Metrics for 2cos (problem 3.3.5)

analyze43.0ms (0.2%)

Memory

-18.6MiB live, 97.0MiB allocated

Algorithm

1×

Search

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

Compiler

Compiled 27 to 19 computations (29.6% saved)

sample9.6s (50.7%)

Memory

-76.4MiB live, 11 564.5MiB allocated

Samples

3.8s	25 796×	0	invalid
3.6s	5 673×	2	valid
514.0ms	2 445×	1	valid
17.0ms	138×	0	valid

Precisions

Click to see histograms. Total time spent on operations: 6.1s

ival-cos: 2.7s (43.3% of total)

const: 950.0ms (15.5% of total)

adjust: 508.0ms (8.3% of total)

ival-mult: 356.0ms (5.8% of total)

ival-<=: 352.0ms (5.7% of total)

ival-sub: 350.0ms (5.7% of total)

ival-add: 288.0ms (4.7% of total)

ival-<: 273.0ms (4.5% of total)

ival-fabs: 241.0ms (3.9% of total)

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

exact: 47.0ms (0.8% of total)

ival-assert: 13.0ms (0.2% of total)

Bogosity

preprocess32.0ms (0.2%)

Memory

-13.9MiB live, 61.7MiB 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))

explain243.0ms (1.3%)

Memory

-8.3MiB live, 469.6MiB allocated

FPErrors

Click to see full error table

Ground Truth	Example	Example	Subexpression
131	-	-	`(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))`
0	-	-	`eps`
0	-	-	`(+.f64 x eps)`
0	-	-	`(cos.f64 x)`
0	-	-	`(cos.f64 (+.f64 x eps))`
0	-	-	`x`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`-.f64`	`(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))`	cancellation	131	0

Confusion

	Predicted +	Predicted -
+	131	1
-	0	124

Precision

1.0

Recall

0.9924242424242424

Confusion?

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

Precision?

1.0

Recall?

0.9924242424242424

Freqs

test

number	freq
0	125
1	131

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

146.0ms	360×	2	valid
38.0ms	144×	1	valid
1.0ms	8×	0	valid

Compiler

Compiled 58 to 28 computations (51.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 160.0ms

ival-cos: 111.0ms (69.4% of total)

ival-add: 23.0ms (14.4% of total)

adjust: 18.0ms (11.3% of total)

ival-sub: 7.0ms (4.4% of total)

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

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

eval0.0ms (0%)

Memory: 0.6MiB live, 0.6MiB allocated
Compiler: Compiled 2 to 2 computations (0% saved)

prune1.0ms (0%)

Memory

2.3MiB live, 2.3MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	53.2%	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))

Compiler

Compiled 9 to 6 computations (33.3% saved)

simplify9.0ms (0%)

Memory

25.1MiB live, 25.1MiB 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)

localize137.0ms (0.7%)

Memory

4.0MiB live, 199.2MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(+.f64 x eps)
✓	accuracy	100.0%	(cos.f64 x)
✓	accuracy	100.0%	(cos.f64 (+.f64 x eps))
✓	accuracy	53.2%	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))

Samples

116.0ms	180×	2	valid
9.0ms	72×	1	valid
0.0ms	4×	0	valid

Compiler

Compiled 20 to 8 computations (60% saved)

Precisions

Click to see histograms. Total time spent on operations: 91.0ms

ival-cos: 77.0ms (85% of total)

adjust: 9.0ms (9.9% of total)

ival-sub: 3.0ms (3.3% of total)

ival-add: 2.0ms (2.2% of total)

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

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

series4.0ms (0%)

Memory

9.4MiB live, 9.4MiB 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	@	0	(- (cos (+ x eps)) (cos x))
0.0ms	x	@	-inf	(- (cos (+ x eps)) (cos x))
0.0ms	x	@	inf	(+ x eps)

rewrite294.0ms (1.5%)

Memory

-0.7MiB live, 622.7MiB 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))

simplify384.0ms (2%)

Memory

-6.7MiB live, 747.9MiB 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)

eval37.0ms (0.2%)

Memory: 2.5MiB live, 120.0MiB allocated
Compiler: Compiled 7 945 to 876 computations (89% saved)

prune45.0ms (0.2%)

Memory

-16.7MiB live, 125.1MiB allocated

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	294	12	306
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	294	13	307

Accuracy

99.8%

Counts

307 → 13

Alt Table

Click to see full alt table

Status	Accuracy	Program
	53.2%	(fma.f64 (cos.f64 x) (cos.f64 eps) (neg.f64 (fma.f64 (sin.f64 x) (sin.f64 eps) (cos.f64 x))))
	53.2%	(/.f64 (/.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))) #s(literal 2 binary64)) (.f64 (cos.f64 (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64))) (cos.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64)))))
	53.2%	(-.f64 (/.f64 (*.f64 (cos.f64 (-.f64 x eps)) (cos.f64 (+.f64 x eps))) (cos.f64 (-.f64 x eps))) (cos.f64 x))
	52.4%	(-.f64 (cos.f64 (+.f64 x eps)) (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)))
▶	52.3%	(-.f64 (cos.f64 (+.f64 x eps)) (fma.f64 x (.f64 x (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal -1/2 binary64))) #s(literal 1 binary64)))
	51.9%	(-.f64 (cos.f64 (+.f64 x eps)) (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)))
✓	53.2%	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
	51.7%	(-.f64 (cos.f64 (+.f64 x eps)) #s(literal 1 binary64))
▶	51.7%	(+.f64 (cos.f64 eps) #s(literal -1 binary64))
▶	99.7%	(.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))
▶	78.4%	(*.f64 (sin.f64 x) (neg.f64 eps))
	99.4%	(.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))))
▶	99.1%	(.f64 eps (-.f64 (.f64 eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x)))

Compiler

Compiled 415 to 270 computations (34.9% saved)

simplify362.0ms (1.9%)

Memory

18.2MiB live, 491.0MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 17 expressions of interest:

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

14 798×	`lower-fma.f32`
14 794×	`lower-fma.f64`
3 518×	`lower-*.f32`
3 498×	`lower-*.f64`
2 500×	`lower-+.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	34	186
0	61	176
1	106	176
2	251	176
3	547	168
4	1049	168
5	2411	168
6	4551	168
7	7369	168
0	8114	163

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

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

localize232.0ms (1.2%)

Memory

5.5MiB live, 282.2MiB allocated

Localize:

Found 17 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(sin.f64 x)
✓	accuracy	100.0%	(cos.f64 x)
✓	accuracy	100.0%	(-.f64 (.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x))
✓	accuracy	99.8%	(.f64 eps (-.f64 (.f64 eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x)))
✓	accuracy	100.0%	(fma.f64 x (.f64 x (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal -1/2 binary64))) #s(literal 1 binary64))
✓	accuracy	100.0%	(fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal -1/2 binary64))
✓	accuracy	100.0%	(cos.f64 (+.f64 x eps))
✓	accuracy	53.4%	(-.f64 (cos.f64 (+.f64 x eps)) (fma.f64 x (.f64 x (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal -1/2 binary64))) #s(literal 1 binary64)))
✓	accuracy	100.0%	(sin.f64 x)
✓	accuracy	100.0%	(neg.f64 eps)
✓	accuracy	100.0%	(*.f64 (sin.f64 x) (neg.f64 eps))
✓	accuracy	100.0%	(cos.f64 eps)
✓	accuracy	53.6%	(+.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	99.9%	(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

157.0ms	184×	2	valid
31.0ms	69×	1	valid
1.0ms	3×	0	valid

Compiler

Compiled 194 to 38 computations (80.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 151.0ms

ival-cos: 55.0ms (36.5% of total)

adjust: 33.0ms (21.9% of total)

ival-mult: 25.0ms (16.6% of total)

ival-add: 20.0ms (13.3% of total)

ival-sin: 6.0ms (4% of total)

const: 5.0ms (3.3% of total)

ival-sub: 5.0ms (3.3% of total)

exact: 1.0ms (0.7% of total)

ival-neg: 1.0ms (0.7% of total)

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

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

series34.0ms (0.2%)

