #s(literal -1/2 binary64) (.f64 eps (cos.f64 x))) (sin.f64 x))
(- (* -1/2 (* eps (cos x))) (sin x))
(-.f64 (.f64 #s(literal -1/2 binary64) (.f64 eps (cos.f64 x))) (sin.f64 x))
(- (* -1/2 (* eps (cos x))) (sin x))
(-.f64 (.f64 #s(literal -1/2 binary64) (.f64 eps (cos.f64 x))) (sin.f64 x))
(* -1/2 (* eps (cos x)))
(.f64 #s(literal -1/2 binary64) (.f64 eps (cos.f64 x)))
(* eps (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))
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(* 2 x)
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(+ eps (* 2 x))
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eps
(* eps (+ 1 (* 2 (/ x eps))))
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(fma.f64 eps (/.f64 (*.f64 x #s(literal 2 binary64)) eps) eps)
(* eps (+ 1 (* 2 (/ x eps))))
(fma.f64 eps (/.f64 (*.f64 x #s(literal 2 binary64)) eps) eps)
eps
(* -1 (* eps (- (* -2 (/ x eps)) 1)))
(fma.f64 eps (/.f64 (*.f64 x #s(literal 2 binary64)) eps) eps)
(* -1 (* eps (- (* -2 (/ x eps)) 1)))
(fma.f64 eps (/.f64 (*.f64 x #s(literal 2 binary64)) eps) eps)
(* -1 (* eps (- (* -2 (/ x eps)) 1)))
(fma.f64 eps (/.f64 (*.f64 x #s(literal 2 binary64)) eps) eps)
(* -1/2 (pow eps 2))
(.f64 eps (.f64 eps #s(literal -1/2 binary64)))
(* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))
(.f64 eps (.f64 eps (fma.f64 #s(literal 1/24 binary64) (*.f64 eps eps) #s(literal -1/2 binary64))))
(* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2))
(.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps (fma.f64 (.f64 eps eps) #s(literal -1/720 binary64) #s(literal 1/24 binary64))) #s(literal -1/2 binary64)))
(* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* (pow eps 2) (- (* 1/40320 (pow eps 2)) 1/720)))) 1/2))
(.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps (fma.f64 (*.f64 eps eps) #s(literal 1/40320 binary64) #s(literal -1/720 binary64))) #s(literal 1/24 binary64)) #s(literal -1/2 binary64)))
(- (cos eps) 1)
(+.f64 #s(literal -1 binary64) (cos.f64 eps))
(- (cos eps) 1)
(+.f64 #s(literal -1 binary64) (cos.f64 eps))
(- (cos eps) 1)
(+.f64 #s(literal -1 binary64) (cos.f64 eps))
(- (cos eps) 1)
(+.f64 #s(literal -1 binary64) (cos.f64 eps))
(- (cos eps) 1)
(+.f64 #s(literal -1 binary64) (cos.f64 eps))
(- (cos eps) 1)
(+.f64 #s(literal -1 binary64) (cos.f64 eps))
(- (cos eps) 1)
(+.f64 #s(literal -1 binary64) (cos.f64 eps))
(- (cos eps) 1)
(+.f64 #s(literal -1 binary64) (cos.f64 eps))
(- (cos eps) 1)
(+.f64 #s(literal -1 binary64) (cos.f64 eps))
(- (+ (cos eps) (* -1/2 (* (pow x 2) (- (cos eps) 1)))) 1)
(.f64 (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) (+.f64 #s(literal -1 binary64) (cos.f64 eps)))
(- (+ (cos eps) (* (pow x 2) (+ (* -1/2 (- (cos eps) 1)) (* 1/24 (* (pow x 2) (- (cos eps) 1)))))) 1)
(+.f64 (cos.f64 eps) (fma.f64 (+.f64 #s(literal -1 binary64) (cos.f64 eps)) (.f64 x (.f64 x (fma.f64 x (*.f64 x #s(literal 1/24 binary64)) #s(literal -1/2 binary64)))) #s(literal -1 binary64)))
(- (+ (cos eps) (* (pow x 2) (+ (* -1/2 (- (cos eps) 1)) (* (pow x 2) (+ (* -1/720 (* (pow x 2) (- (cos eps) 1))) (* 1/24 (- (cos eps) 1))))))) 1)
(fma.f64 x (.f64 x (.f64 (.f64 x (fma.f64 x (cos.f64 eps) (neg.f64 x))) (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)))) (.f64 (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) (+.f64 #s(literal -1 binary64) (cos.f64 eps))))
(* (cos x) (- (cos eps) 1))
(*.f64 (cos.f64 x) (+.f64 #s(literal -1 binary64) (cos.f64 eps)))
(* (cos x) (- (cos eps) 1))
(*.f64 (cos.f64 x) (+.f64 #s(literal -1 binary64) (cos.f64 eps)))
(* (cos x) (- (cos eps) 1))
(*.f64 (cos.f64 x) (+.f64 #s(literal -1 binary64) (cos.f64 eps)))
(* (cos x) (- (cos eps) 1))
(*.f64 (cos.f64 x) (+.f64 #s(literal -1 binary64) (cos.f64 eps)))
(* (cos x) (- (cos eps) 1))
(*.f64 (cos.f64 x) (+.f64 #s(literal -1 binary64) (cos.f64 eps)))
(* (cos x) (- (cos eps) 1))
(*.f64 (cos.f64 x) (+.f64 #s(literal -1 binary64) (cos.f64 eps)))
(* (cos x) (- (cos eps) 1))
(*.f64 (cos.f64 x) (+.f64 #s(literal -1 binary64) (cos.f64 eps)))
(* (cos x) (- (cos eps) 1))
(*.f64 (cos.f64 x) (+.f64 #s(literal -1 binary64) (cos.f64 eps)))
(* -1/2 (* (pow eps 2) (cos x)))
(.f64 (cos.f64 x) (.f64 eps (*.f64 eps #s(literal -1/2 binary64))))
(* (pow eps 2) (+ (* -1/2 (cos x)) (* 1/24 (* (pow eps 2) (cos x)))))
(.f64 (.f64 eps eps) (.f64 (cos.f64 x) (fma.f64 #s(literal 1/24 binary64) (.f64 eps eps) #s(literal -1/2 binary64))))
(* (pow eps 2) (+ (* -1/2 (cos x)) (* (pow eps 2) (+ (* -1/720 (* (pow eps 2) (cos x))) (* 1/24 (cos x))))))
(.f64 (.f64 eps eps) (fma.f64 #s(literal -1/2 binary64) (cos.f64 x) (.f64 (cos.f64 x) (.f64 eps (.f64 eps (fma.f64 (.f64 eps eps) #s(literal -1/720 binary64) #s(literal 1/24 binary64)))))))
(* (pow eps 2) (+ (* -1/2 (cos x)) (* (pow eps 2) (+ (* 1/24 (cos x)) (* (pow eps 2) (+ (* -1/720 (cos x)) (* 1/40320 (* (pow eps 2) (cos x)))))))))
(.f64 (.f64 eps eps) (fma.f64 (cos.f64 x) (fma.f64 #s(literal 1/24 binary64) (.f64 eps eps) #s(literal -1/2 binary64)) (.f64 (.f64 (cos.f64 x) (fma.f64 (.f64 eps eps) #s(literal 1/40320 binary64) #s(literal -1/720 binary64))) (.f64 (.f64 eps eps) (*.f64 eps eps)))))
(* (cos x) (- (cos eps) 1))
(*.f64 (cos.f64 x) (+.f64 #s(literal -1 binary64) (cos.f64 eps)))
(* (cos x) (- (cos eps) 1))
(*.f64 (cos.f64 x) (+.f64 #s(literal -1 binary64) (cos.f64 eps)))
(* (cos x) (- (cos eps) 1))
(*.f64 (cos.f64 x) (+.f64 #s(literal -1 binary64) (cos.f64 eps)))
(* (cos x) (- (cos eps) 1))
(*.f64 (cos.f64 x) (+.f64 #s(literal -1 binary64) (cos.f64 eps)))
(* (cos x) (- (cos eps) 1))
(*.f64 (cos.f64 x) (+.f64 #s(literal -1 binary64) (cos.f64 eps)))
(* (cos x) (- (cos eps) 1))
(*.f64 (cos.f64 x) (+.f64 #s(literal -1 binary64) (cos.f64 eps)))
(* (cos x) (- (cos eps) 1))
(*.f64 (cos.f64 x) (+.f64 #s(literal -1 binary64) (cos.f64 eps)))
(* (cos x) (- (cos eps) 1))
(*.f64 (cos.f64 x) (+.f64 #s(literal -1 binary64) (cos.f64 eps)))
1
#s(literal 1 binary64)
(+ 1 (* -1/2 (pow eps 2)))
(fma.f64 eps (*.f64 eps #s(literal -1/2 binary64)) #s(literal 1 binary64))
(+ 1 (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))
(fma.f64 eps (.f64 eps (fma.f64 #s(literal 1/24 binary64) (.f64 eps eps) #s(literal -1/2 binary64))) #s(literal 1 binary64))
(+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2)))
(fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps (fma.f64 (*.f64 eps eps) #s(literal -1/720 binary64) #s(literal 1/24 binary64))) #s(literal -1/2 binary64)) #s(literal 1 binary64))
(cos eps)
(cos.f64 eps)
(cos eps)
(cos.f64 eps)
(cos eps)
(cos.f64 eps)
(cos eps)
(cos.f64 eps)
(cos eps)
(cos.f64 eps)
(cos eps)
(cos.f64 eps)
(cos eps)
(cos.f64 eps)
(cos eps)
(cos.f64 eps)

eval116.0ms (0.6%)

Memory: 12.4MiB live, 297.8MiB allocated
Compiler: Compiled 19 847 to 2 333 computations (88.2% saved)

prune83.0ms (0.5%)

Memory

-24.6MiB live, 214.9MiB allocated

Pruning

28 alts after pruning (23 fresh and 5 done)

	Pruned	Kept	Total
New	856	15	871
Fresh	11	8	19
Picked	2	3	5
Done	1	2	3
Total	870	28	898

Accuracy

100.0%

Counts

898 → 28

Alt Table

Click to see full alt table

Status	Accuracy	Program
	80.4%	(fma.f64 (sin.f64 x) (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps #s(literal -1/120 binary64)) #s(literal 1/6 binary64)) #s(literal -1 binary64))) (.f64 (cos.f64 x) (+.f64 (cos.f64 eps) #s(literal -1 binary64))))
	80.4%	(fma.f64 (sin.f64 x) (neg.f64 (fma.f64 (fma.f64 eps (.f64 eps #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) (.f64 eps (.f64 eps eps)) eps)) (.f64 (cos.f64 x) (+.f64 (cos.f64 eps) #s(literal -1 binary64))))
✓	80.9%	(fma.f64 (sin.f64 x) (neg.f64 (sin.f64 eps)) (*.f64 (cos.f64 x) (+.f64 (cos.f64 eps) #s(literal -1 binary64))))
	99.5%	(fma.f64 (sin.f64 x) (neg.f64 (sin.f64 eps)) (.f64 (cos.f64 x) (.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps (fma.f64 (.f64 eps eps) #s(literal 1/40320 binary64) #s(literal -1/720 binary64))) #s(literal 1/24 binary64)) #s(literal -1/2 binary64)))))
	99.4%	(fma.f64 (sin.f64 x) (neg.f64 (sin.f64 eps)) (.f64 (cos.f64 x) (.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps (fma.f64 (*.f64 eps eps) #s(literal -1/720 binary64) #s(literal 1/24 binary64))) #s(literal -1/2 binary64)))))
▶	97.2%	(fma.f64 x (fma.f64 x (.f64 #s(literal 1/4 binary64) (.f64 eps eps)) (neg.f64 eps)) (.f64 eps (.f64 eps #s(literal -1/2 binary64))))
	97.5%	(fma.f64 eps (-.f64 (.f64 eps #s(literal -1/2 binary64)) x) (.f64 x (.f64 x (.f64 eps (fma.f64 eps #s(literal 1/4 binary64) (*.f64 x #s(literal 1/6 binary64)))))))
	81.0%	(-.f64 (-.f64 (.f64 (cos.f64 eps) (cos.f64 x)) (cos.f64 x)) (.f64 (sin.f64 x) (sin.f64 eps)))
✓	54.8%	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
	53.1%	(-.f64 (cos.f64 (+.f64 x eps)) #s(literal 1 binary64))
✓	53.1%	(+.f64 (cos.f64 eps) #s(literal -1 binary64))
	99.3%	(.f64 (.f64 (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64))) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) #s(literal -2 binary64))
	99.2%	(.f64 (.f64 (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 eps (*.f64 eps #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64))) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) #s(literal -2 binary64))
	99.1%	(.f64 (.f64 (.f64 eps (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64))) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) #s(literal -2 binary64))
▶	98.9%	(.f64 (.f64 (*.f64 eps #s(literal 1/2 binary64)) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) #s(literal -2 binary64))
▶	99.6%	(.f64 (.f64 (sin.f64 (/.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) eps))) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) #s(literal -2 binary64))
	22.0%	(.f64 (.f64 (sin.f64 (.f64 (fma.f64 (fma.f64 x (.f64 x x) (.f64 eps (.f64 eps eps))) (/.f64 #s(literal 1 binary64) (fma.f64 eps (-.f64 eps x) (.f64 x x))) (neg.f64 x)) #s(literal 1/2 binary64))) (sin.f64 (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)))) #s(literal -2 binary64))
▶	81.4%	(.f64 (.f64 (sin.f64 (.f64 (fma.f64 (.f64 (+.f64 x eps) (-.f64 x eps)) (/.f64 #s(literal 1 binary64) (-.f64 x eps)) (neg.f64 x)) #s(literal 1/2 binary64))) (sin.f64 (*.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)))) #s(literal -2 binary64))
	99.6%	(.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)))) #s(literal -2 binary64))
✓	99.7%	(.f64 (.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) #s(literal -2 binary64))
	79.9%	(*.f64 (sin.f64 x) (neg.f64 eps))
	97.5%	(.f64 eps (fma.f64 x (fma.f64 x (fma.f64 eps #s(literal 1/4 binary64) (.f64 x #s(literal 1/6 binary64))) #s(literal -1 binary64)) (*.f64 eps #s(literal -1/2 binary64))))
✓	98.9%	(.f64 eps (-.f64 (.f64 eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x)))
	98.6%	(.f64 eps (-.f64 (.f64 eps #s(literal -1/2 binary64)) (sin.f64 x)))
	97.2%	(.f64 eps (-.f64 (.f64 eps #s(literal -1/2 binary64)) x))
	54.4%	(.f64 eps (.f64 eps #s(literal -1/2 binary64)))
	52.3%	(.f64 #s(literal 1/2 binary64) (.f64 x x))
▶	53.0%	#s(literal 0 binary64)

Compiler

Compiled 891 to 573 computations (35.7% saved)

simplify215.0ms (1.2%)

Memory

20.0MiB live, 375.8MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 16 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(.f64 (sin.f64 (.f64 (fma.f64 (.f64 (+.f64 x eps) (-.f64 x eps)) (/.f64 #s(literal 1 binary64) (-.f64 x eps)) (neg.f64 x)) #s(literal 1/2 binary64))) (sin.f64 (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64))))
✓	cost-diff	0	(.f64 (.f64 (sin.f64 (.f64 (fma.f64 (.f64 (+.f64 x eps) (-.f64 x eps)) (/.f64 #s(literal 1 binary64) (-.f64 x eps)) (neg.f64 x)) #s(literal 1/2 binary64))) (sin.f64 (*.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)))) #s(literal -2 binary64))
✓	cost-diff	320	(*.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64))
✓	cost-diff	2112	(fma.f64 (*.f64 (+.f64 x eps) (-.f64 x eps)) (/.f64 #s(literal 1 binary64) (-.f64 x eps)) (neg.f64 x))
✓	cost-diff	0	(sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
✓	cost-diff	0	(*.f64 eps #s(literal 1/2 binary64))
✓	cost-diff	0	(.f64 (.f64 eps #s(literal 1/2 binary64)) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))
✓	cost-diff	512	(.f64 (.f64 (*.f64 eps #s(literal 1/2 binary64)) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) #s(literal -2 binary64))
✓	cost-diff	0	(*.f64 eps eps)
✓	cost-diff	0	(.f64 #s(literal 1/4 binary64) (.f64 eps eps))
✓	cost-diff	128	(fma.f64 x (.f64 #s(literal 1/4 binary64) (.f64 eps eps)) (neg.f64 eps))
✓	cost-diff	512	(fma.f64 x (fma.f64 x (.f64 #s(literal 1/4 binary64) (.f64 eps eps)) (neg.f64 eps)) (.f64 eps (.f64 eps #s(literal -1/2 binary64))))
✓	cost-diff	0	(sin.f64 (/.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) eps)))
✓	cost-diff	0	(*.f64 (sin.f64 (/.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) eps))) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))
✓	cost-diff	0	(.f64 (.f64 (sin.f64 (/.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) eps))) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) #s(literal -2 binary64))
✓	cost-diff	1088	(/.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) eps))

Rules

7 722×	`lower-fma.f32`
7 714×	`lower-fma.f64`
3 120×	`lower-*.f32`
3 098×	`lower-*.f64`
2 318×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	38	289
0	72	199
1	131	199
2	279	195
3	698	195
4	2723	193
5	6867	193
0	8118	190

Stop Event

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

Calls

Call 1

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

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

localize125.0ms (0.7%)

Memory

-21.1MiB live, 186.5MiB allocated

Localize:

Found 16 expressions of interest:

New	Metric	Score	Program
✓	accuracy	99.8%	(.f64 (sin.f64 (.f64 (fma.f64 (.f64 (+.f64 x eps) (-.f64 x eps)) (/.f64 #s(literal 1 binary64) (-.f64 x eps)) (neg.f64 x)) #s(literal 1/2 binary64))) (sin.f64 (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64))))
✓	accuracy	99.7%	(/.f64 #s(literal 1 binary64) (-.f64 x eps))
✓	accuracy	99.6%	(+.f64 x (+.f64 x eps))
✓	accuracy	36.4%	(fma.f64 (*.f64 (+.f64 x eps) (-.f64 x eps)) (/.f64 #s(literal 1 binary64) (-.f64 x eps)) (neg.f64 x))
✓	accuracy	100.0%	(*.f64 eps #s(literal 1/2 binary64))
✓	accuracy	100.0%	(.f64 (.f64 (*.f64 eps #s(literal 1/2 binary64)) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) #s(literal -2 binary64))
✓	accuracy	99.8%	(.f64 (.f64 eps #s(literal 1/2 binary64)) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))
✓	accuracy	99.8%	(sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
✓	accuracy	100.0%	(.f64 #s(literal 1/4 binary64) (.f64 eps eps))
✓	accuracy	100.0%	(neg.f64 eps)
✓	accuracy	100.0%	(fma.f64 x (.f64 #s(literal 1/4 binary64) (.f64 eps eps)) (neg.f64 eps))
✓	accuracy	100.0%	(fma.f64 x (fma.f64 x (.f64 #s(literal 1/4 binary64) (.f64 eps eps)) (neg.f64 eps)) (.f64 eps (.f64 eps #s(literal -1/2 binary64))))
✓	accuracy	100.0%	(.f64 (.f64 (sin.f64 (/.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) eps))) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) #s(literal -2 binary64))
✓	accuracy	99.8%	(sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
✓	accuracy	99.8%	(*.f64 (sin.f64 (/.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) eps))) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))
✓	accuracy	99.7%	(/.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) eps))

Samples

82.0ms	255×	0	valid
1.0ms	1×	3	valid

Compiler

Compiled 307 to 44 computations (85.7% saved)

Precisions

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

ival-mult: 39.0ms (63.1% of total)

ival-sin: 7.0ms (11.3% of total)

ival-div: 6.0ms (9.7% of total)

ival-add: 6.0ms (9.7% of total)

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

ival-sub: 1.0ms (1.6% of total)

exact: 1.0ms (1.6% of total)

adjust: 0.0ms (0% of total)

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

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

series33.0ms (0.2%)

Memory

-4.4MiB live, 73.2MiB allocated

Counts

19 → 384

Calls

Call 1

Inputs
#<alt (/.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) eps))>
#<alt (.f64 (.f64 (sin.f64 (/.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) eps))) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) #s(literal -2 binary64))>
#<alt (*.f64 (sin.f64 (/.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) eps))) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))>
#<alt (sin.f64 (/.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) eps)))>
#<alt (fma.f64 x (fma.f64 x (.f64 #s(literal 1/4 binary64) (.f64 eps eps)) (neg.f64 eps)) (.f64 eps (.f64 eps #s(literal -1/2 binary64))))>
#<alt (fma.f64 x (.f64 #s(literal 1/4 binary64) (.f64 eps eps)) (neg.f64 eps))>
#<alt (.f64 #s(literal 1/4 binary64) (.f64 eps eps))>
#<alt (*.f64 eps eps)>
#<alt (.f64 (.f64 (*.f64 eps #s(literal 1/2 binary64)) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) #s(literal -2 binary64))>
#<alt (.f64 (.f64 eps #s(literal 1/2 binary64)) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))>
#<alt (*.f64 eps #s(literal 1/2 binary64))>
#<alt (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))>
#<alt (fma.f64 (*.f64 (+.f64 x eps) (-.f64 x eps)) (/.f64 #s(literal 1 binary64) (-.f64 x eps)) (neg.f64 x))>
#<alt (*.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64))>
#<alt (.f64 (.f64 (sin.f64 (.f64 (fma.f64 (.f64 (+.f64 x eps) (-.f64 x eps)) (/.f64 #s(literal 1 binary64) (-.f64 x eps)) (neg.f64 x)) #s(literal 1/2 binary64))) (sin.f64 (*.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)))) #s(literal -2 binary64))>
#<alt (.f64 (sin.f64 (.f64 (fma.f64 (.f64 (+.f64 x eps) (-.f64 x eps)) (/.f64 #s(literal 1 binary64) (-.f64 x eps)) (neg.f64 x)) #s(literal 1/2 binary64))) (sin.f64 (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64))))>
#<alt (neg.f64 eps)>
#<alt (+.f64 x (+.f64 x eps))>
#<alt (/.f64 #s(literal 1 binary64) (-.f64 x eps))>