Memory

-11.0MiB live, 31.6MiB allocated

Counts

21 → 396

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

Outputs
#<alt (* 1/2 eps)>
#<alt (+ x (* 1/2 eps))>
#<alt (+ x (* 1/2 eps))>
#<alt (+ x (* 1/2 eps))>
#<alt x>
#<alt (* x (+ 1 (* 1/2 (/ eps x))))>
#<alt (* x (+ 1 (* 1/2 (/ eps x))))>
#<alt (* x (+ 1 (* 1/2 (/ eps x))))>
#<alt x>
#<alt (* -1 (* x (- (* -1/2 (/ eps x)) 1)))>
#<alt (* -1 (* x (- (* -1/2 (/ eps x)) 1)))>
#<alt (* -1 (* x (- (* -1/2 (/ eps x)) 1)))>
#<alt x>
#<alt (+ x (* 1/2 eps))>
#<alt (+ x (* 1/2 eps))>
#<alt (+ x (* 1/2 eps))>
#<alt (* 1/2 eps)>
#<alt (* eps (+ 1/2 (/ x eps)))>
#<alt (* eps (+ 1/2 (/ x eps)))>
#<alt (* eps (+ 1/2 (/ x eps)))>
#<alt (* 1/2 eps)>
#<alt (* -1 (* eps (- (* -1 (/ x eps)) 1/2)))>
#<alt (* -1 (* eps (- (* -1 (/ x eps)) 1/2)))>
#<alt (* -1 (* eps (- (* -1 (/ x eps)) 1/2)))>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt (* -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 (* -1 (* eps x))>
#<alt (* x (+ (* -1 eps) (* 1/6 (* eps (pow x 2)))))>
#<alt (* x (+ (* -1 eps) (* (pow x 2) (+ (* -1/120 (* eps (pow x 2))) (* 1/6 eps)))))>
#<alt (* x (+ (* -1 eps) (* (pow x 2) (+ (* 1/6 eps) (* (pow x 2) (+ (* -1/120 eps) (* 1/5040 (* eps (pow x 2)))))))))>
#<alt (* -1 (* eps (sin x)))>
#<alt (* -1 (* eps (sin x)))>
#<alt (* -1 (* eps (sin x)))>
#<alt (* -1 (* eps (sin x)))>
#<alt (* -1 (* eps (sin x)))>
#<alt (* -1 (* eps (sin x)))>
#<alt (* -1 (* eps (sin x)))>
#<alt (* -1 (* eps (sin x)))>
#<alt (* -1 (* eps (sin x)))>
#<alt (* -1 (* eps (sin x)))>
#<alt (* -1 (* eps (sin x)))>
#<alt (* -1 (* eps (sin x)))>
#<alt (* -1 (* eps (sin x)))>
#<alt (* -1 (* eps (sin x)))>
#<alt (* -1 (* eps (sin x)))>
#<alt (* -1 (* eps (sin x)))>
#<alt (* -1 (* eps (sin x)))>
#<alt (* -1 (* eps (sin x)))>
#<alt (* -1 (* eps (sin x)))>
#<alt (* -1 (* eps (sin x)))>
#<alt x>
#<alt (* x (+ 1 (* -1/6 (pow x 2))))>
#<alt (* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))))>
#<alt (* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))>
#<alt (sin x)>
#<alt (sin x)>
#<alt (sin x)>
#<alt (sin x)>
#<alt (sin x)>
#<alt (sin x)>
#<alt (sin x)>
#<alt (sin x)>
#<alt (* -1 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 (- (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 (* -1/24 (pow x 4))>
#<alt (* (pow x 4) (- (* 1/2 (/ 1 (pow x 2))) 1/24))>
#<alt (* (pow x 4) (- (+ (* 1/2 (/ 1 (pow x 2))) (/ (cos (+ eps x)) (pow x 4))) (+ 1/24 (/ 1 (pow x 4)))))>
#<alt (* (pow x 4) (- (+ (* 1/2 (/ 1 (pow x 2))) (/ (cos (+ eps x)) (pow x 4))) (+ 1/24 (/ 1 (pow x 4)))))>
#<alt (* -1/24 (pow x 4))>
#<alt (* (pow x 4) (- (* 1/2 (/ 1 (pow x 2))) 1/24))>
#<alt (* (pow x 4) (- (+ (* 1/2 (/ 1 (pow x 2))) (/ (cos (- eps (* -1 x))) (pow x 4))) (+ 1/24 (/ 1 (pow x 4)))))>
#<alt (* (pow x 4) (- (+ (* 1/2 (/ 1 (pow x 2))) (/ (cos (- eps (* -1 x))) (pow x 4))) (+ 1/24 (/ 1 (pow x 4)))))>
#<alt (- (cos x) (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2))))>
#<alt (- (+ (cos x) (* -1 (* eps (sin x)))) (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2))))>
#<alt (- (+ (cos x) (* eps (- (* -1/2 (* eps (cos x))) (sin x)))) (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2))))>
#<alt (- (+ (cos x) (* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x)))) (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2))))>
#<alt (- (cos (+ eps x)) (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2))))>
#<alt (- (cos (+ eps x)) (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2))))>
#<alt (- (cos (+ eps x)) (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2))))>
#<alt (- (cos (+ eps x)) (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2))))>
#<alt (- (cos (- x (* -1 eps))) (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2))))>
#<alt (- (cos (- x (* -1 eps))) (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2))))>
#<alt (- (cos (- x (* -1 eps))) (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2))))>
#<alt (- (cos (- x (* -1 eps))) (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2))))>
#<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 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))>
#<alt (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))>
#<alt (* 1/24 (pow x 4))>
#<alt (* (pow x 4) (- 1/24 (* 1/2 (/ 1 (pow x 2)))))>
#<alt (* (pow x 4) (- (+ 1/24 (/ 1 (pow x 4))) (* 1/2 (/ 1 (pow x 2)))))>
#<alt (* (pow x 4) (- (+ 1/24 (/ 1 (pow x 4))) (* 1/2 (/ 1 (pow x 2)))))>
#<alt (* 1/24 (pow x 4))>
#<alt (* (pow x 4) (- 1/24 (* 1/2 (/ 1 (pow x 2)))))>
#<alt (* (pow x 4) (- (+ 1/24 (/ 1 (pow x 4))) (* 1/2 (/ 1 (pow x 2)))))>
#<alt (* (pow x 4) (- (+ 1/24 (/ 1 (pow x 4))) (* 1/2 (/ 1 (pow x 2)))))>
#<alt (* -1 (* eps (sin x)))>
#<alt (* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))>
#<alt (* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))>
#<alt (* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))>
#<alt (* -1/2 (* (pow eps 2) (cos x)))>
#<alt (* (pow eps 2) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))>
#<alt (* (pow eps 2) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))>
#<alt (* (pow eps 2) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))>
#<alt (* -1/2 (* (pow eps 2) (cos x)))>
#<alt (* (pow eps 2) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))>
#<alt (* (pow eps 2) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))>
#<alt (* (pow eps 2) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))>
#<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) (* x (+ (* 1/6 (* eps x)) (* 1/4 (pow eps 2)))))))>
#<alt (* eps (- (* -1/2 (* eps (cos x))) (sin x)))>
#<alt (* eps (- (* -1/2 (* eps (cos x))) (sin x)))>
#<alt (* eps (- (* -1/2 (* eps (cos x))) (sin x)))>
#<alt (* eps (- (* -1/2 (* eps (cos x))) (sin x)))>
#<alt (* eps (- (* -1/2 (* eps (cos x))) (sin x)))>
#<alt (* eps (- (* -1/2 (* eps (cos x))) (sin x)))>
#<alt (* eps (- (* -1/2 (* eps (cos x))) (sin x)))>
#<alt (* eps (- (* -1/2 (* eps (cos x))) (sin x)))>
#<alt (* -1 (sin x))>
#<alt (- (* -1/2 (* eps (cos x))) (sin x))>
#<alt (- (* -1/2 (* eps (cos x))) (sin x))>
#<alt (- (* -1/2 (* eps (cos x))) (sin x))>
#<alt (* -1/2 (* eps (cos x)))>
#<alt (* eps (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))>
#<alt (* eps (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))>
#<alt (* eps (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))>
#<alt (* -1/2 (* eps (cos x)))>
#<alt (* -1 (* eps (+ (* 1/2 (cos x)) (/ (sin x) eps))))>
#<alt (* -1 (* eps (+ (* 1/2 (cos x)) (/ (sin x) eps))))>
#<alt (* -1 (* eps (+ (* 1/2 (cos x)) (/ (sin x) eps))))>
#<alt (* -1/2 eps)>
#<alt (+ (* -1 x) (* -1/2 eps))>
#<alt (+ (* -1/2 eps) (* x (- (* 1/4 (* eps x)) 1)))>
#<alt (+ (* -1/2 eps) (* x (- (* x (+ (* 1/6 x) (* 1/4 eps))) 1)))>
#<alt (- (* -1/2 (* eps (cos x))) (sin x))>
#<alt (- (* -1/2 (* eps (cos x))) (sin x))>
#<alt (- (* -1/2 (* eps (cos x))) (sin x))>
#<alt (- (* -1/2 (* eps (cos x))) (sin x))>
#<alt (- (* -1/2 (* eps (cos x))) (sin x))>
#<alt (- (* -1/2 (* eps (cos x))) (sin x))>
#<alt (- (* -1/2 (* eps (cos x))) (sin x))>
#<alt (- (* -1/2 (* eps (cos x))) (sin x))>
#<alt (* -1/2 (* eps (cos x)))>
#<alt (* -1/2 (* eps (cos x)))>
#<alt (* -1/2 (* eps (cos x)))>
#<alt (* -1/2 (* eps (cos x)))>
#<alt (* -1/2 (* eps (cos x)))>
#<alt (* -1/2 (* eps (cos x)))>
#<alt (* -1/2 (* eps (cos x)))>
#<alt (* -1/2 (* eps (cos x)))>
#<alt (* -1/2 (* eps (cos x)))>
#<alt (* -1/2 (* eps (cos x)))>
#<alt (* -1/2 (* eps (cos x)))>
#<alt (* -1/2 (* eps (cos x)))>
#<alt (* -1/2 eps)>
#<alt (+ (* -1/2 eps) (* 1/4 (* eps (pow x 2))))>
#<alt (+ (* -1/2 eps) (* (pow x 2) (+ (* -1/48 (* eps (pow x 2))) (* 1/4 eps))))>
#<alt (+ (* -1/2 eps) (* (pow x 2) (+ (* 1/4 eps) (* (pow x 2) (+ (* -1/48 eps) (* 1/1440 (* eps (pow x 2))))))))>
#<alt (* -1/2 (* eps (cos x)))>
#<alt (* -1/2 (* eps (cos x)))>
#<alt (* -1/2 (* eps (cos x)))>
#<alt (* -1/2 (* eps (cos x)))>
#<alt (* -1/2 (* eps (cos x)))>
#<alt (* -1/2 (* eps (cos x)))>
#<alt (* -1/2 (* eps (cos x)))>
#<alt (* -1/2 (* eps (cos x)))>
#<alt -1/2>
#<alt (- (* 1/4 (pow x 2)) 1/2)>
#<alt (- (* (pow x 2) (+ 1/4 (* -1/48 (pow x 2)))) 1/2)>
#<alt (- (* (pow x 2) (+ 1/4 (* (pow x 2) (- (* 1/1440 (pow x 2)) 1/48)))) 1/2)>
#<alt (* -1/2 (cos x))>
#<alt (* -1/2 (cos x))>
#<alt (* -1/2 (cos x))>
#<alt (* -1/2 (cos x))>
#<alt (* -1/2 (cos x))>
#<alt (* -1/2 (cos x))>
#<alt (* -1/2 (cos x))>
#<alt (* -1/2 (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>
#<alt (- (* 1/24 (pow x 2)) 1/2)>
#<alt (- (* 1/24 (pow x 2)) 1/2)>
#<alt (- (* 1/24 (pow x 2)) 1/2)>
#<alt (* 1/24 (pow x 2))>
#<alt (* (pow x 2) (- 1/24 (* 1/2 (/ 1 (pow x 2)))))>
#<alt (* (pow x 2) (- 1/24 (* 1/2 (/ 1 (pow x 2)))))>
#<alt (* (pow x 2) (- 1/24 (* 1/2 (/ 1 (pow x 2)))))>
#<alt (* 1/24 (pow x 2))>
#<alt (* (pow x 2) (- 1/24 (* 1/2 (/ 1 (pow x 2)))))>
#<alt (* (pow x 2) (- 1/24 (* 1/2 (/ 1 (pow x 2)))))>
#<alt (* (pow x 2) (- 1/24 (* 1/2 (/ 1 (pow x 2)))))>
#<alt 1>
#<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

99 calls:

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

rewrite367.0ms (1.9%)

Memory

21.4MiB live, 490.7MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

4 532×	`lower-*.f32`
4 512×	`lower-*.f64`
4 460×	`lower-fma.f32`
4 456×	`lower-fma.f64`
4 180×	`lower-/.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	34	142
0	61	136
1	212	136
2	1731	136
0	8625	131