Outputs
#<alt (* 1/2 eps)>
#<alt (* 1/2 eps)>
#<alt (* 1/2 eps)>
#<alt (* 1/2 eps)>
#<alt (* 1/2 eps)>
#<alt (* 1/2 eps)>
#<alt (* 1/2 eps)>
#<alt (* 1/2 eps)>
#<alt (* 1/2 eps)>
#<alt (* 1/2 eps)>
#<alt (* 1/2 eps)>
#<alt (* 1/2 eps)>
#<alt (* -1 (* eps (sin x)))>
#<alt (* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))>
#<alt (* eps (+ (* -1 (sin x)) (* eps (+ (* -2 (* eps (+ (* -1/16 (sin x)) (* -1/48 (sin x))))) (* -1/2 (cos x))))))>
#<alt (* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* eps (+ (* -2 (+ (* -1/16 (sin x)) (* -1/48 (sin x)))) (* 1/24 (* eps (cos x)))))))))>
#<alt (* -2 (* (sin (* 1/2 eps)) (sin (+ x (* 1/2 eps)))))>
#<alt (* -2 (* (sin (* 1/2 eps)) (sin (+ x (* 1/2 eps)))))>
#<alt (* -2 (* (sin (* 1/2 eps)) (sin (+ x (* 1/2 eps)))))>
#<alt (* -2 (* (sin (* 1/2 eps)) (sin (+ x (* 1/2 eps)))))>
#<alt (* -2 (* (sin (* 1/2 eps)) (sin (- x (* -1/2 eps)))))>
#<alt (* -2 (* (sin (* 1/2 eps)) (sin (- x (* -1/2 eps)))))>
#<alt (* -2 (* (sin (* 1/2 eps)) (sin (- x (* -1/2 eps)))))>
#<alt (* -2 (* (sin (* 1/2 eps)) (sin (- x (* -1/2 eps)))))>
#<alt (* -2 (pow (sin (* 1/2 eps)) 2))>
#<alt (+ (* -2 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (* -2 (pow (sin (* 1/2 eps)) 2)))>
#<alt (+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (pow (sin (* 1/2 eps)) 2)))))>
#<alt (+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* 1/3 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (pow (sin (* 1/2 eps)) 2))))))>
#<alt (* -2 (* (sin (* 1/2 eps)) (sin (+ x (* 1/2 eps)))))>
#<alt (* -2 (* (sin (* 1/2 eps)) (sin (+ x (* 1/2 eps)))))>
#<alt (* -2 (* (sin (* 1/2 eps)) (sin (+ x (* 1/2 eps)))))>
#<alt (* -2 (* (sin (* 1/2 eps)) (sin (+ x (* 1/2 eps)))))>
#<alt (* -2 (* (sin (* 1/2 eps)) (sin (- (* 1/2 eps) (* -1 x)))))>
#<alt (* -2 (* (sin (* 1/2 eps)) (sin (- (* 1/2 eps) (* -1 x)))))>
#<alt (* -2 (* (sin (* 1/2 eps)) (sin (- (* 1/2 eps) (* -1 x)))))>
#<alt (* -2 (* (sin (* 1/2 eps)) (sin (- (* 1/2 eps) (* -1 x)))))>
#<alt (* 1/2 (* eps (sin x)))>
#<alt (* eps (+ (* 1/4 (* eps (cos x))) (* 1/2 (sin x))))>
#<alt (* eps (+ (* 1/2 (sin x)) (* eps (+ (* 1/4 (cos x)) (* eps (+ (* -1/16 (sin x)) (* -1/48 (sin x))))))))>
#<alt (* eps (+ (* 1/2 (sin x)) (* eps (+ (* 1/4 (cos x)) (* eps (+ (* -1/16 (sin x)) (+ (* -1/48 (sin x)) (* -1/48 (* eps (cos x))))))))))>
#<alt (* (sin (* 1/2 eps)) (sin (+ x (* 1/2 eps))))>
#<alt (* (sin (* 1/2 eps)) (sin (+ x (* 1/2 eps))))>
#<alt (* (sin (* 1/2 eps)) (sin (+ x (* 1/2 eps))))>
#<alt (* (sin (* 1/2 eps)) (sin (+ x (* 1/2 eps))))>
#<alt (* (sin (* 1/2 eps)) (sin (- x (* -1/2 eps))))>
#<alt (* (sin (* 1/2 eps)) (sin (- x (* -1/2 eps))))>
#<alt (* (sin (* 1/2 eps)) (sin (- x (* -1/2 eps))))>
#<alt (* (sin (* 1/2 eps)) (sin (- x (* -1/2 eps))))>
#<alt (pow (sin (* 1/2 eps)) 2)>
#<alt (+ (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (pow (sin (* 1/2 eps)) 2))>
#<alt (+ (* x (+ (* -1/2 (* x (pow (sin (* 1/2 eps)) 2))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (pow (sin (* 1/2 eps)) 2))>
#<alt (+ (* x (+ (* x (+ (* -1/2 (pow (sin (* 1/2 eps)) 2)) (* -1/6 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (pow (sin (* 1/2 eps)) 2))>
#<alt (* (sin (* 1/2 eps)) (sin (+ x (* 1/2 eps))))>
#<alt (* (sin (* 1/2 eps)) (sin (+ x (* 1/2 eps))))>
#<alt (* (sin (* 1/2 eps)) (sin (+ x (* 1/2 eps))))>
#<alt (* (sin (* 1/2 eps)) (sin (+ x (* 1/2 eps))))>
#<alt (* (sin (* 1/2 eps)) (sin (- (* 1/2 eps) (* -1 x))))>
#<alt (* (sin (* 1/2 eps)) (sin (- (* 1/2 eps) (* -1 x))))>
#<alt (* (sin (* 1/2 eps)) (sin (- (* 1/2 eps) (* -1 x))))>
#<alt (* (sin (* 1/2 eps)) (sin (- (* 1/2 eps) (* -1 x))))>
#<alt (* 1/2 eps)>
#<alt (* eps (+ 1/2 (* -1/48 (pow eps 2))))>
#<alt (* eps (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))>
#<alt (* eps (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))>
#<alt (sin (* 1/2 eps))>
#<alt (sin (* 1/2 eps))>
#<alt (sin (* 1/2 eps))>
#<alt (sin (* 1/2 eps))>
#<alt (sin (* 1/2 eps))>
#<alt (sin (* 1/2 eps))>
#<alt (sin (* 1/2 eps))>
#<alt (sin (* 1/2 eps))>
#<alt (* -1/2 (pow eps 2))>
#<alt (+ (* -1 (* eps x)) (* -1/2 (pow eps 2)))>
#<alt (+ (* -1/2 (pow eps 2)) (* x (+ (* -1 eps) (* 1/4 (* (pow eps 2) x)))))>
#<alt (+ (* -1/2 (pow eps 2)) (* x (+ (* -1 eps) (* 1/4 (* (pow eps 2) x)))))>
#<alt (* 1/4 (* (pow eps 2) (pow x 2)))>
#<alt (* (pow x 2) (+ (* -1 (/ eps x)) (* 1/4 (pow eps 2))))>
#<alt (* (pow x 2) (- (+ (* -1/2 (/ (pow eps 2) (pow x 2))) (* 1/4 (pow eps 2))) (/ eps x)))>
#<alt (* (pow x 2) (- (+ (* -1/2 (/ (pow eps 2) (pow x 2))) (* 1/4 (pow eps 2))) (/ eps x)))>
#<alt (* 1/4 (* (pow eps 2) (pow x 2)))>
#<alt (* (pow x 2) (+ (* -1 (/ eps x)) (* 1/4 (pow eps 2))))>
#<alt (* (pow x 2) (+ (* -1 (/ (+ eps (* 1/2 (/ (pow eps 2) x))) x)) (* 1/4 (pow eps 2))))>
#<alt (* (pow x 2) (+ (* -1 (/ (+ eps (* 1/2 (/ (pow eps 2) x))) x)) (* 1/4 (pow eps 2))))>
#<alt (* -1 (* eps x))>
#<alt (* eps (+ (* -1 x) (* eps (- (* 1/4 (pow x 2)) 1/2))))>
#<alt (* eps (+ (* -1 x) (* eps (- (* 1/4 (pow x 2)) 1/2))))>
#<alt (* eps (+ (* -1 x) (* eps (- (* 1/4 (pow x 2)) 1/2))))>
#<alt (* (pow eps 2) (- (* 1/4 (pow x 2)) 1/2))>
#<alt (* (pow eps 2) (- (+ (* -1 (/ x eps)) (* 1/4 (pow x 2))) 1/2))>
#<alt (* (pow eps 2) (- (+ (* -1 (/ x eps)) (* 1/4 (pow x 2))) 1/2))>
#<alt (* (pow eps 2) (- (+ (* -1 (/ x eps)) (* 1/4 (pow x 2))) 1/2))>
#<alt (* (pow eps 2) (- (* 1/4 (pow x 2)) 1/2))>
#<alt (* (pow eps 2) (- (+ (* -1 (/ x eps)) (* 1/4 (pow x 2))) 1/2))>
#<alt (* (pow eps 2) (- (+ (* -1 (/ x eps)) (* 1/4 (pow x 2))) 1/2))>
#<alt (* (pow eps 2) (- (+ (* -1 (/ x eps)) (* 1/4 (pow x 2))) 1/2))>
#<alt (* -1 eps)>
#<alt (- (* 1/4 (* (pow eps 2) x)) eps)>
#<alt (- (* 1/4 (* (pow eps 2) x)) eps)>
#<alt (- (* 1/4 (* (pow eps 2) x)) eps)>
#<alt (* 1/4 (* (pow eps 2) x))>
#<alt (* x (+ (* -1 (/ eps x)) (* 1/4 (pow eps 2))))>
#<alt (* x (+ (* -1 (/ eps x)) (* 1/4 (pow eps 2))))>
#<alt (* x (+ (* -1 (/ eps x)) (* 1/4 (pow eps 2))))>
#<alt (* 1/4 (* (pow eps 2) x))>
#<alt (* -1 (* x (+ (* -1/4 (pow eps 2)) (/ eps x))))>
#<alt (* -1 (* x (+ (* -1/4 (pow eps 2)) (/ eps x))))>
#<alt (* -1 (* x (+ (* -1/4 (pow eps 2)) (/ eps x))))>
#<alt (* -1 eps)>
#<alt (* eps (- (* 1/4 (* eps x)) 1))>
#<alt (* eps (- (* 1/4 (* eps x)) 1))>
#<alt (* eps (- (* 1/4 (* eps x)) 1))>
#<alt (* 1/4 (* (pow eps 2) x))>
#<alt (* (pow eps 2) (- (* 1/4 x) (/ 1 eps)))>
#<alt (* (pow eps 2) (- (* 1/4 x) (/ 1 eps)))>
#<alt (* (pow eps 2) (- (* 1/4 x) (/ 1 eps)))>
#<alt (* 1/4 (* (pow eps 2) x))>
#<alt (* (pow eps 2) (- (* 1/4 x) (/ 1 eps)))>
#<alt (* (pow eps 2) (- (* 1/4 x) (/ 1 eps)))>
#<alt (* (pow eps 2) (- (* 1/4 x) (/ 1 eps)))>
#<alt (* 1/4 (pow eps 2))>
#<alt (* 1/4 (pow eps 2))>
#<alt (* 1/4 (pow eps 2))>
#<alt (* 1/4 (pow eps 2))>
#<alt (* 1/4 (pow eps 2))>
#<alt (* 1/4 (pow eps 2))>
#<alt (* 1/4 (pow eps 2))>
#<alt (* 1/4 (pow eps 2))>
#<alt (* 1/4 (pow eps 2))>
#<alt (* 1/4 (pow eps 2))>
#<alt (* 1/4 (pow eps 2))>
#<alt (* 1/4 (pow eps 2))>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (* -1 (* eps (sin x)))>
#<alt (* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))>
#<alt (* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* 1/8 (* eps (sin x)))))))>
#<alt (* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/48 (* eps (cos x))) (* 1/8 (sin x))))))))>
#<alt (* -1 (* eps (sin (+ x (* 1/2 eps)))))>
#<alt (* -1 (* eps (sin (+ x (* 1/2 eps)))))>
#<alt (* -1 (* eps (sin (+ x (* 1/2 eps)))))>
#<alt (* -1 (* eps (sin (+ x (* 1/2 eps)))))>
#<alt (* -1 (* eps (sin (- x (* -1/2 eps)))))>
#<alt (* -1 (* eps (sin (- x (* -1/2 eps)))))>
#<alt (* -1 (* eps (sin (- x (* -1/2 eps)))))>
#<alt (* -1 (* eps (sin (- x (* -1/2 eps)))))>
#<alt (* -1 (* eps (sin (* 1/2 eps))))>
#<alt (+ (* -1 (* eps (sin (* 1/2 eps)))) (* -1 (* eps (* x (cos (* 1/2 eps))))))>
#<alt (+ (* -1 (* eps (sin (* 1/2 eps)))) (* x (+ (* -1 (* eps (cos (* 1/2 eps)))) (* 1/2 (* eps (* x (sin (* 1/2 eps))))))))>
#<alt (+ (* -1 (* eps (sin (* 1/2 eps)))) (* x (+ (* -1 (* eps (cos (* 1/2 eps)))) (* x (+ (* 1/6 (* eps (* x (cos (* 1/2 eps))))) (* 1/2 (* eps (sin (* 1/2 eps)))))))))>
#<alt (* -1 (* eps (sin (+ x (* 1/2 eps)))))>
#<alt (* -1 (* eps (sin (+ x (* 1/2 eps)))))>
#<alt (* -1 (* eps (sin (+ x (* 1/2 eps)))))>
#<alt (* -1 (* eps (sin (+ x (* 1/2 eps)))))>
#<alt (* -1 (* eps (sin (- (* 1/2 eps) (* -1 x)))))>
#<alt (* -1 (* eps (sin (- (* 1/2 eps) (* -1 x)))))>
#<alt (* -1 (* eps (sin (- (* 1/2 eps) (* -1 x)))))>
#<alt (* -1 (* eps (sin (- (* 1/2 eps) (* -1 x)))))>
#<alt (* 1/2 (* eps (sin x)))>
#<alt (* eps (+ (* 1/4 (* eps (cos x))) (* 1/2 (sin x))))>
#<alt (* eps (+ (* 1/2 (sin x)) (* eps (+ (* -1/16 (* eps (sin x))) (* 1/4 (cos x))))))>
#<alt (* eps (+ (* 1/2 (sin x)) (* eps (+ (* 1/4 (cos x)) (* eps (+ (* -1/16 (sin x)) (* -1/96 (* eps (cos x)))))))))>
#<alt (* 1/2 (* eps (sin (+ x (* 1/2 eps)))))>
#<alt (* 1/2 (* eps (sin (+ x (* 1/2 eps)))))>
#<alt (* 1/2 (* eps (sin (+ x (* 1/2 eps)))))>
#<alt (* 1/2 (* eps (sin (+ x (* 1/2 eps)))))>
#<alt (* 1/2 (* eps (sin (- x (* -1/2 eps)))))>
#<alt (* 1/2 (* eps (sin (- x (* -1/2 eps)))))>
#<alt (* 1/2 (* eps (sin (- x (* -1/2 eps)))))>
#<alt (* 1/2 (* eps (sin (- x (* -1/2 eps)))))>
#<alt (* 1/2 (* eps (sin (* 1/2 eps))))>
#<alt (+ (* 1/2 (* eps (sin (* 1/2 eps)))) (* 1/2 (* eps (* x (cos (* 1/2 eps))))))>
#<alt (+ (* 1/2 (* eps (sin (* 1/2 eps)))) (* x (+ (* -1/4 (* eps (* x (sin (* 1/2 eps))))) (* 1/2 (* eps (cos (* 1/2 eps)))))))>
#<alt (+ (* 1/2 (* eps (sin (* 1/2 eps)))) (* x (+ (* 1/2 (* eps (cos (* 1/2 eps)))) (* x (+ (* -1/4 (* eps (sin (* 1/2 eps)))) (* -1/12 (* eps (* x (cos (* 1/2 eps))))))))))>
#<alt (* 1/2 (* eps (sin (+ x (* 1/2 eps)))))>
#<alt (* 1/2 (* eps (sin (+ x (* 1/2 eps)))))>
#<alt (* 1/2 (* eps (sin (+ x (* 1/2 eps)))))>
#<alt (* 1/2 (* eps (sin (+ x (* 1/2 eps)))))>
#<alt (* 1/2 (* eps (sin (- (* 1/2 eps) (* -1 x)))))>
#<alt (* 1/2 (* eps (sin (- (* 1/2 eps) (* -1 x)))))>
#<alt (* 1/2 (* eps (sin (- (* 1/2 eps) (* -1 x)))))>
#<alt (* 1/2 (* eps (sin (- (* 1/2 eps) (* -1 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 (sin x)>
#<alt (+ (sin x) (* 1/2 (* eps (cos x))))>
#<alt (+ (sin x) (* eps (+ (* -1/8 (* eps (sin x))) (* 1/2 (cos x)))))>
#<alt (+ (sin x) (* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/8 (sin x)) (* -1/48 (* eps (cos x))))))))>
#<alt (sin (+ x (* 1/2 eps)))>
#<alt (sin (+ x (* 1/2 eps)))>
#<alt (sin (+ x (* 1/2 eps)))>
#<alt (sin (+ x (* 1/2 eps)))>
#<alt (sin (- x (* -1/2 eps)))>
#<alt (sin (- x (* -1/2 eps)))>
#<alt (sin (- x (* -1/2 eps)))>
#<alt (sin (- x (* -1/2 eps)))>
#<alt (sin (* 1/2 eps))>
#<alt (+ (sin (* 1/2 eps)) (* x (cos (* 1/2 eps))))>
#<alt (+ (sin (* 1/2 eps)) (* x (+ (cos (* 1/2 eps)) (* -1/2 (* x (sin (* 1/2 eps)))))))>
#<alt (+ (sin (* 1/2 eps)) (* x (+ (cos (* 1/2 eps)) (* x (+ (* -1/2 (sin (* 1/2 eps))) (* -1/6 (* x (cos (* 1/2 eps)))))))))>
#<alt (sin (+ x (* 1/2 eps)))>
#<alt (sin (+ x (* 1/2 eps)))>
#<alt (sin (+ x (* 1/2 eps)))>
#<alt (sin (+ x (* 1/2 eps)))>
#<alt (sin (- (* 1/2 eps) (* -1 x)))>
#<alt (sin (- (* 1/2 eps) (* -1 x)))>
#<alt (sin (- (* 1/2 eps) (* -1 x)))>
#<alt (sin (- (* 1/2 eps) (* -1 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>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt (* 1/2 eps)>
#<alt (+ x (* 1/2 eps))>
#<alt (+ x (* 1/2 eps))>
#<alt (+ x (* 1/2 eps))>
#<alt x>
#<alt (* x (+ 1 (* 1/2 (/ eps x))))>
#<alt (* x (+ 1 (* 1/2 (/ eps x))))>
#<alt (* x (+ 1 (* 1/2 (/ eps x))))>
#<alt x>
#<alt (* -1 (* x (- (* -1/2 (/ eps x)) 1)))>
#<alt (* -1 (* x (- (* -1/2 (/ eps x)) 1)))>
#<alt (* -1 (* x (- (* -1/2 (/ eps x)) 1)))>
#<alt x>
#<alt (+ x (* 1/2 eps))>
#<alt (+ x (* 1/2 eps))>
#<alt (+ x (* 1/2 eps))>
#<alt (* 1/2 eps)>
#<alt (* eps (+ 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 (* -2 (pow (sin (* 1/2 eps)) 2))>
#<alt (+ (* -2 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (* -2 (pow (sin (* 1/2 eps)) 2)))>
#<alt (+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (pow (sin (* 1/2 eps)) 2)))))>
#<alt (+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* 1/3 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (pow (sin (* 1/2 eps)) 2))))))>
#<alt (* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))>
#<alt (* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))>
#<alt (* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))>
#<alt (* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))>
#<alt (* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x))))))>
#<alt (* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x))))))>
#<alt (* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x))))))>
#<alt (* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x))))))>
#<alt (* -1 (* eps (sin x)))>
#<alt (* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))>
#<alt (* eps (+ (* -1 (sin x)) (* eps (+ (* -2 (* eps (+ (* -1/16 (sin x)) (* -1/48 (sin x))))) (* -1/2 (cos x))))))>
#<alt (* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* eps (+ (* -2 (+ (* -1/16 (sin x)) (* -1/48 (sin x)))) (* 1/24 (* eps (cos x)))))))))>
#<alt (* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))>
#<alt (* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))>
#<alt (* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))>
#<alt (* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))>
#<alt (* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps))))))>
#<alt (* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps))))))>
#<alt (* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps))))))>
#<alt (* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps))))))>
#<alt (pow (sin (* 1/2 eps)) 2)>
#<alt (+ (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (pow (sin (* 1/2 eps)) 2))>
#<alt (+ (* x (+ (* -1/2 (* x (pow (sin (* 1/2 eps)) 2))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (pow (sin (* 1/2 eps)) 2))>
#<alt (+ (* x (+ (* x (+ (* -1/2 (pow (sin (* 1/2 eps)) 2)) (* -1/6 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (pow (sin (* 1/2 eps)) 2))>
#<alt (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))>
#<alt (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))>
#<alt (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))>
#<alt (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))>
#<alt (* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x)))))>
#<alt (* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x)))))>
#<alt (* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x)))))>
#<alt (* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x)))))>
#<alt (* 1/2 (* eps (sin x)))>
#<alt (* eps (+ (* 1/4 (* eps (cos x))) (* 1/2 (sin x))))>
#<alt (* eps (+ (* 1/2 (sin x)) (* eps (+ (* 1/4 (cos x)) (* eps (+ (* -1/16 (sin x)) (* -1/48 (sin x))))))))>
#<alt (* eps (+ (* 1/2 (sin x)) (* eps (+ (* 1/4 (cos x)) (* eps (+ (* -1/16 (sin x)) (+ (* -1/48 (sin x)) (* -1/48 (* eps (cos x))))))))))>
#<alt (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))>
#<alt (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))>
#<alt (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))>
#<alt (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))>
#<alt (* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps)))))>
#<alt (* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps)))))>
#<alt (* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps)))))>
#<alt (* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps)))))>
#<alt (* -1 eps)>
#<alt (* -1 eps)>
#<alt (* -1 eps)>
#<alt (* -1 eps)>
#<alt (* -1 eps)>
#<alt (* -1 eps)>
#<alt (* -1 eps)>
#<alt (* -1 eps)>
#<alt (* -1 eps)>
#<alt (* -1 eps)>
#<alt (* -1 eps)>
#<alt (* -1 eps)>
#<alt eps>
#<alt (+ eps (* 2 x))>
#<alt (+ eps (* 2 x))>
#<alt (+ eps (* 2 x))>
#<alt (* 2 x)>
#<alt (* x (+ 2 (/ eps x)))>
#<alt (* x (+ 2 (/ eps x)))>
#<alt (* x (+ 2 (/ eps x)))>
#<alt (* 2 x)>
#<alt (* -1 (* x (- (* -1 (/ eps x)) 2)))>
#<alt (* -1 (* x (- (* -1 (/ eps x)) 2)))>
#<alt (* -1 (* x (- (* -1 (/ eps x)) 2)))>
#<alt (* 2 x)>
#<alt (+ eps (* 2 x))>
#<alt (+ eps (* 2 x))>
#<alt (+ eps (* 2 x))>
#<alt eps>
#<alt (* eps (+ 1 (* 2 (/ x eps))))>
#<alt (* eps (+ 1 (* 2 (/ x eps))))>
#<alt (* eps (+ 1 (* 2 (/ x eps))))>
#<alt eps>
#<alt (* -1 (* eps (- (* -2 (/ x eps)) 1)))>
#<alt (* -1 (* eps (- (* -2 (/ x eps)) 1)))>
#<alt (* -1 (* eps (- (* -2 (/ x eps)) 1)))>
#<alt (/ -1 eps)>
#<alt (- (* -1 (/ x (pow eps 2))) (/ 1 eps))>
#<alt (- (* x (- (* -1 (/ x (pow eps 3))) (/ 1 (pow eps 2)))) (/ 1 eps))>
#<alt (- (* x (- (* x (- (* -1 (/ x (pow eps 4))) (/ 1 (pow eps 3)))) (/ 1 (pow eps 2)))) (/ 1 eps))>
#<alt (/ 1 x)>
#<alt (/ (+ 1 (/ eps x)) x)>
#<alt (/ (- (+ 1 (/ (pow eps 2) (pow x 2))) (* -1 (/ eps x))) x)>
#<alt (/ (- (+ 1 (/ (pow eps 3) (pow x 3))) (+ (* -1 (/ eps x)) (* -1 (/ (pow eps 2) (pow x 2))))) x)>
#<alt (/ 1 x)>
#<alt (* -1 (/ (- (* -1 (/ eps x)) 1) x))>
#<alt (* -1 (/ (- (* -1 (/ (- (/ (pow eps 2) x) (* -1 eps)) x)) 1) x))>
#<alt (* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (* -1 (/ (pow eps 3) x)) (pow eps 2)) x)) (* -1 eps)) x)) 1) x))>
#<alt (/ 1 x)>
#<alt (+ (/ 1 x) (/ eps (pow x 2)))>
#<alt (+ (* eps (+ (/ 1 (pow x 2)) (/ eps (pow x 3)))) (/ 1 x))>
#<alt (+ (* eps (+ (* eps (+ (/ 1 (pow x 3)) (/ eps (pow x 4)))) (/ 1 (pow x 2)))) (/ 1 x))>
#<alt (/ -1 eps)>
#<alt (/ (- (* -1 (/ x eps)) 1) eps)>
#<alt (/ (- (* -1 (/ (pow x 2) (pow eps 2))) (+ 1 (/ x eps))) eps)>
#<alt (/ (- (* -1 (/ (pow x 3) (pow eps 3))) (+ 1 (+ (/ x eps) (/ (pow x 2) (pow eps 2))))) eps)>
#<alt (/ -1 eps)>
#<alt (* -1 (/ (+ 1 (/ x eps)) eps))>
#<alt (* -1 (/ (+ 1 (* -1 (/ (- (* -1 (/ (pow x 2) eps)) x) eps))) eps))>
#<alt (* -1 (/ (+ 1 (* -1 (/ (- (* -1 (/ (- (/ (pow x 3) eps) (* -1 (pow x 2))) eps)) x) eps))) eps))>