Stop Event

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

Counts

21 → 638

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

Outputs
(+.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))
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(/.f64 (fma.f64 (-.f64 (.f64 eps (.f64 eps eps)) #s(literal 0 binary64)) (-.f64 x x) (.f64 (.f64 eps eps) (-.f64 (.f64 x x) (.f64 x x)))) (.f64 (.f64 eps eps) (-.f64 x x)))
(/.f64 (fma.f64 (neg.f64 (.f64 eps eps)) (fma.f64 x x (-.f64 (.f64 x x) (.f64 x x))) (.f64 (neg.f64 eps) (fma.f64 x (.f64 x x) (.f64 x (.f64 x x))))) (.f64 (neg.f64 eps) (fma.f64 x x (-.f64 (.f64 x x) (.f64 x x)))))
(/.f64 (fma.f64 (neg.f64 (.f64 eps eps)) (-.f64 x x) (.f64 (neg.f64 eps) (-.f64 (.f64 x x) (.f64 x x)))) (*.f64 (neg.f64 eps) (-.f64 x x)))
(/.f64 (fma.f64 (-.f64 #s(literal 0 binary64) (.f64 eps eps)) (fma.f64 x x (-.f64 (.f64 x x) (.f64 x x))) (.f64 (neg.f64 eps) (fma.f64 x (.f64 x x) (.f64 x (.f64 x x))))) (.f64 (neg.f64 eps) (fma.f64 x x (-.f64 (.f64 x x) (.f64 x x)))))
(/.f64 (fma.f64 (-.f64 #s(literal 0 binary64) (.f64 eps eps)) (-.f64 x x) (.f64 (neg.f64 eps) (-.f64 (.f64 x x) (.f64 x x)))) (*.f64 (neg.f64 eps) (-.f64 x x)))
(/.f64 (fma.f64 (neg.f64 (.f64 eps (.f64 eps eps))) (fma.f64 x x (-.f64 (.f64 x x) (.f64 x x))) (.f64 (neg.f64 (.f64 eps eps)) (fma.f64 x (.f64 x x) (.f64 x (.f64 x x))))) (.f64 (neg.f64 (.f64 eps eps)) (fma.f64 x x (-.f64 (.f64 x x) (*.f64 x x)))))
(/.f64 (fma.f64 (neg.f64 (.f64 eps (.f64 eps eps))) (-.f64 x x) (.f64 (neg.f64 (.f64 eps eps)) (-.f64 (.f64 x x) (.f64 x x)))) (.f64 (neg.f64 (.f64 eps 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 eps (.f64 eps 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 eps (*.f64 eps eps))))
(/.f64 (fma.f64 (fma.f64 x (.f64 x x) (.f64 x (.f64 x x))) (.f64 eps eps) (.f64 (fma.f64 x x (-.f64 (.f64 x x) (.f64 x x))) (.f64 eps (.f64 eps eps)))) (.f64 (fma.f64 x x (-.f64 (.f64 x x) (.f64 x x))) (*.f64 eps eps)))
(/.f64 (fma.f64 (fma.f64 x (.f64 x x) (.f64 x (.f64 x x))) eps (.f64 (fma.f64 x x (-.f64 (.f64 x x) (.f64 x x))) (.f64 eps eps))) (.f64 (fma.f64 x x (-.f64 (.f64 x x) (.f64 x x))) eps))
(/.f64 (fma.f64 (fma.f64 x (.f64 x x) (.f64 x (.f64 x x))) (.f64 eps eps) (.f64 (fma.f64 x x (-.f64 (.f64 x x) (.f64 x x))) (-.f64 (.f64 eps (.f64 eps eps)) #s(literal 0 binary64)))) (.f64 (fma.f64 x x (-.f64 (.f64 x x) (.f64 x x))) (*.f64 eps eps)))
(/.f64 (fma.f64 (fma.f64 x (.f64 x x) (.f64 x (.f64 x x))) (neg.f64 eps) (.f64 (fma.f64 x x (-.f64 (.f64 x x) (.f64 x x))) (neg.f64 (.f64 eps eps)))) (.f64 (fma.f64 x x (-.f64 (.f64 x x) (.f64 x x))) (neg.f64 eps)))
(/.f64 (fma.f64 (fma.f64 x (.f64 x x) (.f64 x (.f64 x x))) (neg.f64 eps) (.f64 (fma.f64 x x (-.f64 (.f64 x x) (.f64 x x))) (-.f64 #s(literal 0 binary64) (.f64 eps eps)))) (.f64 (fma.f64 x x (-.f64 (.f64 x x) (.f64 x x))) (neg.f64 eps)))
(/.f64 (fma.f64 (fma.f64 x (.f64 x x) (.f64 x (.f64 x x))) (neg.f64 (.f64 eps eps)) (.f64 (fma.f64 x x (-.f64 (.f64 x x) (.f64 x x))) (neg.f64 (.f64 eps (.f64 eps eps))))) (.f64 (fma.f64 x x (-.f64 (.f64 x x) (.f64 x x))) (neg.f64 (*.f64 eps 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 eps (.f64 eps eps)) (.f64 (-.f64 x x) #s(literal 1 binary64))) (.f64 (-.f64 x x) (/.f64 eps (.f64 eps eps))))
(/.f64 (fma.f64 (-.f64 (.f64 x x) (.f64 x x)) (.f64 eps eps) (.f64 (-.f64 x x) (.f64 eps (.f64 eps eps)))) (.f64 (-.f64 x x) (.f64 eps eps)))
(/.f64 (fma.f64 (-.f64 (.f64 x x) (.f64 x x)) eps (.f64 (-.f64 x x) (.f64 eps eps))) (*.f64 (-.f64 x x) eps))
(/.f64 (fma.f64 (-.f64 (.f64 x x) (.f64 x x)) (.f64 eps eps) (.f64 (-.f64 x x) (-.f64 (.f64 eps (.f64 eps eps)) #s(literal 0 binary64)))) (.f64 (-.f64 x x) (.f64 eps eps)))
(/.f64 (fma.f64 (-.f64 (.f64 x x) (.f64 x x)) (neg.f64 eps) (.f64 (-.f64 x x) (neg.f64 (.f64 eps eps)))) (*.f64 (-.f64 x x) (neg.f64 eps)))
(/.f64 (fma.f64 (-.f64 (.f64 x x) (.f64 x x)) (neg.f64 eps) (.f64 (-.f64 x x) (-.f64 #s(literal 0 binary64) (.f64 eps eps)))) (*.f64 (-.f64 x x) (neg.f64 eps)))
(/.f64 (fma.f64 (-.f64 (.f64 x x) (.f64 x x)) (neg.f64 (.f64 eps eps)) (.f64 (-.f64 x x) (neg.f64 (.f64 eps (.f64 eps eps))))) (.f64 (-.f64 x x) (neg.f64 (.f64 eps eps))))
(/.f64 (-.f64 (.f64 (.f64 x x) (-.f64 x (+.f64 x eps))) (.f64 (-.f64 x (+.f64 x eps)) (.f64 (+.f64 x eps) (+.f64 x eps)))) (*.f64 (-.f64 x (+.f64 x eps)) (-.f64 x (+.f64 x eps))))
(/.f64 (neg.f64 (neg.f64 (fma.f64 (+.f64 x eps) (.f64 (+.f64 x eps) (+.f64 x eps)) (.f64 x (.f64 x x))))) (neg.f64 (neg.f64 (fma.f64 (+.f64 x eps) (-.f64 (+.f64 x eps) x) (.f64 x x)))))
(/.f64 (neg.f64 (neg.f64 (*.f64 (+.f64 x (+.f64 x eps)) (-.f64 x (+.f64 x eps))))) (neg.f64 (neg.f64 (-.f64 x (+.f64 x eps)))))
(/.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 eps) (+.f64 x eps)) (.f64 x x))) (neg.f64 (-.f64 (+.f64 x eps) 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)))))
(/.f64 (+.f64 (pow.f64 (+.f64 x (+.f64 x eps)) #s(literal 3 binary64)) #s(literal 0 binary64)) (fma.f64 (+.f64 x (+.f64 x eps)) (+.f64 x (+.f64 x eps)) (-.f64 #s(literal 0 binary64) (*.f64 (+.f64 x (+.f64 x eps)) #s(literal 0 binary64)))))
(/.f64 (+.f64 (pow.f64 (+.f64 (+.f64 x x) #s(literal 0 binary64)) #s(literal 3 binary64)) (.f64 eps (.f64 eps eps))) (fma.f64 (+.f64 (+.f64 x x) #s(literal 0 binary64)) (+.f64 (+.f64 x x) #s(literal 0 binary64)) (-.f64 (.f64 eps eps) (.f64 (+.f64 (+.f64 x x) #s(literal 0 binary64)) eps))))
(pow.f64 (/.f64 (fma.f64 (+.f64 x eps) (-.f64 (+.f64 x eps) x) (.f64 x x)) (fma.f64 (+.f64 x eps) (.f64 (+.f64 x eps) (+.f64 x eps)) (.f64 x (.f64 x x)))) #s(literal -1 binary64))
(pow.f64 (/.f64 (-.f64 x (+.f64 x eps)) (*.f64 (+.f64 x (+.f64 x eps)) (-.f64 x (+.f64 x eps)))) #s(literal -1 binary64))
(.f64 (fma.f64 (+.f64 x eps) (.f64 (+.f64 x eps) (+.f64 x eps)) (.f64 x (.f64 x x))) (/.f64 #s(literal 1 binary64) (fma.f64 (+.f64 x eps) (-.f64 (+.f64 x eps) x) (*.f64 x x))))
(.f64 (.f64 (+.f64 x (+.f64 x eps)) (-.f64 x (+.f64 x eps))) (/.f64 #s(literal 1 binary64) (-.f64 x (+.f64 x eps))))
(+.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) x)) (cos.f64 (.f64 #s(literal 1/2 binary64) (+.f64 x eps)))) (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) x)) (sin.f64 (.f64 #s(literal 1/2 binary64) (+.f64 x eps)))))
(+.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (+.f64 x eps))) (cos.f64 (.f64 #s(literal 1/2 binary64) x))) (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) (+.f64 x eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) x))))
(+.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (+.f64 x x))) (cos.f64 (.f64 eps #s(literal 1/2 binary64)))) (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) (+.f64 x x))) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))))
(+.f64 (.f64 (sin.f64 (.f64 x #s(literal 1/2 binary64))) (cos.f64 (.f64 (+.f64 x eps) #s(literal 1/2 binary64)))) (.f64 (cos.f64 (.f64 x #s(literal 1/2 binary64))) (sin.f64 (.f64 (+.f64 x eps) #s(literal 1/2 binary64)))))
(+.f64 (.f64 (sin.f64 (.f64 (+.f64 x eps) #s(literal 1/2 binary64))) (cos.f64 (.f64 x #s(literal 1/2 binary64)))) (.f64 (cos.f64 (.f64 (+.f64 x eps) #s(literal 1/2 binary64))) (sin.f64 (.f64 x #s(literal 1/2 binary64)))))
(+.f64 (.f64 (sin.f64 (.f64 (+.f64 x x) #s(literal 1/2 binary64))) (cos.f64 (.f64 eps #s(literal 1/2 binary64)))) (.f64 (cos.f64 (.f64 (+.f64 x x) #s(literal 1/2 binary64))) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))))
(sin.f64 (*.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)))
(fma.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) x)) (cos.f64 (.f64 #s(literal 1/2 binary64) (+.f64 x eps))) (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) x)) (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 x eps)))))
(fma.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (+.f64 x eps))) (cos.f64 (.f64 #s(literal 1/2 binary64) x)) (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) (+.f64 x eps))) (sin.f64 (*.f64 #s(literal 1/2 binary64) x))))
(fma.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (+.f64 x x))) (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) (+.f64 x x))) (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))))
(fma.f64 (sin.f64 (.f64 x #s(literal 1/2 binary64))) (cos.f64 (.f64 (+.f64 x eps) #s(literal 1/2 binary64))) (.f64 (cos.f64 (.f64 x #s(literal 1/2 binary64))) (sin.f64 (*.f64 (+.f64 x eps) #s(literal 1/2 binary64)))))
(fma.f64 (sin.f64 (.f64 (+.f64 x eps) #s(literal 1/2 binary64))) (cos.f64 (.f64 x #s(literal 1/2 binary64))) (.f64 (cos.f64 (.f64 (+.f64 x eps) #s(literal 1/2 binary64))) (sin.f64 (*.f64 x #s(literal 1/2 binary64)))))
(fma.f64 (sin.f64 (.f64 (+.f64 x x) #s(literal 1/2 binary64))) (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (cos.f64 (.f64 (+.f64 x x) #s(literal 1/2 binary64))) (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))))
(+.f64 #s(literal -1/2 binary64) (.f64 #s(literal 1/24 binary64) (.f64 x x)))
(+.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal -1/2 binary64))
(-.f64 (/.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/576 binary64)) (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #s(literal 1/2 binary64))) (/.f64 #s(literal 1/4 binary64) (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #s(literal 1/2 binary64))))
(-.f64 (/.f64 #s(literal 1/4 binary64) (-.f64 #s(literal -1/2 binary64) (.f64 #s(literal 1/24 binary64) (.f64 x x)))) (/.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/576 binary64)) (-.f64 #s(literal -1/2 binary64) (.f64 #s(literal 1/24 binary64) (.f64 x x)))))
(fma.f64 x (*.f64 x #s(literal 1/24 binary64)) #s(literal -1/2 binary64))
(fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal -1/2 binary64))
(fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64))
(fma.f64 (*.f64 x #s(literal 1/24 binary64)) x #s(literal -1/2 binary64))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (-.f64 (fma.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/576 binary64) #s(literal 1/4 binary64)) (.f64 (.f64 x x) #s(literal -1/48 binary64))) (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/13824 binary64)) #s(literal -1/8 binary64)))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (fma.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/576 binary64) #s(literal -1/4 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (fma.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/576 binary64) #s(literal 1/4 binary64)) (.f64 (.f64 x x) #s(literal -1/48 binary64))) (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/13824 binary64)) #s(literal -1/8 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (fma.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/576 binary64) #s(literal -1/4 binary64))))
(/.f64 (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/13824 binary64)) #s(literal -1/8 binary64)) (-.f64 (fma.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/576 binary64) #s(literal 1/4 binary64)) (.f64 (.f64 x x) #s(literal -1/48 binary64))))
(/.f64 (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/13824 binary64)) #s(literal -1/8 binary64)) (+.f64 #s(literal 1/4 binary64) (-.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/576 binary64)) (.f64 (*.f64 x x) #s(literal -1/48 binary64)))))
(/.f64 (fma.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/576 binary64) #s(literal -1/4 binary64)) (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #s(literal 1/2 binary64)))
(/.f64 (neg.f64 (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/13824 binary64)) #s(literal -1/8 binary64))) (neg.f64 (-.f64 (fma.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/576 binary64) #s(literal 1/4 binary64)) (.f64 (.f64 x x) #s(literal -1/48 binary64)))))
(/.f64 (neg.f64 (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/13824 binary64)) #s(literal -1/8 binary64))) (neg.f64 (+.f64 #s(literal 1/4 binary64) (-.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/576 binary64)) (.f64 (*.f64 x x) #s(literal -1/48 binary64))))))
(/.f64 (neg.f64 (fma.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/576 binary64) #s(literal -1/4 binary64))) (neg.f64 (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #s(literal 1/2 binary64))))
(/.f64 (-.f64 #s(literal 1/4 binary64) (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/576 binary64))) (-.f64 #s(literal -1/2 binary64) (.f64 #s(literal 1/24 binary64) (.f64 x x))))
(/.f64 (-.f64 (.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/576 binary64)) (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #s(literal 1/2 binary64))) (.f64 (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) #s(literal 1/4 binary64))) (.f64 (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (fma.f64 x (*.f64 x #s(literal 1/24 binary64)) #s(literal 1/2 binary64))))
(/.f64 (neg.f64 (neg.f64 (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/13824 binary64)) #s(literal -1/8 binary64)))) (neg.f64 (neg.f64 (-.f64 (fma.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/576 binary64) #s(literal 1/4 binary64)) (.f64 (.f64 x x) #s(literal -1/48 binary64))))))
(/.f64 (neg.f64 (neg.f64 (fma.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/576 binary64) #s(literal -1/4 binary64)))) (neg.f64 (neg.f64 (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #s(literal 1/2 binary64)))))
(/.f64 (neg.f64 (-.f64 #s(literal 1/4 binary64) (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/576 binary64)))) (neg.f64 (-.f64 #s(literal -1/2 binary64) (.f64 #s(literal 1/24 binary64) (.f64 x x)))))
(pow.f64 (/.f64 (-.f64 (fma.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/576 binary64) #s(literal 1/4 binary64)) (.f64 (.f64 x x) #s(literal -1/48 binary64))) (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/13824 binary64)) #s(literal -1/8 binary64))) #s(literal -1 binary64))
(pow.f64 (/.f64 (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (fma.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/576 binary64) #s(literal -1/4 binary64))) #s(literal -1 binary64))
(.f64 (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/13824 binary64)) #s(literal -1/8 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/576 binary64) #s(literal 1/4 binary64)) (.f64 (*.f64 x x) #s(literal -1/48 binary64)))))
(.f64 (fma.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/576 binary64) #s(literal -1/4 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 x (*.f64 x #s(literal 1/24 binary64)) #s(literal 1/2 binary64))))
(cos.f64 x)

simplify403.0ms (2.1%)

Memory

-5.7MiB live, 652.9MiB allocated

Algorithm

1×	egg-herbie

Rules

12 362×	`lower-fma.f64`
12 362×	`lower-fma.f32`
5 382×	`lower-*.f64`
5 382×	`lower-*.f32`
4 584×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	393	3454
1	1186	3321
2	3177	3276
3	7671	3276
0	8249	3063

Stop Event

1×	iter limit
1×	node limit

Counts

396 → 371

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)
(* -1 (* eps x))
(* x (+ (* -1 eps) (* 1/6 (* eps (pow x 2)))))
(* x (+ (* -1 eps) (* (pow x 2) (+ (* -1/120 (* eps (pow x 2))) (* 1/6 eps)))))
(* x (+ (* -1 eps) (* (pow x 2) (+ (* 1/6 eps) (* (pow x 2) (+ (* -1/120 eps) (* 1/5040 (* eps (pow x 2)))))))))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
x
(* x (+ 1 (* -1/6 (pow x 2))))
(* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))))
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))
(sin x)
(sin x)
(sin x)
(sin x)
(sin x)
(sin x)
(sin x)
(sin x)
(* -1 eps)
(* -1 eps)
(* -1 eps)
(* -1 eps)
(* -1 eps)
(* -1 eps)
(* -1 eps)
(* -1 eps)
(* -1 eps)
(* -1 eps)
(* -1 eps)
(* -1 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)
(* -1/24 (pow x 4))
(* (pow x 4) (- (* 1/2 (/ 1 (pow x 2))) 1/24))
(* (pow x 4) (- (+ (* 1/2 (/ 1 (pow x 2))) (/ (cos (+ eps x)) (pow x 4))) (+ 1/24 (/ 1 (pow x 4)))))
(* (pow x 4) (- (+ (* 1/2 (/ 1 (pow x 2))) (/ (cos (+ eps x)) (pow x 4))) (+ 1/24 (/ 1 (pow x 4)))))
(* -1/24 (pow x 4))
(* (pow x 4) (- (* 1/2 (/ 1 (pow x 2))) 1/24))
(* (pow x 4) (- (+ (* 1/2 (/ 1 (pow x 2))) (/ (cos (- eps (* -1 x))) (pow x 4))) (+ 1/24 (/ 1 (pow x 4)))))
(* (pow x 4) (- (+ (* 1/2 (/ 1 (pow x 2))) (/ (cos (- eps (* -1 x))) (pow x 4))) (+ 1/24 (/ 1 (pow x 4)))))
(- (cos x) (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2))))
(- (+ (cos x) (* -1 (* eps (sin x)))) (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2))))
(- (+ (cos x) (* eps (- (* -1/2 (* eps (cos x))) (sin x)))) (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2))))
(- (+ (cos x) (* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x)))) (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2))))
(- (cos (+ eps x)) (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2))))
(- (cos (+ eps x)) (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2))))
(- (cos (+ eps x)) (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2))))
(- (cos (+ eps x)) (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2))))
(- (cos (- x (* -1 eps))) (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2))))
(- (cos (- x (* -1 eps))) (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2))))
(- (cos (- x (* -1 eps))) (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2))))
(- (cos (- x (* -1 eps))) (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2))))
(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 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))
(+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))
(* 1/24 (pow x 4))
(* (pow x 4) (- 1/24 (* 1/2 (/ 1 (pow x 2)))))
(* (pow x 4) (- (+ 1/24 (/ 1 (pow x 4))) (* 1/2 (/ 1 (pow x 2)))))
(* (pow x 4) (- (+ 1/24 (/ 1 (pow x 4))) (* 1/2 (/ 1 (pow x 2)))))
(* 1/24 (pow x 4))
(* (pow x 4) (- 1/24 (* 1/2 (/ 1 (pow x 2)))))
(* (pow x 4) (- (+ 1/24 (/ 1 (pow x 4))) (* 1/2 (/ 1 (pow x 2)))))
(* (pow x 4) (- (+ 1/24 (/ 1 (pow x 4))) (* 1/2 (/ 1 (pow x 2)))))
(* -1 (* eps (sin x)))
(* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))
(* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))
(* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))
(* -1/2 (* (pow eps 2) (cos x)))
(* (pow eps 2) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))
(* (pow eps 2) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))
(* (pow eps 2) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))
(* -1/2 (* (pow eps 2) (cos x)))
(* (pow eps 2) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))
(* (pow eps 2) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))
(* (pow eps 2) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))
(* -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) (* x (+ (* 1/6 (* eps x)) (* 1/4 (pow eps 2)))))))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(* -1 (sin x))
(- (* -1/2 (* eps (cos x))) (sin x))
(- (* -1/2 (* eps (cos x))) (sin x))
(- (* -1/2 (* eps (cos x))) (sin x))
(* -1/2 (* eps (cos x)))
(* eps (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))
(* eps (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))
(* eps (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))
(* -1/2 (* eps (cos x)))
(* -1 (* eps (+ (* 1/2 (cos x)) (/ (sin x) eps))))
(* -1 (* eps (+ (* 1/2 (cos x)) (/ (sin x) eps))))
(* -1 (* eps (+ (* 1/2 (cos x)) (/ (sin x) eps))))
(* -1/2 eps)
(+ (* -1 x) (* -1/2 eps))
(+ (* -1/2 eps) (* x (- (* 1/4 (* eps x)) 1)))
(+ (* -1/2 eps) (* x (- (* x (+ (* 1/6 x) (* 1/4 eps))) 1)))
(- (* -1/2 (* eps (cos x))) (sin x))
(- (* -1/2 (* eps (cos x))) (sin x))
(- (* -1/2 (* eps (cos x))) (sin x))
(- (* -1/2 (* eps (cos x))) (sin x))
(- (* -1/2 (* eps (cos x))) (sin x))
(- (* -1/2 (* eps (cos x))) (sin x))
(- (* -1/2 (* eps (cos x))) (sin x))
(- (* -1/2 (* eps (cos x))) (sin x))
(* -1/2 (* eps (cos x)))
(* -1/2 (* eps (cos x)))
(* -1/2 (* eps (cos x)))
(* -1/2 (* eps (cos x)))
(* -1/2 (* eps (cos x)))
(* -1/2 (* eps (cos x)))
(* -1/2 (* eps (cos x)))
(* -1/2 (* eps (cos x)))
(* -1/2 (* eps (cos x)))
(* -1/2 (* eps (cos x)))
(* -1/2 (* eps (cos x)))
(* -1/2 (* eps (cos x)))
(* -1/2 eps)
(+ (* -1/2 eps) (* 1/4 (* eps (pow x 2))))
(+ (* -1/2 eps) (* (pow x 2) (+ (* -1/48 (* eps (pow x 2))) (* 1/4 eps))))
(+ (* -1/2 eps) (* (pow x 2) (+ (* 1/4 eps) (* (pow x 2) (+ (* -1/48 eps) (* 1/1440 (* eps (pow x 2))))))))
(* -1/2 (* eps (cos x)))
(* -1/2 (* eps (cos x)))
(* -1/2 (* eps (cos x)))
(* -1/2 (* eps (cos x)))
(* -1/2 (* eps (cos x)))
(* -1/2 (* eps (cos x)))
(* -1/2 (* eps (cos x)))
(* -1/2 (* eps (cos x)))
-1/2
(- (* 1/4 (pow x 2)) 1/2)
(- (* (pow x 2) (+ 1/4 (* -1/48 (pow x 2)))) 1/2)
(- (* (pow x 2) (+ 1/4 (* (pow x 2) (- (* 1/1440 (pow x 2)) 1/48)))) 1/2)
(* -1/2 (cos x))
(* -1/2 (cos x))
(* -1/2 (cos x))
(* -1/2 (cos x))
(* -1/2 (cos x))
(* -1/2 (cos x))
(* -1/2 (cos x))
(* -1/2 (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
(- (* 1/24 (pow x 2)) 1/2)
(- (* 1/24 (pow x 2)) 1/2)
(- (* 1/24 (pow x 2)) 1/2)
(* 1/24 (pow x 2))
(* (pow x 2) (- 1/24 (* 1/2 (/ 1 (pow x 2)))))
(* (pow x 2) (- 1/24 (* 1/2 (/ 1 (pow x 2)))))
(* (pow x 2) (- 1/24 (* 1/2 (/ 1 (pow x 2)))))
(* 1/24 (pow x 2))
(* (pow x 2) (- 1/24 (* 1/2 (/ 1 (pow x 2)))))
(* (pow x 2) (- 1/24 (* 1/2 (/ 1 (pow x 2)))))
(* (pow x 2) (- 1/24 (* 1/2 (/ 1 (pow x 2)))))
1
(+ 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
(* 1/2 eps)
(*.f64 #s(literal 1/2 binary64) eps)
(+ x (* 1/2 eps))
(fma.f64 #s(literal 1/2 binary64) eps x)
(+ x (* 1/2 eps))
(fma.f64 #s(literal 1/2 binary64) eps x)
(+ x (* 1/2 eps))
(fma.f64 #s(literal 1/2 binary64) eps x)
x
(* x (+ 1 (* 1/2 (/ eps x))))
(fma.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 eps x) x) x)
(* x (+ 1 (* 1/2 (/ eps x))))
(fma.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 eps x) x) x)
(* x (+ 1 (* 1/2 (/ eps x))))
(fma.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 eps x) x) x)
x
(* -1 (* x (- (* -1/2 (/ eps x)) 1)))
(fma.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) (neg.f64 x) x)
(* -1 (* x (- (* -1/2 (/ eps x)) 1)))
(fma.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) (neg.f64 x) x)
(* -1 (* x (- (* -1/2 (/ eps x)) 1)))
(fma.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) (neg.f64 x) x)
x
(+ x (* 1/2 eps))
(fma.f64 #s(literal 1/2 binary64) eps x)
(+ x (* 1/2 eps))
(fma.f64 #s(literal 1/2 binary64) eps x)
(+ x (* 1/2 eps))
(fma.f64 #s(literal 1/2 binary64) eps x)
(* 1/2 eps)
(*.f64 #s(literal 1/2 binary64) eps)
(* eps (+ 1/2 (/ x eps)))
(*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)))
(* eps (+ 1/2 (/ x eps)))
(*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)))
(* eps (+ 1/2 (/ x eps)))
(*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)))
(* 1/2 eps)
(*.f64 #s(literal 1/2 binary64) eps)
(* -1 (* eps (- (* -1 (/ x eps)) 1/2)))
(*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)))
(* -1 (* eps (- (* -1 (/ x eps)) 1/2)))
(*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)))
(* -1 (* eps (- (* -1 (/ x eps)) 1/2)))
(*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)))
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
(* -1 (* eps (sin x)))
(*.f64 eps (sin.f64 (neg.f64 x)))
(* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))
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1
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(.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x)))
(* -1/2 (* eps (cos x)))
(.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x)))
(* -1/2 (* eps (cos x)))
(.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x)))
(* -1/2 (* eps (cos x)))
(.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x)))
(* -1/2 eps)
(*.f64 eps #s(literal -1/2 binary64))
(+ (* -1/2 eps) (* 1/4 (* eps (pow x 2))))
(.f64 eps (fma.f64 x (.f64 x #s(literal 1/4 binary64)) #s(literal -1/2 binary64)))
(+ (* -1/2 eps) (* (pow x 2) (+ (* -1/48 (* eps (pow x 2))) (* 1/4 eps))))
(fma.f64 (.f64 x x) (.f64 eps (fma.f64 x (.f64 x #s(literal -1/48 binary64)) #s(literal 1/4 binary64))) (.f64 eps #s(literal -1/2 binary64)))
(+ (* -1/2 eps) (* (pow x 2) (+ (* 1/4 eps) (* (pow x 2) (+ (* -1/48 eps) (* 1/1440 (* eps (pow x 2))))))))
(fma.f64 (.f64 (fma.f64 x (.f64 x (.f64 eps (fma.f64 (.f64 x x) #s(literal 1/1440 binary64) #s(literal -1/48 binary64)))) (.f64 eps #s(literal 1/4 binary64))) x) x (.f64 eps #s(literal -1/2 binary64)))
(* -1/2 (* eps (cos x)))
(.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x)))
(* -1/2 (* eps (cos x)))
(.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x)))
(* -1/2 (* eps (cos x)))
(.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x)))
(* -1/2 (* eps (cos x)))
(.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x)))
(* -1/2 (* eps (cos x)))
(.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x)))
(* -1/2 (* eps (cos x)))
(.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x)))
(* -1/2 (* eps (cos x)))
(.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x)))
(* -1/2 (* eps (cos x)))
(.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x)))
-1/2
#s(literal -1/2 binary64)
(- (* 1/4 (pow x 2)) 1/2)
(fma.f64 x (*.f64 x #s(literal 1/4 binary64)) #s(literal -1/2 binary64))
(- (* (pow x 2) (+ 1/4 (* -1/48 (pow x 2)))) 1/2)
(fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal -1/48 binary64)) #s(literal 1/4 binary64)) #s(literal -1/2 binary64))
(- (* (pow x 2) (+ 1/4 (* (pow x 2) (- (* 1/1440 (pow x 2)) 1/48)))) 1/2)
(fma.f64 (.f64 x x) (fma.f64 x (.f64 x (fma.f64 (*.f64 x x) #s(literal 1/1440 binary64) #s(literal -1/48 binary64))) #s(literal 1/4 binary64)) #s(literal -1/2 binary64))
(* -1/2 (cos x))
(*.f64 #s(literal -1/2 binary64) (cos.f64 x))
(* -1/2 (cos x))
(*.f64 #s(literal -1/2 binary64) (cos.f64 x))
(* -1/2 (cos x))
(*.f64 #s(literal -1/2 binary64) (cos.f64 x))
(* -1/2 (cos x))
(*.f64 #s(literal -1/2 binary64) (cos.f64 x))
(* -1/2 (cos x))
(*.f64 #s(literal -1/2 binary64) (cos.f64 x))
(* -1/2 (cos x))
(*.f64 #s(literal -1/2 binary64) (cos.f64 x))
(* -1/2 (cos x))
(*.f64 #s(literal -1/2 binary64) (cos.f64 x))
(* -1/2 (cos x))
(*.f64 #s(literal -1/2 binary64) (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 (fma.f64 x (.f64 x #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (.f64 x #s(literal -1/2 binary64)))) (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 (*.f64 #s(literal 1/2 binary64) 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 (cos.f64 x) (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)) (.f64 eps (*.f64 (sin.f64 x) #s(literal -1/8 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
#s(literal -1/2 binary64)
(- (* 1/24 (pow x 2)) 1/2)
(fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal -1/2 binary64))
(- (* 1/24 (pow x 2)) 1/2)
(fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal -1/2 binary64))
(- (* 1/24 (pow x 2)) 1/2)
(fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal -1/2 binary64))
(* 1/24 (pow x 2))
(.f64 #s(literal 1/24 binary64) (.f64 x x))
(* (pow x 2) (- 1/24 (* 1/2 (/ 1 (pow x 2)))))
(.f64 x (.f64 x (+.f64 #s(literal 1/24 binary64) (/.f64 #s(literal -1/2 binary64) (*.f64 x x)))))
(* (pow x 2) (- 1/24 (* 1/2 (/ 1 (pow x 2)))))
(.f64 x (.f64 x (+.f64 #s(literal 1/24 binary64) (/.f64 #s(literal -1/2 binary64) (*.f64 x x)))))
(* (pow x 2) (- 1/24 (* 1/2 (/ 1 (pow x 2)))))
(.f64 x (.f64 x (+.f64 #s(literal 1/24 binary64) (/.f64 #s(literal -1/2 binary64) (*.f64 x x)))))
(* 1/24 (pow x 2))
(.f64 #s(literal 1/24 binary64) (.f64 x x))
(* (pow x 2) (- 1/24 (* 1/2 (/ 1 (pow x 2)))))
(.f64 x (.f64 x (+.f64 #s(literal 1/24 binary64) (/.f64 #s(literal -1/2 binary64) (*.f64 x x)))))
(* (pow x 2) (- 1/24 (* 1/2 (/ 1 (pow x 2)))))
(.f64 x (.f64 x (+.f64 #s(literal 1/24 binary64) (/.f64 #s(literal -1/2 binary64) (*.f64 x x)))))
(* (pow x 2) (- 1/24 (* 1/2 (/ 1 (pow x 2)))))
(.f64 x (.f64 x (+.f64 #s(literal 1/24 binary64) (/.f64 #s(literal -1/2 binary64) (*.f64 x 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 (.f64 x 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 #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)

eval130.0ms (0.7%)