Calls

96 calls:

Time	Variable		Point	Expression
2.0ms	eps	@	0	(* (* (* eps 1/2) (sin (+ (* 1/2 eps) x))) -2)
1.0ms	eps	@	inf	(+ (* x (+ (* x (* 1/4 (* eps eps))) (neg eps))) (* eps (* eps -1/2)))
1.0ms	eps	@	-inf	(+ (* x (+ (* x (* 1/4 (* eps eps))) (neg eps))) (* eps (* eps -1/2)))
1.0ms	x	@	inf	(* (* (sin (/ 1/2 (/ 1 eps))) (sin (+ (* 1/2 eps) x))) -2)
1.0ms	x	@	-inf	(* (* (sin (* (+ (* (* (+ x eps) (- x eps)) (/ 1 (- x eps))) (neg x)) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) -2)

rewrite284.0ms (1.6%)

Memory

21.1MiB live, 457.2MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

4 716×	`lower-*.f32`
4 688×	`lower-*.f64`
4 032×	`lower-/.f32`
4 026×	`lower-/.f64`
3 590×	`lower-fma.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	37	188
0	71	174
1	248	150
2	1952	150
0	8247	146

Stop Event

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

Counts

19 → 523

Calls

Call 1

Inputs
(/.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) eps))
(.f64 (.f64 (sin.f64 (/.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) eps))) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) #s(literal -2 binary64))
(*.f64 (sin.f64 (/.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) eps))) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))
(sin.f64 (/.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) eps)))
(fma.f64 x (fma.f64 x (.f64 #s(literal 1/4 binary64) (.f64 eps eps)) (neg.f64 eps)) (.f64 eps (.f64 eps #s(literal -1/2 binary64))))
(fma.f64 x (.f64 #s(literal 1/4 binary64) (.f64 eps eps)) (neg.f64 eps))
(.f64 #s(literal 1/4 binary64) (.f64 eps eps))
(*.f64 eps eps)
(.f64 (.f64 (*.f64 eps #s(literal 1/2 binary64)) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) #s(literal -2 binary64))
(.f64 (.f64 eps #s(literal 1/2 binary64)) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))
(*.f64 eps #s(literal 1/2 binary64))
(sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(fma.f64 (*.f64 (+.f64 x eps) (-.f64 x eps)) (/.f64 #s(literal 1 binary64) (-.f64 x eps)) (neg.f64 x))
(*.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64))
(.f64 (.f64 (sin.f64 (.f64 (fma.f64 (.f64 (+.f64 x eps) (-.f64 x eps)) (/.f64 #s(literal 1 binary64) (-.f64 x eps)) (neg.f64 x)) #s(literal 1/2 binary64))) (sin.f64 (*.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)))) #s(literal -2 binary64))
(.f64 (sin.f64 (.f64 (fma.f64 (.f64 (+.f64 x eps) (-.f64 x eps)) (/.f64 #s(literal 1 binary64) (-.f64 x eps)) (neg.f64 x)) #s(literal 1/2 binary64))) (sin.f64 (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64))))
(neg.f64 eps)
(+.f64 x (+.f64 x eps))
(/.f64 #s(literal 1 binary64) (-.f64 x eps))

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

simplify358.0ms (2%)

Memory

19.1MiB live, 736.1MiB allocated

Algorithm

1×	egg-herbie

Rules

12 052×	`lower-fma.f64`
12 052×	`lower-fma.f32`
5 334×	`lower-*.f64`
5 334×	`lower-*.f32`
3 848×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	423	3730
1	1320	3624
2	3646	3538
0	8072	3277

Stop Event

1×	iter limit
1×	node limit

Counts

384 → 354

Calls

Call 1

Inputs
(* 1/2 eps)
(* 1/2 eps)
(* 1/2 eps)
(* 1/2 eps)
(* 1/2 eps)
(* 1/2 eps)
(* 1/2 eps)
(* 1/2 eps)
(* 1/2 eps)
(* 1/2 eps)
(* 1/2 eps)
(* 1/2 eps)
(* -1 (* eps (sin x)))
(* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))
(* eps (+ (* -1 (sin x)) (* eps (+ (* -2 (* eps (+ (* -1/16 (sin x)) (* -1/48 (sin x))))) (* -1/2 (cos x))))))
(* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* eps (+ (* -2 (+ (* -1/16 (sin x)) (* -1/48 (sin x)))) (* 1/24 (* eps (cos x)))))))))
(* -2 (* (sin (* 1/2 eps)) (sin (+ x (* 1/2 eps)))))
(* -2 (* (sin (* 1/2 eps)) (sin (+ x (* 1/2 eps)))))
(* -2 (* (sin (* 1/2 eps)) (sin (+ x (* 1/2 eps)))))
(* -2 (* (sin (* 1/2 eps)) (sin (+ x (* 1/2 eps)))))
(* -2 (* (sin (* 1/2 eps)) (sin (- x (* -1/2 eps)))))
(* -2 (* (sin (* 1/2 eps)) (sin (- x (* -1/2 eps)))))
(* -2 (* (sin (* 1/2 eps)) (sin (- x (* -1/2 eps)))))
(* -2 (* (sin (* 1/2 eps)) (sin (- x (* -1/2 eps)))))
(* -2 (pow (sin (* 1/2 eps)) 2))
(+ (* -2 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (* -2 (pow (sin (* 1/2 eps)) 2)))
(+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (pow (sin (* 1/2 eps)) 2)))))
(+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* 1/3 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (pow (sin (* 1/2 eps)) 2))))))
(* -2 (* (sin (* 1/2 eps)) (sin (+ x (* 1/2 eps)))))
(* -2 (* (sin (* 1/2 eps)) (sin (+ x (* 1/2 eps)))))
(* -2 (* (sin (* 1/2 eps)) (sin (+ x (* 1/2 eps)))))
(* -2 (* (sin (* 1/2 eps)) (sin (+ x (* 1/2 eps)))))
(* -2 (* (sin (* 1/2 eps)) (sin (- (* 1/2 eps) (* -1 x)))))
(* -2 (* (sin (* 1/2 eps)) (sin (- (* 1/2 eps) (* -1 x)))))
(* -2 (* (sin (* 1/2 eps)) (sin (- (* 1/2 eps) (* -1 x)))))
(* -2 (* (sin (* 1/2 eps)) (sin (- (* 1/2 eps) (* -1 x)))))
(* 1/2 (* eps (sin x)))
(* eps (+ (* 1/4 (* eps (cos x))) (* 1/2 (sin x))))
(* eps (+ (* 1/2 (sin x)) (* eps (+ (* 1/4 (cos x)) (* eps (+ (* -1/16 (sin x)) (* -1/48 (sin x))))))))
(* eps (+ (* 1/2 (sin x)) (* eps (+ (* 1/4 (cos x)) (* eps (+ (* -1/16 (sin x)) (+ (* -1/48 (sin x)) (* -1/48 (* eps (cos x))))))))))
(* (sin (* 1/2 eps)) (sin (+ x (* 1/2 eps))))
(* (sin (* 1/2 eps)) (sin (+ x (* 1/2 eps))))
(* (sin (* 1/2 eps)) (sin (+ x (* 1/2 eps))))
(* (sin (* 1/2 eps)) (sin (+ x (* 1/2 eps))))
(* (sin (* 1/2 eps)) (sin (- x (* -1/2 eps))))
(* (sin (* 1/2 eps)) (sin (- x (* -1/2 eps))))
(* (sin (* 1/2 eps)) (sin (- x (* -1/2 eps))))
(* (sin (* 1/2 eps)) (sin (- x (* -1/2 eps))))
(pow (sin (* 1/2 eps)) 2)
(+ (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (pow (sin (* 1/2 eps)) 2))
(+ (* x (+ (* -1/2 (* x (pow (sin (* 1/2 eps)) 2))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (pow (sin (* 1/2 eps)) 2))
(+ (* x (+ (* x (+ (* -1/2 (pow (sin (* 1/2 eps)) 2)) (* -1/6 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (pow (sin (* 1/2 eps)) 2))
(* (sin (* 1/2 eps)) (sin (+ x (* 1/2 eps))))
(* (sin (* 1/2 eps)) (sin (+ x (* 1/2 eps))))
(* (sin (* 1/2 eps)) (sin (+ x (* 1/2 eps))))
(* (sin (* 1/2 eps)) (sin (+ x (* 1/2 eps))))
(* (sin (* 1/2 eps)) (sin (- (* 1/2 eps) (* -1 x))))
(* (sin (* 1/2 eps)) (sin (- (* 1/2 eps) (* -1 x))))
(* (sin (* 1/2 eps)) (sin (- (* 1/2 eps) (* -1 x))))
(* (sin (* 1/2 eps)) (sin (- (* 1/2 eps) (* -1 x))))
(* 1/2 eps)
(* eps (+ 1/2 (* -1/48 (pow eps 2))))
(* eps (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))
(* eps (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(* -1/2 (pow eps 2))
(+ (* -1 (* eps x)) (* -1/2 (pow eps 2)))
(+ (* -1/2 (pow eps 2)) (* x (+ (* -1 eps) (* 1/4 (* (pow eps 2) x)))))
(+ (* -1/2 (pow eps 2)) (* x (+ (* -1 eps) (* 1/4 (* (pow eps 2) x)))))
(* 1/4 (* (pow eps 2) (pow x 2)))
(* (pow x 2) (+ (* -1 (/ eps x)) (* 1/4 (pow eps 2))))
(* (pow x 2) (- (+ (* -1/2 (/ (pow eps 2) (pow x 2))) (* 1/4 (pow eps 2))) (/ eps x)))
(* (pow x 2) (- (+ (* -1/2 (/ (pow eps 2) (pow x 2))) (* 1/4 (pow eps 2))) (/ eps x)))
(* 1/4 (* (pow eps 2) (pow x 2)))
(* (pow x 2) (+ (* -1 (/ eps x)) (* 1/4 (pow eps 2))))
(* (pow x 2) (+ (* -1 (/ (+ eps (* 1/2 (/ (pow eps 2) x))) x)) (* 1/4 (pow eps 2))))
(* (pow x 2) (+ (* -1 (/ (+ eps (* 1/2 (/ (pow eps 2) x))) x)) (* 1/4 (pow eps 2))))
(* -1 (* eps x))
(* eps (+ (* -1 x) (* eps (- (* 1/4 (pow x 2)) 1/2))))
(* eps (+ (* -1 x) (* eps (- (* 1/4 (pow x 2)) 1/2))))
(* eps (+ (* -1 x) (* eps (- (* 1/4 (pow x 2)) 1/2))))
(* (pow eps 2) (- (* 1/4 (pow x 2)) 1/2))
(* (pow eps 2) (- (+ (* -1 (/ x eps)) (* 1/4 (pow x 2))) 1/2))
(* (pow eps 2) (- (+ (* -1 (/ x eps)) (* 1/4 (pow x 2))) 1/2))
(* (pow eps 2) (- (+ (* -1 (/ x eps)) (* 1/4 (pow x 2))) 1/2))
(* (pow eps 2) (- (* 1/4 (pow x 2)) 1/2))
(* (pow eps 2) (- (+ (* -1 (/ x eps)) (* 1/4 (pow x 2))) 1/2))
(* (pow eps 2) (- (+ (* -1 (/ x eps)) (* 1/4 (pow x 2))) 1/2))
(* (pow eps 2) (- (+ (* -1 (/ x eps)) (* 1/4 (pow x 2))) 1/2))
(* -1 eps)
(- (* 1/4 (* (pow eps 2) x)) eps)
(- (* 1/4 (* (pow eps 2) x)) eps)
(- (* 1/4 (* (pow eps 2) x)) eps)
(* 1/4 (* (pow eps 2) x))
(* x (+ (* -1 (/ eps x)) (* 1/4 (pow eps 2))))
(* x (+ (* -1 (/ eps x)) (* 1/4 (pow eps 2))))
(* x (+ (* -1 (/ eps x)) (* 1/4 (pow eps 2))))
(* 1/4 (* (pow eps 2) x))
(* -1 (* x (+ (* -1/4 (pow eps 2)) (/ eps x))))
(* -1 (* x (+ (* -1/4 (pow eps 2)) (/ eps x))))
(* -1 (* x (+ (* -1/4 (pow eps 2)) (/ eps x))))
(* -1 eps)
(* eps (- (* 1/4 (* eps x)) 1))
(* eps (- (* 1/4 (* eps x)) 1))
(* eps (- (* 1/4 (* eps x)) 1))
(* 1/4 (* (pow eps 2) x))
(* (pow eps 2) (- (* 1/4 x) (/ 1 eps)))
(* (pow eps 2) (- (* 1/4 x) (/ 1 eps)))
(* (pow eps 2) (- (* 1/4 x) (/ 1 eps)))
(* 1/4 (* (pow eps 2) x))
(* (pow eps 2) (- (* 1/4 x) (/ 1 eps)))
(* (pow eps 2) (- (* 1/4 x) (/ 1 eps)))
(* (pow eps 2) (- (* 1/4 x) (/ 1 eps)))
(* 1/4 (pow eps 2))
(* 1/4 (pow eps 2))
(* 1/4 (pow eps 2))
(* 1/4 (pow eps 2))
(* 1/4 (pow eps 2))
(* 1/4 (pow eps 2))
(* 1/4 (pow eps 2))
(* 1/4 (pow eps 2))
(* 1/4 (pow eps 2))
(* 1/4 (pow eps 2))
(* 1/4 (pow eps 2))
(* 1/4 (pow eps 2))
(pow eps 2)
(pow eps 2)
(pow eps 2)
(pow eps 2)
(pow eps 2)
(pow eps 2)
(pow eps 2)
(pow eps 2)
(pow eps 2)
(pow eps 2)
(pow eps 2)
(pow eps 2)
(* -1 (* eps (sin x)))
(* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))
(* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* 1/8 (* eps (sin x)))))))
(* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/48 (* eps (cos x))) (* 1/8 (sin x))))))))
(* -1 (* eps (sin (+ x (* 1/2 eps)))))
(* -1 (* eps (sin (+ x (* 1/2 eps)))))
(* -1 (* eps (sin (+ x (* 1/2 eps)))))
(* -1 (* eps (sin (+ x (* 1/2 eps)))))
(* -1 (* eps (sin (- x (* -1/2 eps)))))
(* -1 (* eps (sin (- x (* -1/2 eps)))))
(* -1 (* eps (sin (- x (* -1/2 eps)))))
(* -1 (* eps (sin (- x (* -1/2 eps)))))
(* -1 (* eps (sin (* 1/2 eps))))
(+ (* -1 (* eps (sin (* 1/2 eps)))) (* -1 (* eps (* x (cos (* 1/2 eps))))))
(+ (* -1 (* eps (sin (* 1/2 eps)))) (* x (+ (* -1 (* eps (cos (* 1/2 eps)))) (* 1/2 (* eps (* x (sin (* 1/2 eps))))))))
(+ (* -1 (* eps (sin (* 1/2 eps)))) (* x (+ (* -1 (* eps (cos (* 1/2 eps)))) (* x (+ (* 1/6 (* eps (* x (cos (* 1/2 eps))))) (* 1/2 (* eps (sin (* 1/2 eps)))))))))
(* -1 (* eps (sin (+ x (* 1/2 eps)))))
(* -1 (* eps (sin (+ x (* 1/2 eps)))))
(* -1 (* eps (sin (+ x (* 1/2 eps)))))
(* -1 (* eps (sin (+ x (* 1/2 eps)))))
(* -1 (* eps (sin (- (* 1/2 eps) (* -1 x)))))
(* -1 (* eps (sin (- (* 1/2 eps) (* -1 x)))))
(* -1 (* eps (sin (- (* 1/2 eps) (* -1 x)))))
(* -1 (* eps (sin (- (* 1/2 eps) (* -1 x)))))
(* 1/2 (* eps (sin x)))
(* eps (+ (* 1/4 (* eps (cos x))) (* 1/2 (sin x))))
(* eps (+ (* 1/2 (sin x)) (* eps (+ (* -1/16 (* eps (sin x))) (* 1/4 (cos x))))))
(* eps (+ (* 1/2 (sin x)) (* eps (+ (* 1/4 (cos x)) (* eps (+ (* -1/16 (sin x)) (* -1/96 (* eps (cos x)))))))))
(* 1/2 (* eps (sin (+ x (* 1/2 eps)))))
(* 1/2 (* eps (sin (+ x (* 1/2 eps)))))
(* 1/2 (* eps (sin (+ x (* 1/2 eps)))))
(* 1/2 (* eps (sin (+ x (* 1/2 eps)))))
(* 1/2 (* eps (sin (- x (* -1/2 eps)))))
(* 1/2 (* eps (sin (- x (* -1/2 eps)))))
(* 1/2 (* eps (sin (- x (* -1/2 eps)))))
(* 1/2 (* eps (sin (- x (* -1/2 eps)))))
(* 1/2 (* eps (sin (* 1/2 eps))))
(+ (* 1/2 (* eps (sin (* 1/2 eps)))) (* 1/2 (* eps (* x (cos (* 1/2 eps))))))
(+ (* 1/2 (* eps (sin (* 1/2 eps)))) (* x (+ (* -1/4 (* eps (* x (sin (* 1/2 eps))))) (* 1/2 (* eps (cos (* 1/2 eps)))))))
(+ (* 1/2 (* eps (sin (* 1/2 eps)))) (* x (+ (* 1/2 (* eps (cos (* 1/2 eps)))) (* x (+ (* -1/4 (* eps (sin (* 1/2 eps)))) (* -1/12 (* eps (* x (cos (* 1/2 eps))))))))))
(* 1/2 (* eps (sin (+ x (* 1/2 eps)))))
(* 1/2 (* eps (sin (+ x (* 1/2 eps)))))
(* 1/2 (* eps (sin (+ x (* 1/2 eps)))))
(* 1/2 (* eps (sin (+ x (* 1/2 eps)))))
(* 1/2 (* eps (sin (- (* 1/2 eps) (* -1 x)))))
(* 1/2 (* eps (sin (- (* 1/2 eps) (* -1 x)))))
(* 1/2 (* eps (sin (- (* 1/2 eps) (* -1 x)))))
(* 1/2 (* eps (sin (- (* 1/2 eps) (* -1 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)
(sin x)
(+ (sin x) (* 1/2 (* eps (cos x))))
(+ (sin x) (* eps (+ (* -1/8 (* eps (sin x))) (* 1/2 (cos x)))))
(+ (sin x) (* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/8 (sin x)) (* -1/48 (* eps (cos x))))))))
(sin (+ x (* 1/2 eps)))
(sin (+ x (* 1/2 eps)))
(sin (+ x (* 1/2 eps)))
(sin (+ x (* 1/2 eps)))
(sin (- x (* -1/2 eps)))
(sin (- x (* -1/2 eps)))
(sin (- x (* -1/2 eps)))
(sin (- x (* -1/2 eps)))
(sin (* 1/2 eps))
(+ (sin (* 1/2 eps)) (* x (cos (* 1/2 eps))))
(+ (sin (* 1/2 eps)) (* x (+ (cos (* 1/2 eps)) (* -1/2 (* x (sin (* 1/2 eps)))))))
(+ (sin (* 1/2 eps)) (* x (+ (cos (* 1/2 eps)) (* x (+ (* -1/2 (sin (* 1/2 eps))) (* -1/6 (* x (cos (* 1/2 eps)))))))))
(sin (+ x (* 1/2 eps)))
(sin (+ x (* 1/2 eps)))
(sin (+ x (* 1/2 eps)))
(sin (+ x (* 1/2 eps)))
(sin (- (* 1/2 eps) (* -1 x)))
(sin (- (* 1/2 eps) (* -1 x)))
(sin (- (* 1/2 eps) (* -1 x)))
(sin (- (* 1/2 eps) (* -1 x)))
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
(* 1/2 eps)
(+ x (* 1/2 eps))
(+ x (* 1/2 eps))
(+ x (* 1/2 eps))
x
(* x (+ 1 (* 1/2 (/ eps x))))
(* x (+ 1 (* 1/2 (/ eps x))))
(* x (+ 1 (* 1/2 (/ eps x))))
x
(* -1 (* x (- (* -1/2 (/ eps x)) 1)))
(* -1 (* x (- (* -1/2 (/ eps x)) 1)))
(* -1 (* x (- (* -1/2 (/ eps x)) 1)))
x
(+ x (* 1/2 eps))
(+ x (* 1/2 eps))
(+ x (* 1/2 eps))
(* 1/2 eps)
(* eps (+ 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)))
(* -2 (pow (sin (* 1/2 eps)) 2))
(+ (* -2 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (* -2 (pow (sin (* 1/2 eps)) 2)))
(+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (pow (sin (* 1/2 eps)) 2)))))
(+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* 1/3 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (pow (sin (* 1/2 eps)) 2))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x))))))
(* -1 (* eps (sin x)))
(* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))
(* eps (+ (* -1 (sin x)) (* eps (+ (* -2 (* eps (+ (* -1/16 (sin x)) (* -1/48 (sin x))))) (* -1/2 (cos x))))))
(* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* eps (+ (* -2 (+ (* -1/16 (sin x)) (* -1/48 (sin x)))) (* 1/24 (* eps (cos x)))))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps))))))
(pow (sin (* 1/2 eps)) 2)
(+ (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (pow (sin (* 1/2 eps)) 2))
(+ (* x (+ (* -1/2 (* x (pow (sin (* 1/2 eps)) 2))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (pow (sin (* 1/2 eps)) 2))
(+ (* x (+ (* x (+ (* -1/2 (pow (sin (* 1/2 eps)) 2)) (* -1/6 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (pow (sin (* 1/2 eps)) 2))
(* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x)))))
(* 1/2 (* eps (sin x)))
(* eps (+ (* 1/4 (* eps (cos x))) (* 1/2 (sin x))))
(* eps (+ (* 1/2 (sin x)) (* eps (+ (* 1/4 (cos x)) (* eps (+ (* -1/16 (sin x)) (* -1/48 (sin x))))))))
(* eps (+ (* 1/2 (sin x)) (* eps (+ (* 1/4 (cos x)) (* eps (+ (* -1/16 (sin x)) (+ (* -1/48 (sin x)) (* -1/48 (* eps (cos x))))))))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps)))))
(* -1 eps)
(* -1 eps)
(* -1 eps)
(* -1 eps)
(* -1 eps)
(* -1 eps)
(* -1 eps)
(* -1 eps)
(* -1 eps)
(* -1 eps)
(* -1 eps)
(* -1 eps)
eps
(+ eps (* 2 x))
(+ eps (* 2 x))
(+ eps (* 2 x))
(* 2 x)
(* x (+ 2 (/ eps x)))
(* x (+ 2 (/ eps x)))
(* x (+ 2 (/ eps x)))
(* 2 x)
(* -1 (* x (- (* -1 (/ eps x)) 2)))
(* -1 (* x (- (* -1 (/ eps x)) 2)))
(* -1 (* x (- (* -1 (/ eps x)) 2)))
(* 2 x)
(+ eps (* 2 x))
(+ eps (* 2 x))
(+ eps (* 2 x))
eps
(* eps (+ 1 (* 2 (/ x eps))))
(* eps (+ 1 (* 2 (/ x eps))))
(* eps (+ 1 (* 2 (/ x eps))))
eps
(* -1 (* eps (- (* -2 (/ x eps)) 1)))
(* -1 (* eps (- (* -2 (/ x eps)) 1)))
(* -1 (* eps (- (* -2 (/ x eps)) 1)))
(/ -1 eps)
(- (* -1 (/ x (pow eps 2))) (/ 1 eps))
(- (* x (- (* -1 (/ x (pow eps 3))) (/ 1 (pow eps 2)))) (/ 1 eps))
(- (* x (- (* x (- (* -1 (/ x (pow eps 4))) (/ 1 (pow eps 3)))) (/ 1 (pow eps 2)))) (/ 1 eps))
(/ 1 x)
(/ (+ 1 (/ eps x)) x)
(/ (- (+ 1 (/ (pow eps 2) (pow x 2))) (* -1 (/ eps x))) x)
(/ (- (+ 1 (/ (pow eps 3) (pow x 3))) (+ (* -1 (/ eps x)) (* -1 (/ (pow eps 2) (pow x 2))))) x)
(/ 1 x)
(* -1 (/ (- (* -1 (/ eps x)) 1) x))
(* -1 (/ (- (* -1 (/ (- (/ (pow eps 2) x) (* -1 eps)) x)) 1) x))
(* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (* -1 (/ (pow eps 3) x)) (pow eps 2)) x)) (* -1 eps)) x)) 1) x))
(/ 1 x)
(+ (/ 1 x) (/ eps (pow x 2)))
(+ (* eps (+ (/ 1 (pow x 2)) (/ eps (pow x 3)))) (/ 1 x))
(+ (* eps (+ (* eps (+ (/ 1 (pow x 3)) (/ eps (pow x 4)))) (/ 1 (pow x 2)))) (/ 1 x))
(/ -1 eps)
(/ (- (* -1 (/ x eps)) 1) eps)
(/ (- (* -1 (/ (pow x 2) (pow eps 2))) (+ 1 (/ x eps))) eps)
(/ (- (* -1 (/ (pow x 3) (pow eps 3))) (+ 1 (+ (/ x eps) (/ (pow x 2) (pow eps 2))))) eps)
(/ -1 eps)
(* -1 (/ (+ 1 (/ x eps)) eps))
(* -1 (/ (+ 1 (* -1 (/ (- (* -1 (/ (pow x 2) eps)) x) eps))) eps))
(* -1 (/ (+ 1 (* -1 (/ (- (* -1 (/ (- (/ (pow x 3) eps) (* -1 (pow x 2))) eps)) x) eps))) eps))

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

eval166.0ms (0.9%)

Memory: -17.0MiB live, 214.8MiB allocated
Compiler: Compiled 25 473 to 2 877 computations (88.7% saved)

prune304.0ms (1.7%)

Memory

3.4MiB live, 205.9MiB allocated

Pruning

31 alts after pruning (25 fresh and 6 done)

	Pruned	Kept	Total
New	902	12	914
Fresh	5	13	18
Picked	3	2	5
Done	1	4	5
Total	911	31	942