Memory: 12.3MiB live, 316.3MiB allocated
Compiler: Compiled 29 963 to 3 193 computations (89.3% saved)

prune118.0ms (0.6%)

Memory

3.9MiB live, 284.1MiB allocated

Pruning

29 alts after pruning (24 fresh and 5 done)

	Pruned	Kept	Total
New	1 065	21	1 086
Fresh	4	3	7
Picked	1	4	5
Done	0	1	1
Total	1 070	29	1 099

Accuracy

100.0%

Counts

1 099 → 29

Alt Table

Click to see full alt table

Status	Accuracy	Program
	99.1%	(fma.f64 (.f64 (cos.f64 x) (.f64 eps #s(literal -1/2 binary64))) eps (neg.f64 (*.f64 eps (sin.f64 x))))
	53.2%	(fma.f64 (cos.f64 x) (cos.f64 eps) (neg.f64 (fma.f64 (sin.f64 x) (sin.f64 eps) (cos.f64 x))))
	98.5%	(fma.f64 x (fma.f64 x (.f64 eps (fma.f64 eps #s(literal 1/4 binary64) (.f64 x #s(literal 1/6 binary64)))) (neg.f64 eps)) (.f64 eps (.f64 eps #s(literal -1/2 binary64))))
	97.9%	(fma.f64 eps (.f64 eps #s(literal -1/2 binary64)) (.f64 x (-.f64 (.f64 x (.f64 #s(literal 1/4 binary64) (*.f64 eps eps))) eps)))
	53.2%	(/.f64 (/.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))) #s(literal 2 binary64)) (.f64 (cos.f64 (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64))) (cos.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64)))))
	53.2%	(-.f64 (/.f64 (*.f64 (cos.f64 (-.f64 x eps)) (cos.f64 (+.f64 x eps))) (cos.f64 (-.f64 x eps))) (cos.f64 x))
✓	52.3%	(-.f64 (cos.f64 (+.f64 x eps)) (fma.f64 x (.f64 x (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal -1/2 binary64))) #s(literal 1 binary64)))
✓	53.2%	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
✓	51.7%	(+.f64 (cos.f64 eps) #s(literal -1 binary64))
▶	51.6%	(+.f64 #s(literal 1 binary64) #s(literal -1 binary64))
	78.1%	(.f64 (fma.f64 (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) (.f64 x (*.f64 x x)) x) (neg.f64 eps))
	78.0%	(.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 x (*.f64 x x)) x) (neg.f64 eps))
▶	99.8%	(.f64 (.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (fma.f64 (sin.f64 (.f64 (+.f64 x x) #s(literal 1/2 binary64))) (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (cos.f64 (.f64 (+.f64 x x) #s(literal 1/2 binary64))) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))))) #s(literal -2 binary64))
	99.4%	(.f64 (.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (fma.f64 eps (fma.f64 (cos.f64 x) (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)) (.f64 eps (.f64 (sin.f64 x) #s(literal -1/8 binary64)))) (sin.f64 x))) #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))
▶	32.5%	(.f64 (.f64 (sin.f64 (.f64 (.f64 (/.f64 eps (.f64 eps (.f64 eps eps))) (/.f64 eps (/.f64 #s(literal 1 binary64) (.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))
	99.7%	(.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))
✓	78.4%	(*.f64 (sin.f64 x) (neg.f64 eps))
	78.1%	(.f64 x (fma.f64 (.f64 x x) (.f64 eps (fma.f64 #s(literal -1/120 binary64) (.f64 x x) #s(literal 1/6 binary64))) (neg.f64 eps)))
	78.0%	(.f64 x (.f64 eps (fma.f64 x (*.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64))))
▶	98.3%	(.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 (fma.f64 (.f64 x x) (fma.f64 x (.f64 x (fma.f64 (*.f64 x x) #s(literal 1/1440 binary64) #s(literal -1/48 binary64))) #s(literal 1/4 binary64)) #s(literal -1/2 binary64))) (sin.f64 x)))
	98.9%	(.f64 eps (-.f64 (.f64 eps (fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal -1/48 binary64)) #s(literal 1/4 binary64)) #s(literal -1/2 binary64))) (sin.f64 x)))
▶	98.9%	(.f64 eps (-.f64 (.f64 eps (fma.f64 x (*.f64 x #s(literal 1/4 binary64)) #s(literal -1/2 binary64))) (sin.f64 x)))
✓	99.1%	(.f64 eps (-.f64 (.f64 eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x)))
	98.7%	(.f64 eps (-.f64 (.f64 eps #s(literal -1/2 binary64)) (sin.f64 x)))
	97.9%	(.f64 eps (-.f64 (.f64 eps #s(literal -1/2 binary64)) x))
	52.9%	(.f64 eps (.f64 eps #s(literal -1/2 binary64)))
	77.8%	(*.f64 eps (neg.f64 x))

Compiler

Compiled 919 to 581 computations (36.8% saved)

simplify481.0ms (2.5%)

Memory

-12.7MiB live, 506.2MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 17 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	320	(*.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64))
✓	cost-diff	320	(/.f64 eps (.f64 eps (.f64 eps eps)))
✓	cost-diff	1088	(/.f64 eps (/.f64 #s(literal 1 binary64) (*.f64 eps eps)))
✓	cost-diff	1984	(.f64 (/.f64 eps (.f64 eps (.f64 eps eps))) (/.f64 eps (/.f64 #s(literal 1 binary64) (.f64 eps eps))))
✓	cost-diff	0	(fma.f64 x (*.f64 x #s(literal 1/4 binary64)) #s(literal -1/2 binary64))
✓	cost-diff	0	(.f64 eps (fma.f64 x (.f64 x #s(literal 1/4 binary64)) #s(literal -1/2 binary64)))
✓	cost-diff	0	(-.f64 (.f64 eps (fma.f64 x (.f64 x #s(literal 1/4 binary64)) #s(literal -1/2 binary64))) (sin.f64 x))
✓	cost-diff	0	(.f64 eps (-.f64 (.f64 eps (fma.f64 x (*.f64 x #s(literal 1/4 binary64)) #s(literal -1/2 binary64))) (sin.f64 x)))
✓	cost-diff	0	(fma.f64 eps #s(literal 1/4 binary64) (*.f64 x #s(literal 1/6 binary64)))
✓	cost-diff	0	(fma.f64 x (fma.f64 eps #s(literal 1/4 binary64) (*.f64 x #s(literal 1/6 binary64))) #s(literal -1 binary64))
✓	cost-diff	0	(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)))
✓	cost-diff	0	(.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))))
✓	cost-diff	192	(+.f64 #s(literal 1 binary64) #s(literal -1 binary64))
✓	cost-diff	0	(.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (fma.f64 (sin.f64 (.f64 (+.f64 x x) #s(literal 1/2 binary64))) (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (cos.f64 (.f64 (+.f64 x x) #s(literal 1/2 binary64))) (sin.f64 (*.f64 eps #s(literal 1/2 binary64))))))
✓	cost-diff	0	(.f64 (.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (fma.f64 (sin.f64 (.f64 (+.f64 x x) #s(literal 1/2 binary64))) (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (cos.f64 (.f64 (+.f64 x x) #s(literal 1/2 binary64))) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))))) #s(literal -2 binary64))
✓	cost-diff	192	(+.f64 eps #s(literal 0 binary64))
✓	cost-diff	512	(*.f64 (+.f64 x x) #s(literal 1/2 binary64))

Rules

16 760×	`lower-fma.f32`
16 750×	`lower-fma.f64`
5 344×	`lower-*.f32`
5 310×	`lower-*.f64`
2 674×	`lower-+.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	51	411
0	97	367
1	185	329
2	517	275
3	1388	275
4	4317	275
5	7122	275
0	8023	270

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

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

localize160.0ms (0.8%)

Memory

-12.0MiB live, 274.9MiB allocated

Localize:

Found 17 expressions of interest:

New	Metric	Score	Program
✓	accuracy	99.8%	(.f64 (sin.f64 (.f64 (.f64 (/.f64 eps (.f64 eps (.f64 eps eps))) (/.f64 eps (/.f64 #s(literal 1 binary64) (.f64 eps eps)))) #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))
✓	accuracy	84.9%	(/.f64 eps (.f64 eps (.f64 eps eps)))
✓	accuracy	34.4%	(.f64 (/.f64 eps (.f64 eps (.f64 eps eps))) (/.f64 eps (/.f64 #s(literal 1 binary64) (.f64 eps eps))))
✓	accuracy	100.0%	(*.f64 x #s(literal 1/4 binary64))
✓	accuracy	100.0%	(sin.f64 x)
✓	accuracy	100.0%	(.f64 eps (fma.f64 x (.f64 x #s(literal 1/4 binary64)) #s(literal -1/2 binary64)))
✓	accuracy	99.8%	(.f64 eps (-.f64 (.f64 eps (fma.f64 x (*.f64 x #s(literal 1/4 binary64)) #s(literal -1/2 binary64))) (sin.f64 x)))
✓	accuracy	100.0%	(fma.f64 x (fma.f64 eps #s(literal 1/4 binary64) (*.f64 x #s(literal 1/6 binary64))) #s(literal -1 binary64))
✓	accuracy	99.8%	(.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))))
✓	accuracy	99.7%	(fma.f64 eps #s(literal 1/4 binary64) (*.f64 x #s(literal 1/6 binary64)))
✓	accuracy	99.4%	(*.f64 x #s(literal 1/6 binary64))
✓	accuracy	100.0%	(+.f64 #s(literal 1 binary64) #s(literal -1 binary64))
✓	accuracy	100.0%	(fma.f64 (sin.f64 (.f64 (+.f64 x x) #s(literal 1/2 binary64))) (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (cos.f64 (.f64 (+.f64 x x) #s(literal 1/2 binary64))) (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))))
✓	accuracy	100.0%	(.f64 (.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (fma.f64 (sin.f64 (.f64 (+.f64 x x) #s(literal 1/2 binary64))) (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (cos.f64 (.f64 (+.f64 x x) #s(literal 1/2 binary64))) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))))) #s(literal -2 binary64))
✓	accuracy	100.0%	(.f64 (cos.f64 (.f64 (+.f64 x x) #s(literal 1/2 binary64))) (sin.f64 (*.f64 eps #s(literal 1/2 binary64))))
✓	accuracy	99.8%	(.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (fma.f64 (sin.f64 (.f64 (+.f64 x x) #s(literal 1/2 binary64))) (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (cos.f64 (.f64 (+.f64 x x) #s(literal 1/2 binary64))) (sin.f64 (*.f64 eps #s(literal 1/2 binary64))))))

Samples

91.0ms	251×	0	valid
4.0ms	5×	1	exit

Compiler

Compiled 431 to 58 computations (86.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 72.0ms

ival-mult: 34.0ms (47% of total)

ival-sin: 11.0ms (15.2% of total)

ival-add: 10.0ms (13.8% of total)

ival-cos: 6.0ms (8.3% of total)

ival-div: 5.0ms (6.9% of total)

const: 4.0ms (5.5% of total)

adjust: 1.0ms (1.4% of total)

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

exact: 1.0ms (1.4% of total)

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

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

series36.0ms (0.2%)

Memory

1.5MiB live, 41.0MiB allocated

Counts

24 → 444

Calls

Call 1

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

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

Calls

111 calls:

Time	Variable		Point	Expression
11.0ms	x	@	-inf	(+ (* x (+ (* x (+ (* eps 1/4) (* x 1/6))) -1)) (* eps -1/2))
1.0ms	x	@	inf	(* (* (sin (* (+ eps 0) 1/2)) (+ (* (sin (* (+ x x) 1/2)) (cos (* eps 1/2))) (* (cos (* (+ x x) 1/2)) (sin (* eps 1/2))))) -2)
1.0ms	x	@	-inf	(* (* (sin (* (+ eps 0) 1/2)) (+ (* (sin (* (+ x x) 1/2)) (cos (* eps 1/2))) (* (cos (* (+ x x) 1/2)) (sin (* eps 1/2))))) -2)
1.0ms	eps	@	inf	(* (* (sin (* (+ eps 0) 1/2)) (+ (* (sin (* (+ x x) 1/2)) (cos (* eps 1/2))) (* (cos (* (+ x x) 1/2)) (sin (* eps 1/2))))) -2)
1.0ms	eps	@	-inf	(* (* (sin (* (+ eps 0) 1/2)) (+ (* (sin (* (+ x x) 1/2)) (cos (* eps 1/2))) (* (cos (* (+ x x) 1/2)) (sin (* eps 1/2))))) -2)

rewrite385.0ms (2%)

Memory

13.9MiB live, 640.9MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

5 716×	`lower-fma.f32`
5 706×	`lower-fma.f64`
3 814×	`lower-*.f32`
3 788×	`lower-*.f64`
3 696×	`lower-/.f32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	50	261
0	95	239
1	323	145
2	3070	135
0	9461	135

Stop Event

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

Counts

24 → 1 214

Calls

Call 1

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

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

simplify524.0ms (2.8%)

Memory

-14.5MiB live, 598.7MiB allocated

Algorithm

1×	egg-herbie

Rules

15 816×	`lower-fma.f64`
15 816×	`lower-fma.f32`
7 354×	`lower-*.f64`
7 354×	`lower-*.f32`
3 566×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	421	4855
1	1350	4682
2	4084	4648
0	8122	4331

Stop Event

1×	iter limit
1×	node limit

Counts

444 → 401

Calls

Call 1

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

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

eval312.0ms (1.6%)

Memory: 21.3MiB live, 278.5MiB allocated
Compiler: Compiled 53 391 to 5 312 computations (90.1% saved)

prune508.0ms (2.7%)

Memory

-14.1MiB live, 358.6MiB allocated

Pruning

36 alts after pruning (29 fresh and 7 done)

	Pruned	Kept	Total
New	1 600	16	1 616
Fresh	6	13	19
Picked	3	2	5
Done	0	5	5
Total	1 609	36	1 645

Accuracy

100.0%

Counts

1 645 → 36

Alt Table

Click to see full alt table

Status	Accuracy	Program
	98.5%	(fma.f64 (.f64 eps (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) (.f64 eps #s(literal 1/4 binary64))) #s(literal -1 binary64))) x (.f64 eps (.f64 eps #s(literal -1/2 binary64))))
	98.9%	(fma.f64 (.f64 eps (fma.f64 #s(literal 1/4 binary64) (.f64 x x) #s(literal -1/2 binary64))) eps (*.f64 (neg.f64 (sin.f64 x)) eps))
	53.2%	(fma.f64 (cos.f64 x) (cos.f64 eps) (neg.f64 (fma.f64 (sin.f64 x) (sin.f64 eps) (cos.f64 x))))
	98.1%	(fma.f64 x (neg.f64 eps) (.f64 eps (.f64 eps #s(literal -1/2 binary64))))
	53.2%	(/.f64 (/.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))) #s(literal 2 binary64)) (.f64 (cos.f64 (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64))) (cos.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64)))))
	53.2%	(-.f64 (/.f64 (*.f64 (cos.f64 (-.f64 x eps)) (cos.f64 (+.f64 x eps))) (cos.f64 (-.f64 x eps))) (cos.f64 x))
✓	52.3%	(-.f64 (cos.f64 (+.f64 x eps)) (fma.f64 x (.f64 x (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal -1/2 binary64))) #s(literal 1 binary64)))
✓	53.2%	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
✓	51.7%	(+.f64 (cos.f64 eps) #s(literal -1 binary64))
	78.1%	(.f64 (fma.f64 (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) (.f64 x (*.f64 x x)) x) (neg.f64 eps))
▶	99.8%	(.f64 (.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (fma.f64 (sin.f64 (.f64 (+.f64 x x) #s(literal 1/2 binary64))) (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (cos.f64 x) (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))))) #s(literal -2 binary64))
	99.4%	(.f64 (.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (fma.f64 (sin.f64 (.f64 (+.f64 x x) #s(literal 1/2 binary64))) (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 eps (.f64 (cos.f64 x) (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)))))) #s(literal -2 binary64))
	99.4%	(.f64 (.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (fma.f64 eps (fma.f64 (cos.f64 x) (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)) (.f64 eps (.f64 (sin.f64 x) #s(literal -1/8 binary64)))) (sin.f64 x))) #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))
	21.8%	(.f64 (.f64 (sin.f64 (.f64 (.f64 (/.f64 (.f64 eps eps) (.f64 eps (.f64 eps (.f64 eps eps)))) (/.f64 eps (/.f64 #s(literal 1 binary64) (.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))
▶	32.5%	(.f64 (.f64 (sin.f64 (.f64 (.f64 (/.f64 eps (.f64 eps (.f64 eps eps))) (/.f64 eps (/.f64 #s(literal 1 binary64) (*.f64 eps eps)))) #s(literal 1/2 binary64))) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x))) #s(literal -2 binary64))
	99.7%	(.f64 (.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x))) #s(literal -2 binary64))
✓	78.4%	(*.f64 (sin.f64 x) (neg.f64 eps))
	78.1%	(.f64 x (fma.f64 (.f64 x x) (.f64 eps (fma.f64 #s(literal -1/120 binary64) (.f64 x x) #s(literal 1/6 binary64))) (neg.f64 eps)))
✓	98.3%	(.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))))
	98.3%	(.f64 eps (fma.f64 x (fma.f64 x (.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64)) (*.f64 eps #s(literal -1/2 binary64))))
▶	98.2%	(.f64 eps (/.f64 (-.f64 (.f64 #s(literal 1/4 binary64) (.f64 eps eps)) (.f64 (.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) (.f64 eps #s(literal 1/4 binary64))) #s(literal -1 binary64))) (.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) (.f64 eps #s(literal 1/4 binary64))) #s(literal -1 binary64))))) (-.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) (*.f64 eps #s(literal 1/4 binary64))) #s(literal -1 binary64))))))
	98.9%	(.f64 eps (-.f64 (.f64 eps (fma.f64 (.f64 x x) (fma.f64 x (.f64 x (fma.f64 (*.f64 x x) #s(literal 1/1440 binary64) #s(literal -1/48 binary64))) #s(literal 1/4 binary64)) #s(literal -1/2 binary64))) (sin.f64 x)))
	98.9%	(.f64 eps (-.f64 (.f64 eps (fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal -1/48 binary64)) #s(literal 1/4 binary64)) #s(literal -1/2 binary64))) (sin.f64 x)))
	98.6%	(.f64 eps (-.f64 (.f64 eps (fma.f64 x (.f64 x #s(literal 1/4 binary64)) #s(literal -1/2 binary64))) (fma.f64 (.f64 x (.f64 x x)) (fma.f64 (.f64 x x) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) x)))
	98.7%	(.f64 eps (-.f64 (.f64 eps (fma.f64 x (.f64 x #s(literal 1/4 binary64)) #s(literal -1/2 binary64))) (fma.f64 (.f64 x (.f64 x x)) (fma.f64 x (.f64 x (fma.f64 x (*.f64 x #s(literal -1/5040 binary64)) #s(literal 1/120 binary64))) #s(literal -1/6 binary64)) x)))
✓	98.9%	(.f64 eps (-.f64 (.f64 eps (fma.f64 x (*.f64 x #s(literal 1/4 binary64)) #s(literal -1/2 binary64))) (sin.f64 x)))
✓	99.1%	(.f64 eps (-.f64 (.f64 eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x)))
	98.7%	(.f64 eps (-.f64 (.f64 eps #s(literal -1/2 binary64)) (sin.f64 x)))
	97.9%	(.f64 eps (-.f64 (.f64 eps #s(literal -1/2 binary64)) x))
▶	78.0%	(.f64 eps (.f64 x (fma.f64 x (*.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64))))
	53.0%	(.f64 eps (.f64 eps (fma.f64 x (*.f64 x #s(literal 1/4 binary64)) #s(literal -1/2 binary64))))
	52.9%	(.f64 eps (.f64 eps #s(literal -1/2 binary64)))
	51.8%	(.f64 eps (.f64 #s(literal 1/4 binary64) (.f64 x (.f64 x eps))))
	77.8%	(*.f64 eps (neg.f64 x))
▶	51.6%	#s(literal 0 binary64)

Compiler

Compiled 1 254 to 767 computations (38.8% saved)

simplify817.0ms (4.3%)

Memory

-1.4MiB live, 314.7MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 16 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(.f64 (.f64 (sin.f64 (.f64 (.f64 (/.f64 eps (.f64 eps (.f64 eps eps))) (/.f64 eps (/.f64 #s(literal 1 binary64) (*.f64 eps eps)))) #s(literal 1/2 binary64))) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x))) #s(literal -2 binary64))
✓	cost-diff	320	(/.f64 eps (.f64 eps (.f64 eps eps)))
✓	cost-diff	1088	(/.f64 eps (/.f64 #s(literal 1 binary64) (*.f64 eps eps)))
✓	cost-diff	1984	(.f64 (/.f64 eps (.f64 eps (.f64 eps eps))) (/.f64 eps (/.f64 #s(literal 1 binary64) (.f64 eps eps))))
✓	cost-diff	0	(/.f64 (-.f64 (.f64 #s(literal 1/4 binary64) (.f64 eps eps)) (.f64 (.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) (.f64 eps #s(literal 1/4 binary64))) #s(literal -1 binary64))) (.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) (.f64 eps #s(literal 1/4 binary64))) #s(literal -1 binary64))))) (-.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) (.f64 eps #s(literal 1/4 binary64))) #s(literal -1 binary64)))))
✓	cost-diff	0	(.f64 eps (/.f64 (-.f64 (.f64 #s(literal 1/4 binary64) (.f64 eps eps)) (.f64 (.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) (.f64 eps #s(literal 1/4 binary64))) #s(literal -1 binary64))) (.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) (.f64 eps #s(literal 1/4 binary64))) #s(literal -1 binary64))))) (-.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) (*.f64 eps #s(literal 1/4 binary64))) #s(literal -1 binary64))))))
✓	cost-diff	128	(-.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) (*.f64 eps #s(literal 1/4 binary64))) #s(literal -1 binary64))))
✓	cost-diff	128	(-.f64 (.f64 #s(literal 1/4 binary64) (.f64 eps eps)) (.f64 (.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) (.f64 eps #s(literal 1/4 binary64))) #s(literal -1 binary64))) (.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) (*.f64 eps #s(literal 1/4 binary64))) #s(literal -1 binary64)))))
✓	cost-diff	0	(*.f64 x #s(literal 1/6 binary64))
✓	cost-diff	0	(fma.f64 x (*.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64))
✓	cost-diff	0	(.f64 x (fma.f64 x (.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64)))
✓	cost-diff	0	(.f64 eps (.f64 x (fma.f64 x (*.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64))))
✓	cost-diff	0	(.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (fma.f64 (sin.f64 (.f64 (+.f64 x x) #s(literal 1/2 binary64))) (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (cos.f64 x) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))))
✓	cost-diff	0	(.f64 (.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (fma.f64 (sin.f64 (.f64 (+.f64 x x) #s(literal 1/2 binary64))) (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (cos.f64 x) (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))))) #s(literal -2 binary64))
✓	cost-diff	192	(+.f64 eps #s(literal 0 binary64))
✓	cost-diff	512	(*.f64 (+.f64 x x) #s(literal 1/2 binary64))

Rules

8 936×	`lower-fma.f32`
8 926×	`lower-fma.f64`
4 410×	`lower-*.f32`
4 372×	`lower-*.f64`
1 718×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	51	501
0	95	453
1	193	427
2	593	391
3	2113	391
4	5645	391
0	8249	385

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

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

localize249.0ms (1.3%)

Memory

1.1MiB live, 82.3MiB allocated

Localize:

Found 16 expressions of interest:

New	Metric	Score	Program
✓	accuracy	99.9%	(.f64 eps (.f64 eps eps))
✓	accuracy	99.8%	(.f64 (sin.f64 (.f64 (.f64 (/.f64 eps (.f64 eps (.f64 eps eps))) (/.f64 eps (/.f64 #s(literal 1 binary64) (.f64 eps eps)))) #s(literal 1/2 binary64))) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))
✓	accuracy	84.9%	(/.f64 eps (.f64 eps (.f64 eps eps)))
✓	accuracy	34.4%	(.f64 (/.f64 eps (.f64 eps (.f64 eps eps))) (/.f64 eps (/.f64 #s(literal 1 binary64) (.f64 eps eps))))
✓	accuracy	99.9%	(-.f64 (.f64 #s(literal 1/4 binary64) (.f64 eps eps)) (.f64 (.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) (.f64 eps #s(literal 1/4 binary64))) #s(literal -1 binary64))) (.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) (*.f64 eps #s(literal 1/4 binary64))) #s(literal -1 binary64)))))
✓	accuracy	99.8%	(.f64 eps (/.f64 (-.f64 (.f64 #s(literal 1/4 binary64) (.f64 eps eps)) (.f64 (.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) (.f64 eps #s(literal 1/4 binary64))) #s(literal -1 binary64))) (.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) (.f64 eps #s(literal 1/4 binary64))) #s(literal -1 binary64))))) (-.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) (*.f64 eps #s(literal 1/4 binary64))) #s(literal -1 binary64))))))
✓	accuracy	99.5%	(fma.f64 x #s(literal 1/6 binary64) (*.f64 eps #s(literal 1/4 binary64)))
✓	accuracy	55.5%	(/.f64 (-.f64 (.f64 #s(literal 1/4 binary64) (.f64 eps eps)) (.f64 (.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) (.f64 eps #s(literal 1/4 binary64))) #s(literal -1 binary64))) (.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) (.f64 eps #s(literal 1/4 binary64))) #s(literal -1 binary64))))) (-.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) (.f64 eps #s(literal 1/4 binary64))) #s(literal -1 binary64)))))
✓	accuracy	100.0%	(fma.f64 x (*.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64))
✓	accuracy	100.0%	(.f64 x (fma.f64 x (.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64)))
✓	accuracy	100.0%	(.f64 eps (.f64 x (fma.f64 x (*.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64))))
✓	accuracy	99.4%	(*.f64 x #s(literal 1/6 binary64))
✓	accuracy	100.0%	(.f64 (.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (fma.f64 (sin.f64 (.f64 (+.f64 x x) #s(literal 1/2 binary64))) (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (cos.f64 x) (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))))) #s(literal -2 binary64))
✓	accuracy	100.0%	(fma.f64 (sin.f64 (.f64 (+.f64 x x) #s(literal 1/2 binary64))) (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (cos.f64 x) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))))
✓	accuracy	100.0%	(.f64 (cos.f64 x) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))
✓	accuracy	99.8%	(.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (fma.f64 (sin.f64 (.f64 (+.f64 x x) #s(literal 1/2 binary64))) (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (cos.f64 x) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))))

Samples

84.0ms	249×	0	valid
4.0ms	5×	1	valid
3.0ms	2×	5	exit

Compiler

Compiled 540 to 56 computations (89.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 67.0ms

ival-mult: 33.0ms (49.2% of total)

ival-add: 8.0ms (11.9% of total)

ival-sin: 8.0ms (11.9% of total)

ival-div: 6.0ms (8.9% of total)

const: 4.0ms (6% of total)

ival-cos: 3.0ms (4.5% of total)

ival-sub: 2.0ms (3% of total)

adjust: 1.0ms (1.5% of total)

exact: 1.0ms (1.5% of total)

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

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

series29.0ms (0.2%)

Memory

12.0MiB live, 12.0MiB allocated

Counts

21 → 396

Calls

Call 1

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

Outputs
#<alt x>
#<alt x>
#<alt x>
#<alt x>
#<alt x>
#<alt x>
#<alt x>
#<alt x>
#<alt x>
#<alt x>
#<alt x>
#<alt x>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt (* -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)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))>
#<alt (* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))>
#<alt (* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))>
#<alt (* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))>
#<alt (* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))>
#<alt (* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))>
#<alt (* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))>
#<alt (* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))>
#<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)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))>
#<alt (* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))>
#<alt (* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))>
#<alt (* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))>
#<alt (* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))>
#<alt (* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))>
#<alt (* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))>
#<alt (* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin 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)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))>
#<alt (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))>
#<alt (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))>
#<alt (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))>
#<alt (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))>
#<alt (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))>
#<alt (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))>
#<alt (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))>
#<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)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))>
#<alt (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))>
#<alt (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))>
#<alt (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))>
#<alt (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))>
#<alt (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))>
#<alt (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))>
#<alt (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))>
#<alt (* eps (* x (- (* 1/6 (pow x 2)) 1)))>
#<alt (* eps (* x (- (* 1/6 (pow x 2)) 1)))>
#<alt (* eps (* x (- (* 1/6 (pow x 2)) 1)))>
#<alt (* eps (* x (- (* 1/6 (pow x 2)) 1)))>
#<alt (* eps (* x (- (* 1/6 (pow x 2)) 1)))>
#<alt (* eps (* x (- (* 1/6 (pow x 2)) 1)))>
#<alt (* eps (* x (- (* 1/6 (pow x 2)) 1)))>
#<alt (* eps (* x (- (* 1/6 (pow x 2)) 1)))>
#<alt (* eps (* x (- (* 1/6 (pow x 2)) 1)))>
#<alt (* eps (* x (- (* 1/6 (pow x 2)) 1)))>
#<alt (* eps (* x (- (* 1/6 (pow x 2)) 1)))>
#<alt (* eps (* x (- (* 1/6 (pow x 2)) 1)))>
#<alt (* -1 (* eps x))>
#<alt (* x (+ (* -1 eps) (* 1/6 (* eps (pow x 2)))))>
#<alt (* x (+ (* -1 eps) (* 1/6 (* eps (pow x 2)))))>
#<alt (* x (+ (* -1 eps) (* 1/6 (* eps (pow x 2)))))>
#<alt (* 1/6 (* eps (pow x 3)))>
#<alt (* (pow x 3) (+ (* -1 (/ eps (pow x 2))) (* 1/6 eps)))>
#<alt (* (pow x 3) (+ (* -1 (/ eps (pow x 2))) (* 1/6 eps)))>
#<alt (* (pow x 3) (+ (* -1 (/ eps (pow x 2))) (* 1/6 eps)))>
#<alt (* 1/6 (* eps (pow x 3)))>
#<alt (* -1 (* (pow x 3) (+ (* -1/6 eps) (/ eps (pow x 2)))))>
#<alt (* -1 (* (pow x 3) (+ (* -1/6 eps) (/ eps (pow x 2)))))>
#<alt (* -1 (* (pow x 3) (+ (* -1/6 eps) (/ eps (pow x 2)))))>
#<alt (* -1 x)>
#<alt (* x (- (* 1/6 (pow x 2)) 1))>
#<alt (* x (- (* 1/6 (pow x 2)) 1))>
#<alt (* x (- (* 1/6 (pow x 2)) 1))>
#<alt (* 1/6 (pow x 3))>
#<alt (* (pow x 3) (- 1/6 (/ 1 (pow x 2))))>
#<alt (* (pow x 3) (- 1/6 (/ 1 (pow x 2))))>
#<alt (* (pow x 3) (- 1/6 (/ 1 (pow x 2))))>
#<alt (* 1/6 (pow x 3))>
#<alt (* -1 (* (pow x 3) (- (/ 1 (pow x 2)) 1/6)))>
#<alt (* -1 (* (pow x 3) (- (/ 1 (pow x 2)) 1/6)))>
#<alt (* -1 (* (pow x 3) (- (/ 1 (pow x 2)) 1/6)))>
#<alt -1>
#<alt (- (* 1/6 (pow x 2)) 1)>
#<alt (- (* 1/6 (pow x 2)) 1)>
#<alt (- (* 1/6 (pow x 2)) 1)>
#<alt (* 1/6 (pow x 2))>
#<alt (* (pow x 2) (- 1/6 (/ 1 (pow x 2))))>
#<alt (* (pow x 2) (- 1/6 (/ 1 (pow x 2))))>
#<alt (* (pow x 2) (- 1/6 (/ 1 (pow x 2))))>
#<alt (* 1/6 (pow x 2))>
#<alt (* (pow x 2) (- 1/6 (/ 1 (pow x 2))))>
#<alt (* (pow x 2) (- 1/6 (/ 1 (pow x 2))))>
#<alt (* (pow x 2) (- 1/6 (/ 1 (pow x 2))))>
#<alt (* 1/6 x)>
#<alt (* 1/6 x)>
#<alt (* 1/6 x)>
#<alt (* 1/6 x)>
#<alt (* 1/6 x)>
#<alt (* 1/6 x)>
#<alt (* 1/6 x)>
#<alt (* 1/6 x)>
#<alt (* 1/6 x)>
#<alt (* 1/6 x)>
#<alt (* 1/6 x)>
#<alt (* 1/6 x)>
#<alt (* -1 (* (pow x 2) (pow (- (* 1/6 (pow x 2)) 1) 2)))>
#<alt (- (* -1/2 (* eps (* (pow x 3) (- (* 1/6 (pow x 2)) 1)))) (* (pow x 2) (pow (- (* 1/6 (pow x 2)) 1) 2)))>
#<alt (- (* eps (- (* eps (- 1/4 (* 1/16 (pow x 4)))) (* 1/2 (* (pow x 3) (- (* 1/6 (pow x 2)) 1))))) (* (pow x 2) (pow (- (* 1/6 (pow x 2)) 1) 2)))>
#<alt (- (* eps (- (* eps (- 1/4 (* 1/16 (pow x 4)))) (* 1/2 (* (pow x 3) (- (* 1/6 (pow x 2)) 1))))) (* (pow x 2) (pow (- (* 1/6 (pow x 2)) 1) 2)))>
#<alt (* (pow eps 2) (- 1/4 (* 1/16 (pow x 4))))>
#<alt (* (pow eps 2) (- (+ 1/4 (* -1/2 (/ (* (pow x 3) (- (* 1/6 (pow x 2)) 1)) eps))) (* 1/16 (pow x 4))))>
#<alt (* (pow eps 2) (- (+ 1/4 (* -1 (/ (* (pow x 2) (pow (- (* 1/6 (pow x 2)) 1) 2)) (pow eps 2)))) (+ (* 1/16 (pow x 4)) (* 1/2 (/ (* (pow x 3) (- (* 1/6 (pow x 2)) 1)) eps)))))>
#<alt (* (pow eps 2) (- (+ 1/4 (* -1 (/ (* (pow x 2) (pow (- (* 1/6 (pow x 2)) 1) 2)) (pow eps 2)))) (+ (* 1/16 (pow x 4)) (* 1/2 (/ (* (pow x 3) (- (* 1/6 (pow x 2)) 1)) eps)))))>
#<alt (* (pow eps 2) (- 1/4 (* 1/16 (pow x 4))))>
#<alt (* (pow eps 2) (- (+ 1/4 (* -1/2 (/ (* (pow x 3) (- (* 1/6 (pow x 2)) 1)) eps))) (* 1/16 (pow x 4))))>
#<alt (* (pow eps 2) (- (+ 1/4 (* -1 (/ (- (/ (* (pow x 2) (pow (- (* 1/6 (pow x 2)) 1) 2)) eps) (* -1/2 (* (pow x 3) (- (* 1/6 (pow x 2)) 1)))) eps))) (* 1/16 (pow x 4))))>
#<alt (* (pow eps 2) (- (+ 1/4 (* -1 (/ (- (/ (* (pow x 2) (pow (- (* 1/6 (pow x 2)) 1) 2)) eps) (* -1/2 (* (pow x 3) (- (* 1/6 (pow x 2)) 1)))) eps))) (* 1/16 (pow x 4))))>
#<alt (* 1/4 (pow eps 2))>
#<alt (+ (* -1 (pow x 2)) (* 1/4 (pow eps 2)))>
#<alt (+ (* 1/4 (pow eps 2)) (* (pow x 2) (- (* 1/2 (* eps x)) 1)))>
#<alt (+ (* 1/4 (pow eps 2)) (* (pow x 2) (- (* x (- (* x (- 1/3 (* 1/16 (pow eps 2)))) (* -1/2 eps))) 1)))>
#<alt (* -1/36 (pow x 6))>
#<alt (* (pow x 6) (- (* -1/12 (/ eps x)) 1/36))>
#<alt (* (pow x 6) (- (/ 1/3 (pow x 2)) (+ 1/36 (+ (* 1/16 (/ (pow eps 2) (pow x 2))) (* 1/12 (/ eps x))))))>
#<alt (* (pow x 6) (- (+ (* 1/2 (/ eps (pow x 3))) (/ 1/3 (pow x 2))) (+ 1/36 (+ (* 1/16 (/ (pow eps 2) (pow x 2))) (* 1/12 (/ eps x))))))>
#<alt (* -1/36 (pow x 6))>
#<alt (* (pow x 6) (- (* -1/12 (/ eps x)) 1/36))>
#<alt (* (pow x 6) (- (* -1 (/ (- (* -1 (/ (- 1/3 (* 1/16 (pow eps 2))) x)) (* -1/12 eps)) x)) 1/36))>
#<alt (* (pow x 6) (- (* -1 (/ (- (* -1 (/ (- (+ 1/3 (* 1/2 (/ eps x))) (* 1/16 (pow eps 2))) x)) (* -1/12 eps)) x)) 1/36))>
#<alt (* -1 (* x (- (* 1/6 (pow x 2)) 1)))>
#<alt (- (* -1 (* eps (+ 1/2 (* 1/4 (pow x 2))))) (* x (- (* 1/6 (pow x 2)) 1)))>
#<alt (- (* -1 (* eps (+ 1/2 (* 1/4 (pow x 2))))) (* x (- (* 1/6 (pow x 2)) 1)))>
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#<alt (* -1 (* eps (- (+ (* -1 (/ (- (+ (* -1 (/ (- (+ (* -1 (/ (* x (* (- (* -1 (/ (* (pow x 2) (pow (- (* 1/6 (pow x 2)) 1) 2)) (- 1/2 (* -1/4 (pow x 2))))) (* -1 (/ (* x (* (- (* 1/6 (pow x 2)) 1) (- (* 1/2 (/ (* (pow x 3) (- (* 1/6 (pow x 2)) 1)) (- 1/2 (* -1/4 (pow x 2))))) (* -1 (/ (* x (* (- 1/4 (* 1/16 (pow x 4))) (- (* 1/6 (pow x 2)) 1))) (pow (- 1/2 (* -1/4 (pow x 2))) 2)))))) (- 1/2 (* -1/4 (pow x 2)))))) (- (* 1/6 (pow x 2)) 1))) (* eps (- 1/2 (* -1/4 (pow x 2)))))) (* -1 (/ (* (pow x 2) (pow (- (* 1/6 (pow x 2)) 1) 2)) (- 1/2 (* -1/4 (pow x 2)))))) (* -1 (/ (* x (* (- (* 1/6 (pow x 2)) 1) (- (* 1/2 (/ (* (pow x 3) (- (* 1/6 (pow x 2)) 1)) (- 1/2 (* -1/4 (pow x 2))))) (* -1 (/ (* x (* (- 1/4 (* 1/16 (pow x 4))) (- (* 1/6 (pow x 2)) 1))) (pow (- 1/2 (* -1/4 (pow x 2))) 2)))))) (- 1/2 (* -1/4 (pow x 2)))))) eps)) (* 1/2 (/ (* (pow x 3) (- (* 1/6 (pow x 2)) 1)) (- 1/2 (* -1/4 (pow x 2)))))) (* -1 (/ (* x (* (- 1/4 (* 1/16 (pow x 4))) (- (* 1/6 (pow x 2)) 1))) (pow (- 1/2 (* -1/4 (pow x 2))) 2)))) eps)) (* 1/4 (/ 1 (- 1/2 (* -1/4 (pow x 2)))))) (* 1/16 (/ (pow x 4) (- 1/2 (* -1/4 (pow x 2))))))))>
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#<alt (* -1 (* (pow x 3) (- (* -1 (/ (- (+ (* -1 (/ (- (+ (* -1 (/ (- (* -3 eps) (+ (* -6 (- (* 1/2 eps) (* 1/4 eps))) (+ (* -3/2 (* eps (- (* 6 (- 1/3 (* 1/16 (pow eps 2)))) (+ 1 (* -3/2 (* eps (- (* 1/2 eps) (* 1/4 eps)))))))) (* 1/2 eps)))) x)) (* 6 (- 1/3 (* 1/16 (pow eps 2))))) (+ 1 (* -3/2 (* eps (- (* 1/2 eps) (* 1/4 eps)))))) x)) (* 1/2 eps)) (* 1/4 eps)) x)) 1/6)))>
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#<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 (sin (* 1/2 eps))>
#<alt (+ (sin (* 1/2 eps)) (* -1/2 (* (pow x 2) (sin (* 1/2 eps)))))>
#<alt (+ (sin (* 1/2 eps)) (* (pow x 2) (+ (* -1/2 (sin (* 1/2 eps))) (* 1/24 (* (pow x 2) (sin (* 1/2 eps)))))))>
#<alt (+ (sin (* 1/2 eps)) (* (pow x 2) (+ (* -1/2 (sin (* 1/2 eps))) (* (pow x 2) (+ (* -1/720 (* (pow x 2) (sin (* 1/2 eps)))) (* 1/24 (sin (* 1/2 eps))))))))>
#<alt (* (cos x) (sin (* 1/2 eps)))>
#<alt (* (cos x) (sin (* 1/2 eps)))>
#<alt (* (cos x) (sin (* 1/2 eps)))>
#<alt (* (cos x) (sin (* 1/2 eps)))>
#<alt (* (cos x) (sin (* 1/2 eps)))>
#<alt (* (cos x) (sin (* 1/2 eps)))>
#<alt (* (cos x) (sin (* 1/2 eps)))>
#<alt (* (cos x) (sin (* 1/2 eps)))>
#<alt (* 1/2 (* eps (cos x)))>
#<alt (* eps (+ (* -1/48 (* (pow eps 2) (cos x))) (* 1/2 (cos x))))>
#<alt (* eps (+ (* 1/2 (cos x)) (* (pow eps 2) (+ (* -1/48 (cos x)) (* 1/3840 (* (pow eps 2) (cos x)))))))>
#<alt (* eps (+ (* 1/2 (cos x)) (* (pow eps 2) (+ (* -1/48 (cos x)) (* (pow eps 2) (+ (* -1/645120 (* (pow eps 2) (cos x))) (* 1/3840 (cos x))))))))>
#<alt (* (cos x) (sin (* 1/2 eps)))>
#<alt (* (cos x) (sin (* 1/2 eps)))>
#<alt (* (cos x) (sin (* 1/2 eps)))>
#<alt (* (cos x) (sin (* 1/2 eps)))>
#<alt (* (cos x) (sin (* 1/2 eps)))>
#<alt (* (cos x) (sin (* 1/2 eps)))>
#<alt (* (cos x) (sin (* 1/2 eps)))>
#<alt (* (cos x) (sin (* 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 (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))>
#<alt (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))>
#<alt (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))>
#<alt (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))>
#<alt (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))>
#<alt (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))>
#<alt (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))>
#<alt (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin 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 (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))>
#<alt (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))>
#<alt (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))>
#<alt (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))>
#<alt (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))>
#<alt (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))>
#<alt (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))>
#<alt (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))>
#<alt (* 1/4 eps)>
#<alt (+ (* 1/6 x) (* 1/4 eps))>
#<alt (+ (* 1/6 x) (* 1/4 eps))>
#<alt (+ (* 1/6 x) (* 1/4 eps))>
#<alt (* 1/6 x)>
#<alt (* x (+ 1/6 (* 1/4 (/ eps x))))>
#<alt (* x (+ 1/6 (* 1/4 (/ eps x))))>
#<alt (* x (+ 1/6 (* 1/4 (/ eps x))))>
#<alt (* 1/6 x)>
#<alt (* -1 (* x (- (* -1/4 (/ eps x)) 1/6)))>
#<alt (* -1 (* x (- (* -1/4 (/ eps x)) 1/6)))>
#<alt (* -1 (* x (- (* -1/4 (/ eps x)) 1/6)))>
#<alt (* 1/6 x)>
#<alt (+ (* 1/6 x) (* 1/4 eps))>
#<alt (+ (* 1/6 x) (* 1/4 eps))>
#<alt (+ (* 1/6 x) (* 1/4 eps))>
#<alt (* 1/4 eps)>
#<alt (* eps (+ 1/4 (* 1/6 (/ x eps))))>
#<alt (* eps (+ 1/4 (* 1/6 (/ x eps))))>
#<alt (* eps (+ 1/4 (* 1/6 (/ x eps))))>
#<alt (* 1/4 eps)>
#<alt (* -1 (* eps (- (* -1/6 (/ x eps)) 1/4)))>
#<alt (* -1 (* eps (- (* -1/6 (/ x eps)) 1/4)))>
#<alt (* -1 (* eps (- (* -1/6 (/ x eps)) 1/4)))>
#<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 (pow eps 3)>
#<alt (pow eps 3)>
#<alt (pow eps 3)>
#<alt (pow eps 3)>
#<alt (pow eps 3)>
#<alt (pow eps 3)>
#<alt (pow eps 3)>
#<alt (pow eps 3)>
#<alt (pow eps 3)>
#<alt (pow eps 3)>
#<alt (pow eps 3)>
#<alt (pow eps 3)>