Accuracy

100.0%

Counts

942 → 31

Alt Table

Click to see full alt table

Status	Accuracy	Program
	80.4%	(fma.f64 (sin.f64 x) (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps #s(literal -1/120 binary64)) #s(literal 1/6 binary64)) #s(literal -1 binary64))) (.f64 (cos.f64 x) (+.f64 (cos.f64 eps) #s(literal -1 binary64))))
	80.4%	(fma.f64 (sin.f64 x) (neg.f64 (fma.f64 (fma.f64 eps (.f64 eps #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) (.f64 eps (.f64 eps eps)) eps)) (.f64 (cos.f64 x) (+.f64 (cos.f64 eps) #s(literal -1 binary64))))
✓	80.9%	(fma.f64 (sin.f64 x) (neg.f64 (sin.f64 eps)) (*.f64 (cos.f64 x) (+.f64 (cos.f64 eps) #s(literal -1 binary64))))
	99.5%	(fma.f64 (sin.f64 x) (neg.f64 (sin.f64 eps)) (.f64 (cos.f64 x) (.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps (fma.f64 (.f64 eps eps) #s(literal 1/40320 binary64) #s(literal -1/720 binary64))) #s(literal 1/24 binary64)) #s(literal -1/2 binary64)))))
	97.3%	(fma.f64 x (neg.f64 eps) (.f64 eps (.f64 eps #s(literal -1/2 binary64))))
	97.5%	(fma.f64 eps (-.f64 (.f64 eps #s(literal -1/2 binary64)) x) (.f64 x (.f64 x (.f64 eps (fma.f64 eps #s(literal 1/4 binary64) (*.f64 x #s(literal 1/6 binary64)))))))
	98.9%	(/.f64 (.f64 #s(literal 1/2 binary64) (.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal -2 binary64))) (/.f64 #s(literal 1 binary64) eps))
	81.0%	(-.f64 (-.f64 (.f64 (cos.f64 eps) (cos.f64 x)) (cos.f64 x)) (.f64 (sin.f64 x) (sin.f64 eps)))
✓	54.8%	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
	53.1%	(-.f64 (cos.f64 (+.f64 x eps)) #s(literal 1 binary64))
✓	53.1%	(+.f64 (cos.f64 eps) #s(literal -1 binary64))
	99.3%	(.f64 (.f64 (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64))) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) #s(literal -2 binary64))
	99.2%	(.f64 (.f64 (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 eps (*.f64 eps #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64))) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) #s(literal -2 binary64))
	99.1%	(.f64 (.f64 (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64))) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) #s(literal -2 binary64))
✓	99.6%	(.f64 (.f64 (sin.f64 (/.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) eps))) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) #s(literal -2 binary64))
	22.0%	(.f64 (.f64 (sin.f64 (.f64 (fma.f64 (fma.f64 x (.f64 x x) (.f64 eps (.f64 eps eps))) (/.f64 #s(literal 1 binary64) (fma.f64 eps (-.f64 eps x) (.f64 x x))) (neg.f64 x)) #s(literal 1/2 binary64))) (sin.f64 (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)))) #s(literal -2 binary64))
	81.4%	(.f64 (.f64 (sin.f64 (.f64 (fma.f64 (.f64 (+.f64 x eps) (-.f64 x eps)) (/.f64 #s(literal 1 binary64) (-.f64 x eps)) (neg.f64 x)) #s(literal 1/2 binary64))) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) #s(literal -2 binary64))
	25.5%	(.f64 (.f64 (sin.f64 (.f64 (/.f64 (fma.f64 (-.f64 #s(literal 0 binary64) (.f64 x x)) (-.f64 eps x) (.f64 (+.f64 #s(literal 0 binary64) x) (-.f64 (.f64 eps eps) (.f64 x x)))) (.f64 (+.f64 #s(literal 0 binary64) x) (-.f64 eps x))) #s(literal 1/2 binary64))) (sin.f64 (*.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)))) #s(literal -2 binary64))
	23.8%	(.f64 (.f64 (sin.f64 (.f64 (/.f64 (fma.f64 #s(literal 1 binary64) (+.f64 #s(literal 0 binary64) (fma.f64 x x (.f64 #s(literal 0 binary64) x))) (.f64 (/.f64 (-.f64 x eps) (.f64 (+.f64 eps x) (-.f64 x eps))) (-.f64 #s(literal 0 binary64) (.f64 x (.f64 x x))))) (.f64 (/.f64 (-.f64 x eps) (.f64 (+.f64 eps x) (-.f64 x eps))) (+.f64 #s(literal 0 binary64) (fma.f64 x x (.f64 #s(literal 0 binary64) x))))) #s(literal 1/2 binary64))) (sin.f64 (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)))) #s(literal -2 binary64))
✓	99.7%	(.f64 (.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) #s(literal -2 binary64))
	96.9%	(.f64 (.f64 x x) (-.f64 (.f64 #s(literal 1/4 binary64) (.f64 eps eps)) (/.f64 (fma.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 eps eps) x) eps) x)))
	54.4%	(.f64 (.f64 eps eps) (fma.f64 x (*.f64 x #s(literal 1/4 binary64)) #s(literal -1/2 binary64)))
	98.9%	(*.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (neg.f64 eps))
	79.9%	(*.f64 (sin.f64 x) (neg.f64 eps))
	53.2%	(.f64 x (.f64 #s(literal 1/4 binary64) (.f64 x (.f64 eps eps))))
	97.5%	(.f64 eps (fma.f64 x (fma.f64 x (fma.f64 eps #s(literal 1/4 binary64) (.f64 x #s(literal 1/6 binary64))) #s(literal -1 binary64)) (*.f64 eps #s(literal -1/2 binary64))))
	97.2%	(*.f64 eps (fma.f64 eps #s(literal -1/2 binary64) (neg.f64 x)))
	54.4%	(.f64 eps (.f64 eps #s(literal -1/2 binary64)))
	78.7%	(*.f64 eps (neg.f64 x))
	52.3%	(.f64 #s(literal 1/2 binary64) (.f64 x x))
✓	53.0%	#s(literal 0 binary64)

Compiler

Compiled 1 831 to 666 computations (63.6% saved)

regimes69.0ms (0.4%)

Memory

-16.2MiB live, 77.1MiB allocated

Counts

63 → 1

Calls

Call 1

Inputs
#s(literal 0 binary64)
(+.f64 #s(literal 1 binary64) #s(literal -1 binary64))
(*.f64 eps (neg.f64 x))
(.f64 #s(literal 1/2 binary64) (.f64 x x))
(.f64 eps (.f64 eps #s(literal -1/2 binary64)))
(.f64 eps (-.f64 (.f64 eps #s(literal -1/2 binary64)) x))
(*.f64 eps (fma.f64 eps #s(literal -1/2 binary64) (neg.f64 x)))
(fma.f64 x (neg.f64 eps) (.f64 eps (.f64 eps #s(literal -1/2 binary64))))
(.f64 x (.f64 #s(literal 1/4 binary64) (.f64 x (.f64 eps eps))))
(.f64 (.f64 eps eps) (fma.f64 x (*.f64 x #s(literal 1/4 binary64)) #s(literal -1/2 binary64)))
(.f64 eps (fma.f64 x (fma.f64 x (fma.f64 eps #s(literal 1/4 binary64) (.f64 x #s(literal 1/6 binary64))) #s(literal -1 binary64)) (*.f64 eps #s(literal -1/2 binary64))))
(fma.f64 x (fma.f64 x (.f64 #s(literal 1/4 binary64) (.f64 eps eps)) (neg.f64 eps)) (.f64 eps (.f64 eps #s(literal -1/2 binary64))))
(fma.f64 eps (-.f64 (.f64 eps #s(literal -1/2 binary64)) x) (.f64 x (.f64 x (.f64 eps (fma.f64 eps #s(literal 1/4 binary64) (*.f64 x #s(literal 1/6 binary64)))))))
(.f64 (.f64 x x) (-.f64 (.f64 #s(literal 1/4 binary64) (.f64 eps eps)) (/.f64 (fma.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 eps eps) x) eps) x)))
(+.f64 (cos.f64 eps) #s(literal -1 binary64))
(-.f64 (cos.f64 (+.f64 x eps)) #s(literal 1 binary64))
(*.f64 (sin.f64 x) (neg.f64 eps))
(.f64 eps (-.f64 (.f64 eps #s(literal -1/2 binary64)) (sin.f64 x)))
(*.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (neg.f64 eps))
(-.f64 (cos.f64 (+.f64 x eps)) (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)))
(-.f64 (-.f64 (cos.f64 (+.f64 x eps)) #s(literal 1 binary64)) (.f64 x (.f64 x #s(literal -1/2 binary64))))
(.f64 (.f64 (*.f64 eps #s(literal 1/2 binary64)) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) #s(literal -2 binary64))
(.f64 (.f64 (.f64 eps (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64))) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) #s(literal -2 binary64))
(.f64 (.f64 (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64))) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) #s(literal -2 binary64))
(/.f64 (.f64 #s(literal 1/2 binary64) (.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal -2 binary64))) (/.f64 #s(literal 1 binary64) eps))
(.f64 (.f64 (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 eps (*.f64 eps #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64))) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) #s(literal -2 binary64))
(.f64 (.f64 (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64))) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) #s(literal -2 binary64))
(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
(.f64 eps (-.f64 (.f64 eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x)))
(.f64 (.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) #s(literal -2 binary64))
(.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)))) #s(literal -2 binary64))
(.f64 (.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (sin.f64 (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)))) #s(literal -2 binary64))
(.f64 (.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (sin.f64 (.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps))))) #s(literal -2 binary64))
(.f64 (.f64 (sin.f64 (/.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) eps))) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) #s(literal -2 binary64))
(.f64 (.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (sin.f64 (.f64 (*.f64 x (+.f64 (/.f64 eps x) #s(literal 2 binary64))) #s(literal 1/2 binary64)))) #s(literal -2 binary64))
(.f64 (.f64 (sin.f64 (.f64 (.f64 (.f64 eps eps) (/.f64 #s(literal 1 binary64) eps)) #s(literal 1/2 binary64))) (sin.f64 (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)))) #s(literal -2 binary64))
(.f64 (.f64 (sin.f64 (.f64 (/.f64 (.f64 eps (.f64 eps eps)) (.f64 eps eps)) #s(literal 1/2 binary64))) (sin.f64 (*.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)))) #s(literal -2 binary64))
(.f64 (.f64 (sin.f64 (.f64 (/.f64 #s(literal 1 binary64) (/.f64 eps (.f64 eps eps))) #s(literal 1/2 binary64))) (sin.f64 (*.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)))) #s(literal -2 binary64))
(.f64 (.f64 (sin.f64 (.f64 (fma.f64 (.f64 (+.f64 x eps) (-.f64 x eps)) (/.f64 #s(literal 1 binary64) (-.f64 x eps)) (neg.f64 x)) #s(literal 1/2 binary64))) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) #s(literal -2 binary64))
(.f64 (.f64 (sin.f64 (.f64 (fma.f64 (.f64 (+.f64 x eps) (-.f64 x eps)) (/.f64 #s(literal 1 binary64) (-.f64 x eps)) (neg.f64 x)) #s(literal 1/2 binary64))) (sin.f64 (*.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)))) #s(literal -2 binary64))
(.f64 (.f64 (sin.f64 (.f64 (/.f64 #s(literal 1 binary64) (/.f64 (.f64 eps eps) (.f64 eps (.f64 eps eps)))) #s(literal 1/2 binary64))) (sin.f64 (*.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)))) #s(literal -2 binary64))
(.f64 (.f64 (sin.f64 (.f64 (fma.f64 (fma.f64 x (.f64 x x) (.f64 eps (.f64 eps eps))) (/.f64 #s(literal 1 binary64) (fma.f64 eps (-.f64 eps x) (.f64 x x))) (neg.f64 x)) #s(literal 1/2 binary64))) (sin.f64 (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)))) #s(literal -2 binary64))
(.f64 (.f64 (sin.f64 (.f64 (/.f64 (.f64 (fma.f64 (+.f64 x eps) eps (.f64 x x)) eps) (fma.f64 (+.f64 x eps) (+.f64 x eps) (-.f64 (.f64 x x) (.f64 x (+.f64 x eps))))) #s(literal 1/2 binary64))) (sin.f64 (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)))) #s(literal -2 binary64))
(.f64 (.f64 (sin.f64 (.f64 (/.f64 (fma.f64 (-.f64 #s(literal 0 binary64) (.f64 x x)) (-.f64 eps x) (.f64 (+.f64 #s(literal 0 binary64) x) (-.f64 (.f64 eps eps) (.f64 x x)))) (.f64 (+.f64 #s(literal 0 binary64) x) (-.f64 eps x))) #s(literal 1/2 binary64))) (sin.f64 (*.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)))) #s(literal -2 binary64))
(-.f64 (.f64 eps (.f64 #s(literal -1/2 binary64) (.f64 eps (cos.f64 x)))) (.f64 (sin.f64 x) (sin.f64 eps)))
(fma.f64 (sin.f64 x) (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps #s(literal -1/120 binary64)) #s(literal 1/6 binary64)) #s(literal -1 binary64))) (.f64 (cos.f64 x) (+.f64 (cos.f64 eps) #s(literal -1 binary64))))
(.f64 eps (fma.f64 eps (fma.f64 (cos.f64 x) (+.f64 #s(literal -1/2 binary64) (.f64 eps (.f64 eps #s(literal 1/24 binary64)))) (.f64 eps (*.f64 #s(literal 1/6 binary64) (sin.f64 x)))) (sin.f64 (neg.f64 x))))
(fma.f64 (sin.f64 x) (neg.f64 (fma.f64 (fma.f64 eps (.f64 eps #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) (.f64 eps (.f64 eps eps)) eps)) (.f64 (cos.f64 x) (+.f64 (cos.f64 eps) #s(literal -1 binary64))))
(.f64 (.f64 (sin.f64 (.f64 (/.f64 (fma.f64 #s(literal 1 binary64) (+.f64 #s(literal 0 binary64) (fma.f64 x x (.f64 #s(literal 0 binary64) x))) (.f64 (/.f64 (-.f64 x eps) (.f64 (+.f64 eps x) (-.f64 x eps))) (-.f64 #s(literal 0 binary64) (.f64 x (.f64 x x))))) (.f64 (/.f64 (-.f64 x eps) (.f64 (+.f64 eps x) (-.f64 x eps))) (+.f64 #s(literal 0 binary64) (fma.f64 x x (.f64 #s(literal 0 binary64) x))))) #s(literal 1/2 binary64))) (sin.f64 (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)))) #s(literal -2 binary64))
(fma.f64 (sin.f64 x) (neg.f64 (sin.f64 eps)) (.f64 (cos.f64 x) (.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps (fma.f64 (*.f64 eps eps) #s(literal -1/720 binary64) #s(literal 1/24 binary64))) #s(literal -1/2 binary64)))))
(fma.f64 (sin.f64 x) (neg.f64 (sin.f64 eps)) (.f64 (cos.f64 x) (.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps (fma.f64 (.f64 eps eps) #s(literal 1/40320 binary64) #s(literal -1/720 binary64))) #s(literal 1/24 binary64)) #s(literal -1/2 binary64)))))
(fma.f64 (sin.f64 x) (neg.f64 (sin.f64 eps)) (*.f64 (cos.f64 x) (+.f64 (cos.f64 eps) #s(literal -1 binary64))))
(/.f64 (-.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 (+.f64 x eps) #s(literal 2 binary64))) #s(literal 1/2 binary64)) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (+.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)))
(fma.f64 x (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (.f64 #s(literal -2 binary64) (sin.f64 (.f64 #s(literal 1/2 binary64) eps)))) (.f64 (pow.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (fma.f64 x x #s(literal -2 binary64))))
(-.f64 (.f64 (.f64 eps eps) (fma.f64 (.f64 eps (.f64 eps (cos.f64 x))) (fma.f64 eps (.f64 eps #s(literal -1/720 binary64)) #s(literal 1/24 binary64)) (.f64 #s(literal -1/2 binary64) (cos.f64 x)))) (*.f64 (sin.f64 x) (sin.f64 eps)))
(-.f64 (.f64 (.f64 eps eps) (fma.f64 (cos.f64 x) (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) (.f64 (.f64 eps eps) (.f64 (cos.f64 x) (.f64 eps (.f64 eps (fma.f64 (.f64 eps eps) #s(literal 1/40320 binary64) #s(literal -1/720 binary64)))))))) (.f64 (sin.f64 x) (sin.f64 eps)))
(fma.f64 (cos.f64 x) (cos.f64 eps) (neg.f64 (fma.f64 (sin.f64 x) (sin.f64 eps) (cos.f64 x))))
(-.f64 (-.f64 (.f64 (cos.f64 eps) (cos.f64 x)) (cos.f64 x)) (.f64 (sin.f64 x) (sin.f64 eps)))
(-.f64 (fma.f64 (cos.f64 x) (cos.f64 eps) (neg.f64 (*.f64 (sin.f64 x) (sin.f64 eps)))) (cos.f64 x))
(-.f64 (+.f64 (neg.f64 (cos.f64 x)) (.f64 (cos.f64 x) (cos.f64 eps))) (.f64 (sin.f64 x) (sin.f64 eps)))
(-.f64 (/.f64 (pow.f64 (cos.f64 (+.f64 x eps)) #s(literal 3 binary64)) (fma.f64 (cos.f64 x) (+.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 (+.f64 x eps) #s(literal 2 binary64))) #s(literal 1/2 binary64)))) (/.f64 (pow.f64 (cos.f64 x) #s(literal 3 binary64)) (fma.f64 (cos.f64 x) (+.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 (+.f64 x eps) #s(literal 2 binary64))) #s(literal 1/2 binary64)))))
(fma.f64 (pow.f64 (cos.f64 (+.f64 x eps)) #s(literal 3 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 (cos.f64 x) (+.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 (+.f64 x eps) #s(literal 2 binary64))) #s(literal 1/2 binary64)))) (neg.f64 (/.f64 (pow.f64 (cos.f64 x) #s(literal 3 binary64)) (fma.f64 (cos.f64 x) (+.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 (+.f64 x eps) #s(literal 2 binary64))) #s(literal 1/2 binary64))))))
(/.f64 (-.f64 (pow.f64 (/.f64 (pow.f64 (cos.f64 (+.f64 x eps)) #s(literal 3 binary64)) (fma.f64 (cos.f64 x) (+.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 (+.f64 x eps) #s(literal 2 binary64))) #s(literal 1/2 binary64)))) #s(literal 2 binary64)) (pow.f64 (/.f64 (pow.f64 (cos.f64 x) #s(literal 3 binary64)) (fma.f64 (cos.f64 x) (+.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 (+.f64 x eps) #s(literal 2 binary64))) #s(literal 1/2 binary64)))) #s(literal 2 binary64))) (+.f64 (/.f64 (pow.f64 (cos.f64 (+.f64 x eps)) #s(literal 3 binary64)) (fma.f64 (cos.f64 x) (+.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 (+.f64 x eps) #s(literal 2 binary64))) #s(literal 1/2 binary64)))) (/.f64 (pow.f64 (cos.f64 x) #s(literal 3 binary64)) (fma.f64 (cos.f64 x) (+.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 (+.f64 x eps) #s(literal 2 binary64))) #s(literal 1/2 binary64))))))

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

Calls

3 calls:

33.0ms	x
21.0ms	eps
12.0ms	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))

Results

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

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes42.0ms (0.2%)

Memory

-4.1MiB live, 35.3MiB allocated

Counts

29 → 1

Calls

Call 1

Inputs
#s(literal 0 binary64)
(+.f64 #s(literal 1 binary64) #s(literal -1 binary64))
(*.f64 eps (neg.f64 x))
(.f64 #s(literal 1/2 binary64) (.f64 x x))
(.f64 eps (.f64 eps #s(literal -1/2 binary64)))
(.f64 eps (-.f64 (.f64 eps #s(literal -1/2 binary64)) x))
(*.f64 eps (fma.f64 eps #s(literal -1/2 binary64) (neg.f64 x)))
(fma.f64 x (neg.f64 eps) (.f64 eps (.f64 eps #s(literal -1/2 binary64))))
(.f64 x (.f64 #s(literal 1/4 binary64) (.f64 x (.f64 eps eps))))
(.f64 (.f64 eps eps) (fma.f64 x (*.f64 x #s(literal 1/4 binary64)) #s(literal -1/2 binary64)))
(.f64 eps (fma.f64 x (fma.f64 x (fma.f64 eps #s(literal 1/4 binary64) (.f64 x #s(literal 1/6 binary64))) #s(literal -1 binary64)) (*.f64 eps #s(literal -1/2 binary64))))
(fma.f64 x (fma.f64 x (.f64 #s(literal 1/4 binary64) (.f64 eps eps)) (neg.f64 eps)) (.f64 eps (.f64 eps #s(literal -1/2 binary64))))
(fma.f64 eps (-.f64 (.f64 eps #s(literal -1/2 binary64)) x) (.f64 x (.f64 x (.f64 eps (fma.f64 eps #s(literal 1/4 binary64) (*.f64 x #s(literal 1/6 binary64)))))))
(.f64 (.f64 x x) (-.f64 (.f64 #s(literal 1/4 binary64) (.f64 eps eps)) (/.f64 (fma.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 eps eps) x) eps) x)))
(+.f64 (cos.f64 eps) #s(literal -1 binary64))
(-.f64 (cos.f64 (+.f64 x eps)) #s(literal 1 binary64))
(*.f64 (sin.f64 x) (neg.f64 eps))
(.f64 eps (-.f64 (.f64 eps #s(literal -1/2 binary64)) (sin.f64 x)))
(*.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (neg.f64 eps))
(-.f64 (cos.f64 (+.f64 x eps)) (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)))
(-.f64 (-.f64 (cos.f64 (+.f64 x eps)) #s(literal 1 binary64)) (.f64 x (.f64 x #s(literal -1/2 binary64))))
(.f64 (.f64 (*.f64 eps #s(literal 1/2 binary64)) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) #s(literal -2 binary64))
(.f64 (.f64 (.f64 eps (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64))) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) #s(literal -2 binary64))
(.f64 (.f64 (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64))) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) #s(literal -2 binary64))
(/.f64 (.f64 #s(literal 1/2 binary64) (.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal -2 binary64))) (/.f64 #s(literal 1 binary64) eps))
(.f64 (.f64 (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 eps (*.f64 eps #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64))) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) #s(literal -2 binary64))
(.f64 (.f64 (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64))) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) #s(literal -2 binary64))
(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
(.f64 eps (-.f64 (.f64 eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x)))

Outputs

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

Calls

3 calls:

27.0ms	x
8.0ms	eps
6.0ms	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))

Results

Accuracy	Segments	Branch
99.3%	1	`x`
99.3%	1	`eps`
99.3%	1	`(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))`

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes22.0ms (0.1%)

Memory

23.9MiB live, 62.8MiB allocated

Counts

26 → 1

Calls

Call 1

Inputs
#s(literal 0 binary64)
(+.f64 #s(literal 1 binary64) #s(literal -1 binary64))
(*.f64 eps (neg.f64 x))
(.f64 #s(literal 1/2 binary64) (.f64 x x))
(.f64 eps (.f64 eps #s(literal -1/2 binary64)))
(.f64 eps (-.f64 (.f64 eps #s(literal -1/2 binary64)) x))
(*.f64 eps (fma.f64 eps #s(literal -1/2 binary64) (neg.f64 x)))
(fma.f64 x (neg.f64 eps) (.f64 eps (.f64 eps #s(literal -1/2 binary64))))
(.f64 x (.f64 #s(literal 1/4 binary64) (.f64 x (.f64 eps eps))))
(.f64 (.f64 eps eps) (fma.f64 x (*.f64 x #s(literal 1/4 binary64)) #s(literal -1/2 binary64)))
(.f64 eps (fma.f64 x (fma.f64 x (fma.f64 eps #s(literal 1/4 binary64) (.f64 x #s(literal 1/6 binary64))) #s(literal -1 binary64)) (*.f64 eps #s(literal -1/2 binary64))))
(fma.f64 x (fma.f64 x (.f64 #s(literal 1/4 binary64) (.f64 eps eps)) (neg.f64 eps)) (.f64 eps (.f64 eps #s(literal -1/2 binary64))))
(fma.f64 eps (-.f64 (.f64 eps #s(literal -1/2 binary64)) x) (.f64 x (.f64 x (.f64 eps (fma.f64 eps #s(literal 1/4 binary64) (*.f64 x #s(literal 1/6 binary64)))))))
(.f64 (.f64 x x) (-.f64 (.f64 #s(literal 1/4 binary64) (.f64 eps eps)) (/.f64 (fma.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 eps eps) x) eps) x)))
(+.f64 (cos.f64 eps) #s(literal -1 binary64))
(-.f64 (cos.f64 (+.f64 x eps)) #s(literal 1 binary64))
(*.f64 (sin.f64 x) (neg.f64 eps))
(.f64 eps (-.f64 (.f64 eps #s(literal -1/2 binary64)) (sin.f64 x)))
(*.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (neg.f64 eps))
(-.f64 (cos.f64 (+.f64 x eps)) (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)))
(-.f64 (-.f64 (cos.f64 (+.f64 x eps)) #s(literal 1 binary64)) (.f64 x (.f64 x #s(literal -1/2 binary64))))
(.f64 (.f64 (*.f64 eps #s(literal 1/2 binary64)) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) #s(literal -2 binary64))
(.f64 (.f64 (.f64 eps (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64))) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) #s(literal -2 binary64))
(.f64 (.f64 (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64))) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) #s(literal -2 binary64))
(/.f64 (.f64 #s(literal 1/2 binary64) (.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal -2 binary64))) (/.f64 #s(literal 1 binary64) eps))
(.f64 (.f64 (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 eps (*.f64 eps #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64))) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) #s(literal -2 binary64))

Outputs

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

Calls

3 calls:

8.0ms	eps
7.0ms	x
6.0ms	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))

Results

Accuracy	Segments	Branch
99.2%	1	`x`
99.2%	1	`eps`
99.2%	1	`(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))`

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes22.0ms (0.1%)

Memory

-32.1MiB live, 48.7MiB allocated

Counts

25 → 1

Calls

Call 1

Inputs
#s(literal 0 binary64)
(+.f64 #s(literal 1 binary64) #s(literal -1 binary64))
(*.f64 eps (neg.f64 x))
(.f64 #s(literal 1/2 binary64) (.f64 x x))
(.f64 eps (.f64 eps #s(literal -1/2 binary64)))
(.f64 eps (-.f64 (.f64 eps #s(literal -1/2 binary64)) x))
(*.f64 eps (fma.f64 eps #s(literal -1/2 binary64) (neg.f64 x)))
(fma.f64 x (neg.f64 eps) (.f64 eps (.f64 eps #s(literal -1/2 binary64))))
(.f64 x (.f64 #s(literal 1/4 binary64) (.f64 x (.f64 eps eps))))
(.f64 (.f64 eps eps) (fma.f64 x (*.f64 x #s(literal 1/4 binary64)) #s(literal -1/2 binary64)))
(.f64 eps (fma.f64 x (fma.f64 x (fma.f64 eps #s(literal 1/4 binary64) (.f64 x #s(literal 1/6 binary64))) #s(literal -1 binary64)) (*.f64 eps #s(literal -1/2 binary64))))
(fma.f64 x (fma.f64 x (.f64 #s(literal 1/4 binary64) (.f64 eps eps)) (neg.f64 eps)) (.f64 eps (.f64 eps #s(literal -1/2 binary64))))
(fma.f64 eps (-.f64 (.f64 eps #s(literal -1/2 binary64)) x) (.f64 x (.f64 x (.f64 eps (fma.f64 eps #s(literal 1/4 binary64) (*.f64 x #s(literal 1/6 binary64)))))))
(.f64 (.f64 x x) (-.f64 (.f64 #s(literal 1/4 binary64) (.f64 eps eps)) (/.f64 (fma.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 eps eps) x) eps) x)))
(+.f64 (cos.f64 eps) #s(literal -1 binary64))
(-.f64 (cos.f64 (+.f64 x eps)) #s(literal 1 binary64))
(*.f64 (sin.f64 x) (neg.f64 eps))
(.f64 eps (-.f64 (.f64 eps #s(literal -1/2 binary64)) (sin.f64 x)))
(*.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (neg.f64 eps))
(-.f64 (cos.f64 (+.f64 x eps)) (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)))
(-.f64 (-.f64 (cos.f64 (+.f64 x eps)) #s(literal 1 binary64)) (.f64 x (.f64 x #s(literal -1/2 binary64))))
(.f64 (.f64 (*.f64 eps #s(literal 1/2 binary64)) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) #s(literal -2 binary64))
(.f64 (.f64 (.f64 eps (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64))) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) #s(literal -2 binary64))
(.f64 (.f64 (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64))) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) #s(literal -2 binary64))
(/.f64 (.f64 #s(literal 1/2 binary64) (.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal -2 binary64))) (/.f64 #s(literal 1 binary64) eps))

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

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
99.1%	1	`x`
99.1%	1	`eps`
99.1%	1	`(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))`

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes19.0ms (0.1%)

Memory

0.7MiB live, 40.1MiB allocated

Counts

22 → 1

Calls

Call 1

Inputs
#s(literal 0 binary64)
(+.f64 #s(literal 1 binary64) #s(literal -1 binary64))
(*.f64 eps (neg.f64 x))
(.f64 #s(literal 1/2 binary64) (.f64 x x))
(.f64 eps (.f64 eps #s(literal -1/2 binary64)))
(.f64 eps (-.f64 (.f64 eps #s(literal -1/2 binary64)) x))
(*.f64 eps (fma.f64 eps #s(literal -1/2 binary64) (neg.f64 x)))
(fma.f64 x (neg.f64 eps) (.f64 eps (.f64 eps #s(literal -1/2 binary64))))
(.f64 x (.f64 #s(literal 1/4 binary64) (.f64 x (.f64 eps eps))))
(.f64 (.f64 eps eps) (fma.f64 x (*.f64 x #s(literal 1/4 binary64)) #s(literal -1/2 binary64)))
(.f64 eps (fma.f64 x (fma.f64 x (fma.f64 eps #s(literal 1/4 binary64) (.f64 x #s(literal 1/6 binary64))) #s(literal -1 binary64)) (*.f64 eps #s(literal -1/2 binary64))))
(fma.f64 x (fma.f64 x (.f64 #s(literal 1/4 binary64) (.f64 eps eps)) (neg.f64 eps)) (.f64 eps (.f64 eps #s(literal -1/2 binary64))))
(fma.f64 eps (-.f64 (.f64 eps #s(literal -1/2 binary64)) x) (.f64 x (.f64 x (.f64 eps (fma.f64 eps #s(literal 1/4 binary64) (*.f64 x #s(literal 1/6 binary64)))))))
(.f64 (.f64 x x) (-.f64 (.f64 #s(literal 1/4 binary64) (.f64 eps eps)) (/.f64 (fma.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 eps eps) x) eps) x)))
(+.f64 (cos.f64 eps) #s(literal -1 binary64))
(-.f64 (cos.f64 (+.f64 x eps)) #s(literal 1 binary64))
(*.f64 (sin.f64 x) (neg.f64 eps))
(.f64 eps (-.f64 (.f64 eps #s(literal -1/2 binary64)) (sin.f64 x)))
(*.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (neg.f64 eps))
(-.f64 (cos.f64 (+.f64 x eps)) (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)))
(-.f64 (-.f64 (cos.f64 (+.f64 x eps)) #s(literal 1 binary64)) (.f64 x (.f64 x #s(literal -1/2 binary64))))
(.f64 (.f64 (*.f64 eps #s(literal 1/2 binary64)) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) #s(literal -2 binary64))

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

Calls

3 calls:

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

Results

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

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes17.0ms (0.1%)

Memory

6.7MiB live, 45.2MiB allocated

Counts

18 → 1

Calls

Call 1

Inputs
#s(literal 0 binary64)
(+.f64 #s(literal 1 binary64) #s(literal -1 binary64))
(*.f64 eps (neg.f64 x))
(.f64 #s(literal 1/2 binary64) (.f64 x x))
(.f64 eps (.f64 eps #s(literal -1/2 binary64)))
(.f64 eps (-.f64 (.f64 eps #s(literal -1/2 binary64)) x))
(*.f64 eps (fma.f64 eps #s(literal -1/2 binary64) (neg.f64 x)))
(fma.f64 x (neg.f64 eps) (.f64 eps (.f64 eps #s(literal -1/2 binary64))))
(.f64 x (.f64 #s(literal 1/4 binary64) (.f64 x (.f64 eps eps))))
(.f64 (.f64 eps eps) (fma.f64 x (*.f64 x #s(literal 1/4 binary64)) #s(literal -1/2 binary64)))
(.f64 eps (fma.f64 x (fma.f64 x (fma.f64 eps #s(literal 1/4 binary64) (.f64 x #s(literal 1/6 binary64))) #s(literal -1 binary64)) (*.f64 eps #s(literal -1/2 binary64))))
(fma.f64 x (fma.f64 x (.f64 #s(literal 1/4 binary64) (.f64 eps eps)) (neg.f64 eps)) (.f64 eps (.f64 eps #s(literal -1/2 binary64))))
(fma.f64 eps (-.f64 (.f64 eps #s(literal -1/2 binary64)) x) (.f64 x (.f64 x (.f64 eps (fma.f64 eps #s(literal 1/4 binary64) (*.f64 x #s(literal 1/6 binary64)))))))
(.f64 (.f64 x x) (-.f64 (.f64 #s(literal 1/4 binary64) (.f64 eps eps)) (/.f64 (fma.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 eps eps) x) eps) x)))
(+.f64 (cos.f64 eps) #s(literal -1 binary64))
(-.f64 (cos.f64 (+.f64 x eps)) #s(literal 1 binary64))
(*.f64 (sin.f64 x) (neg.f64 eps))
(.f64 eps (-.f64 (.f64 eps #s(literal -1/2 binary64)) (sin.f64 x)))

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

Calls

3 calls:

6.0ms	x
5.0ms	eps
4.0ms	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))

Results

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

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes15.0ms (0.1%)

Memory

28.3MiB live, 28.3MiB allocated

Counts

17 → 1

Calls

Call 1

Inputs
#s(literal 0 binary64)
(+.f64 #s(literal 1 binary64) #s(literal -1 binary64))
(*.f64 eps (neg.f64 x))
(.f64 #s(literal 1/2 binary64) (.f64 x x))
(.f64 eps (.f64 eps #s(literal -1/2 binary64)))
(.f64 eps (-.f64 (.f64 eps #s(literal -1/2 binary64)) x))
(*.f64 eps (fma.f64 eps #s(literal -1/2 binary64) (neg.f64 x)))
(fma.f64 x (neg.f64 eps) (.f64 eps (.f64 eps #s(literal -1/2 binary64))))
(.f64 x (.f64 #s(literal 1/4 binary64) (.f64 x (.f64 eps eps))))
(.f64 (.f64 eps eps) (fma.f64 x (*.f64 x #s(literal 1/4 binary64)) #s(literal -1/2 binary64)))
(.f64 eps (fma.f64 x (fma.f64 x (fma.f64 eps #s(literal 1/4 binary64) (.f64 x #s(literal 1/6 binary64))) #s(literal -1 binary64)) (*.f64 eps #s(literal -1/2 binary64))))
(fma.f64 x (fma.f64 x (.f64 #s(literal 1/4 binary64) (.f64 eps eps)) (neg.f64 eps)) (.f64 eps (.f64 eps #s(literal -1/2 binary64))))
(fma.f64 eps (-.f64 (.f64 eps #s(literal -1/2 binary64)) x) (.f64 x (.f64 x (.f64 eps (fma.f64 eps #s(literal 1/4 binary64) (*.f64 x #s(literal 1/6 binary64)))))))
(.f64 (.f64 x x) (-.f64 (.f64 #s(literal 1/4 binary64) (.f64 eps eps)) (/.f64 (fma.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 eps eps) x) eps) x)))
(+.f64 (cos.f64 eps) #s(literal -1 binary64))
(-.f64 (cos.f64 (+.f64 x eps)) #s(literal 1 binary64))
(*.f64 (sin.f64 x) (neg.f64 eps))

Outputs
(fma.f64 eps (-.f64 (.f64 eps #s(literal -1/2 binary64)) x) (.f64 x (.f64 x (.f64 eps (fma.f64 eps #s(literal 1/4 binary64) (*.f64 x #s(literal 1/6 binary64)))))))

Calls

3 calls:

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

Results

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

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes12.0ms (0.1%)

Memory

-9.9MiB live, 29.6MiB allocated

Counts

12 → 1

Calls

Call 1

Inputs
#s(literal 0 binary64)
(+.f64 #s(literal 1 binary64) #s(literal -1 binary64))
(*.f64 eps (neg.f64 x))
(.f64 #s(literal 1/2 binary64) (.f64 x x))
(.f64 eps (.f64 eps #s(literal -1/2 binary64)))
(.f64 eps (-.f64 (.f64 eps #s(literal -1/2 binary64)) x))
(*.f64 eps (fma.f64 eps #s(literal -1/2 binary64) (neg.f64 x)))
(fma.f64 x (neg.f64 eps) (.f64 eps (.f64 eps #s(literal -1/2 binary64))))
(.f64 x (.f64 #s(literal 1/4 binary64) (.f64 x (.f64 eps eps))))
(.f64 (.f64 eps eps) (fma.f64 x (*.f64 x #s(literal 1/4 binary64)) #s(literal -1/2 binary64)))
(.f64 eps (fma.f64 x (fma.f64 x (fma.f64 eps #s(literal 1/4 binary64) (.f64 x #s(literal 1/6 binary64))) #s(literal -1 binary64)) (*.f64 eps #s(literal -1/2 binary64))))
(fma.f64 x (fma.f64 x (.f64 #s(literal 1/4 binary64) (.f64 eps eps)) (neg.f64 eps)) (.f64 eps (.f64 eps #s(literal -1/2 binary64))))

Outputs
(.f64 eps (fma.f64 x (fma.f64 x (fma.f64 eps #s(literal 1/4 binary64) (.f64 x #s(literal 1/6 binary64))) #s(literal -1 binary64)) (*.f64 eps #s(literal -1/2 binary64))))

Calls

3 calls:

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

Results

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

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes12.0ms (0.1%)

Memory

-16.9MiB live, 24.8MiB allocated

Counts

10 → 1

Calls

Call 1

Inputs
#s(literal 0 binary64)
(+.f64 #s(literal 1 binary64) #s(literal -1 binary64))
(*.f64 eps (neg.f64 x))
(.f64 #s(literal 1/2 binary64) (.f64 x x))
(.f64 eps (.f64 eps #s(literal -1/2 binary64)))
(.f64 eps (-.f64 (.f64 eps #s(literal -1/2 binary64)) x))
(*.f64 eps (fma.f64 eps #s(literal -1/2 binary64) (neg.f64 x)))
(fma.f64 x (neg.f64 eps) (.f64 eps (.f64 eps #s(literal -1/2 binary64))))
(.f64 x (.f64 #s(literal 1/4 binary64) (.f64 x (.f64 eps eps))))
(.f64 (.f64 eps eps) (fma.f64 x (*.f64 x #s(literal 1/4 binary64)) #s(literal -1/2 binary64)))

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

Calls

3 calls:

5.0ms	x
3.0ms	eps
3.0ms	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))

Results

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

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes8.0ms (0%)

Memory

18.9MiB live, 18.9MiB allocated

Counts

7 → 1

Calls

Call 1

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

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

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
97.2%	1	`x`
97.2%	1	`eps`
97.2%	1	`(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))`

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes7.0ms (0%)

Memory

-22.4MiB live, 17.2MiB allocated

Counts

5 → 1

Calls

Call 1

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

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

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
78.7%	1	`x`
78.7%	1	`eps`
78.7%	1	`(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))`

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes4.0ms (0%)

Memory

13.1MiB live, 13.1MiB allocated

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts

2 → 1

Calls

Call 1

Inputs
#s(literal 0 binary64)
(+.f64 #s(literal 1 binary64) #s(literal -1 binary64))

Outputs
#s(literal 0 binary64)

Calls

3 calls:

1.0ms	eps
1.0ms	x
1.0ms	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))

Results

Accuracy	Segments	Branch
53.0%	1	`eps`
53.0%	1	`(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))`
53.0%	1	`x`

Compiler

Compiled 15 to 10 computations (33.3% saved)

simplify10.0ms (0.1%)

Memory

-16.5MiB live, 23.0MiB allocated

Algorithm

1×	egg-herbie

Rules

64×	`*-commutative_binary64`
16×	`+-commutative_binary64`
16×	`sub-neg_binary64`
12×	`neg-sub0_binary64`
12×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	56	147
1	91	147
2	110	147
3	122	147
4	127	147
5	128	147

Stop Event

1×

saturated

Calls

Call 1

Inputs
(.f64 (.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) #s(literal -2 binary64))
(.f64 (.f64 (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64))) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) #s(literal -2 binary64))
(.f64 (.f64 (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 eps (*.f64 eps #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64))) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) #s(literal -2 binary64))
(.f64 (.f64 (.f64 eps (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64))) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) #s(literal -2 binary64))
(*.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (neg.f64 eps))
(.f64 eps (-.f64 (.f64 eps #s(literal -1/2 binary64)) (sin.f64 x)))
(fma.f64 eps (-.f64 (.f64 eps #s(literal -1/2 binary64)) x) (.f64 x (.f64 x (.f64 eps (fma.f64 eps #s(literal 1/4 binary64) (*.f64 x #s(literal 1/6 binary64)))))))
(.f64 eps (fma.f64 x (fma.f64 x (fma.f64 eps #s(literal 1/4 binary64) (.f64 x #s(literal 1/6 binary64))) #s(literal -1 binary64)) (*.f64 eps #s(literal -1/2 binary64))))
(fma.f64 x (neg.f64 eps) (.f64 eps (.f64 eps #s(literal -1/2 binary64))))
(.f64 eps (-.f64 (.f64 eps #s(literal -1/2 binary64)) x))
(*.f64 eps (neg.f64 x))
#s(literal 0 binary64)

Outputs
(.f64 (.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) #s(literal -2 binary64))
(.f64 (.f64 (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64))) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) #s(literal -2 binary64))
(.f64 #s(literal -2 binary64) (.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))))
(.f64 (.f64 (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 eps (*.f64 eps #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64))) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) #s(literal -2 binary64))
(.f64 #s(literal -2 binary64) (.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 eps (*.f64 eps #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))))
(.f64 (.f64 (.f64 eps (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64))) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) #s(literal -2 binary64))
(.f64 #s(literal -2 binary64) (.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (.f64 eps (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)))))
(*.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (neg.f64 eps))
(.f64 eps (-.f64 (.f64 eps #s(literal -1/2 binary64)) (sin.f64 x)))
(fma.f64 eps (-.f64 (.f64 eps #s(literal -1/2 binary64)) x) (.f64 x (.f64 x (.f64 eps (fma.f64 eps #s(literal 1/4 binary64) (*.f64 x #s(literal 1/6 binary64)))))))
(.f64 eps (fma.f64 x (fma.f64 x (fma.f64 eps #s(literal 1/4 binary64) (.f64 x #s(literal 1/6 binary64))) #s(literal -1 binary64)) (*.f64 eps #s(literal -1/2 binary64))))
(fma.f64 x (neg.f64 eps) (.f64 eps (.f64 eps #s(literal -1/2 binary64))))
(.f64 eps (-.f64 (.f64 eps #s(literal -1/2 binary64)) x))
(*.f64 eps (neg.f64 x))
#s(literal 0 binary64)

soundness1.3s (7%)

Memory

1.2MiB live, 882.8MiB allocated

Rules

14 158×	`lower-fma.f64`
14 158×	`lower-fma.f32`
13 614×	`lower-fma.f64`
13 614×	`lower-fma.f32`
12 352×	`lower-fma.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	16
0	10	16
1	54	16
2	380	16
3	4694	16
0	8209	16
0	422	4073
1	1298	3982
2	3586	3906
0	8100	3640
0	37	172
0	69	168
1	213	154
2	1486	152
0	8942	147
0	621	5490
1	1946	5245
2	5534	5151
0	8293	4821
0	105	498
1	277	495
2	609	495
3	2398	494
4	7880	494
0	8026	474
0	423	3730
1	1320	3624
2	3646	3538
0	8072	3277

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×	node limit
1×	iter limit

Compiler

Compiled 505 to 302 computations (40.2% saved)

preprocess71.0ms (0.4%)

Memory: 32.4MiB live, 71.4MiB allocated
Compiler: Compiled 384 to 174 computations (54.7% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

Iter	Nodes	Cost
0	18	41
1	38	37
2	81	35
3	152	35
4	278	35
5	370	35
6	448	35
7	485	35
8	531	35
9	546	35
10	554	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	41
1	38	37
2	81	35
3	152	35
4	278	35
5	370	35
6	448	35
7	485	35
8	531	35
9	546	35
10	554	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

analyze43.0ms (0.2%)

sample9.7s (53.6%)

preprocess94.0ms (0.5%)

explain258.0ms (1.4%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify11.0ms (0.1%)

localize108.0ms (0.6%)

series4.0ms (0%)

rewrite337.0ms (1.9%)

simplify386.0ms (2.1%)

eval39.0ms (0.2%)

prune56.0ms (0.3%)

simplify356.0ms (2%)

localize540.0ms (3%)

series107.0ms (0.6%)

rewrite257.0ms (1.4%)

simplify725.0ms (4%)

eval253.0ms (1.4%)

prune195.0ms (1.1%)

simplify321.0ms (1.8%)

localize139.0ms (0.8%)

series69.0ms (0.4%)

rewrite370.0ms (2%)

simplify446.0ms (2.5%)

eval116.0ms (0.6%)

prune83.0ms (0.5%)

simplify215.0ms (1.2%)

localize125.0ms (0.7%)

series33.0ms (0.2%)

rewrite284.0ms (1.6%)

simplify358.0ms (2%)

eval166.0ms (0.9%)

prune304.0ms (1.7%)

regimes69.0ms (0.4%)

regimes42.0ms (0.2%)

regimes22.0ms (0.1%)

regimes22.0ms (0.1%)

regimes19.0ms (0.1%)

regimes17.0ms (0.1%)

regimes15.0ms (0.1%)

regimes12.0ms (0.1%)

regimes12.0ms (0.1%)

regimes8.0ms (0%)

regimes7.0ms (0%)

regimes4.0ms (0%)

simplify10.0ms (0.1%)

soundness1.3s (7%)

preprocess71.0ms (0.4%)

end0.0ms (0%)

Profiling

Iter	Nodes	Cost
0	18	41
1	38	37
2	81	35
3	152	35
4	278	35
5	370	35
6	448	35
7	485	35
8	531	35
9	546	35
10	554	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