Calls

99 calls:

Time	Variable		Point	Expression
2.0ms	x	@	-inf	(/ (- (* 1/4 (* eps eps)) (* (* x (+ (* x (+ (* x 1/6) (* eps 1/4))) -1)) (* x (+ (* x (+ (* x 1/6) (* eps 1/4))) -1)))) (- (* eps -1/2) (* x (+ (* x (+ (* x 1/6) (* eps 1/4))) -1))))
2.0ms	eps	@	inf	(* eps (/ (- (* 1/4 (* eps eps)) (* (* x (+ (* x (+ (* x 1/6) (* eps 1/4))) -1)) (* x (+ (* x (+ (* x 1/6) (* eps 1/4))) -1)))) (- (* eps -1/2) (* x (+ (* x (+ (* x 1/6) (* eps 1/4))) -1)))))
2.0ms	eps	@	-inf	(* eps (/ (- (* 1/4 (* eps eps)) (* (* x (+ (* x (+ (* x 1/6) (* eps 1/4))) -1)) (* x (+ (* x (+ (* x 1/6) (* eps 1/4))) -1)))) (- (* eps -1/2) (* x (+ (* x (+ (* x 1/6) (* eps 1/4))) -1)))))
1.0ms	x	@	inf	(* eps (/ (- (* 1/4 (* eps eps)) (* (* x (+ (* x (+ (* x 1/6) (* eps 1/4))) -1)) (* x (+ (* x (+ (* x 1/6) (* eps 1/4))) -1)))) (- (* eps -1/2) (* x (+ (* x (+ (* x 1/6) (* eps 1/4))) -1)))))
1.0ms	eps	@	0	(* eps (/ (- (* 1/4 (* eps eps)) (* (* x (+ (* x (+ (* x 1/6) (* eps 1/4))) -1)) (* x (+ (* x (+ (* x 1/6) (* eps 1/4))) -1)))) (- (* eps -1/2) (* x (+ (* x (+ (* x 1/6) (* eps 1/4))) -1)))))

rewrite440.0ms (2.3%)

Memory

-0.4MiB live, 478.4MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

5 102×	`lower-*.f32`
5 084×	`lower-fma.f32`
5 074×	`lower-fma.f64`
5 066×	`lower-*.f64`
3 648×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	51	338
0	95	284
1	336	194
2	3095	191
0	8994	187

Stop Event

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

Counts

21 → 1 003

Calls

Call 1

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

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

simplify383.0ms (2%)

Memory

2.4MiB live, 798.9MiB allocated

Algorithm

1×	egg-herbie

Rules

10 808×	`lower-fma.f64`
10 808×	`lower-fma.f32`
7 198×	`lower-*.f64`
7 198×	`lower-*.f32`
4 120×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	717	7645
1	2424	7411
0	8325	6785

Stop Event

1×	iter limit
1×	node limit

Counts

396 → 360

Calls

Call 1

Inputs
x
x
x
x
x
x
x
x
x
x
x
x
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
(* -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)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))
(* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))
(* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))
(* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))
(* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))
(* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))
(* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))
(* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))
(* -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)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))
(* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))
(* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))
(* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))
(* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))
(* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))
(* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))
(* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin 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)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))
(* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))
(* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))
(* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))
(* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))
(* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))
(* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))
(* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))
(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)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))
(* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))
(* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))
(* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))
(* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))
(* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))
(* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))
(* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))
(* eps (* x (- (* 1/6 (pow x 2)) 1)))
(* eps (* x (- (* 1/6 (pow x 2)) 1)))
(* eps (* x (- (* 1/6 (pow x 2)) 1)))
(* eps (* x (- (* 1/6 (pow x 2)) 1)))
(* eps (* x (- (* 1/6 (pow x 2)) 1)))
(* eps (* x (- (* 1/6 (pow x 2)) 1)))
(* eps (* x (- (* 1/6 (pow x 2)) 1)))
(* eps (* x (- (* 1/6 (pow x 2)) 1)))
(* eps (* x (- (* 1/6 (pow x 2)) 1)))
(* eps (* x (- (* 1/6 (pow x 2)) 1)))
(* eps (* x (- (* 1/6 (pow x 2)) 1)))
(* eps (* x (- (* 1/6 (pow x 2)) 1)))
(* -1 (* eps x))
(* x (+ (* -1 eps) (* 1/6 (* eps (pow x 2)))))
(* x (+ (* -1 eps) (* 1/6 (* eps (pow x 2)))))
(* x (+ (* -1 eps) (* 1/6 (* eps (pow x 2)))))
(* 1/6 (* eps (pow x 3)))
(* (pow x 3) (+ (* -1 (/ eps (pow x 2))) (* 1/6 eps)))
(* (pow x 3) (+ (* -1 (/ eps (pow x 2))) (* 1/6 eps)))
(* (pow x 3) (+ (* -1 (/ eps (pow x 2))) (* 1/6 eps)))
(* 1/6 (* eps (pow x 3)))
(* -1 (* (pow x 3) (+ (* -1/6 eps) (/ eps (pow x 2)))))
(* -1 (* (pow x 3) (+ (* -1/6 eps) (/ eps (pow x 2)))))
(* -1 (* (pow x 3) (+ (* -1/6 eps) (/ eps (pow x 2)))))
(* -1 x)
(* x (- (* 1/6 (pow x 2)) 1))
(* x (- (* 1/6 (pow x 2)) 1))
(* x (- (* 1/6 (pow x 2)) 1))
(* 1/6 (pow x 3))
(* (pow x 3) (- 1/6 (/ 1 (pow x 2))))
(* (pow x 3) (- 1/6 (/ 1 (pow x 2))))
(* (pow x 3) (- 1/6 (/ 1 (pow x 2))))
(* 1/6 (pow x 3))
(* -1 (* (pow x 3) (- (/ 1 (pow x 2)) 1/6)))
(* -1 (* (pow x 3) (- (/ 1 (pow x 2)) 1/6)))
(* -1 (* (pow x 3) (- (/ 1 (pow x 2)) 1/6)))
-1
(- (* 1/6 (pow x 2)) 1)
(- (* 1/6 (pow x 2)) 1)
(- (* 1/6 (pow x 2)) 1)
(* 1/6 (pow x 2))
(* (pow x 2) (- 1/6 (/ 1 (pow x 2))))
(* (pow x 2) (- 1/6 (/ 1 (pow x 2))))
(* (pow x 2) (- 1/6 (/ 1 (pow x 2))))
(* 1/6 (pow x 2))
(* (pow x 2) (- 1/6 (/ 1 (pow x 2))))
(* (pow x 2) (- 1/6 (/ 1 (pow x 2))))
(* (pow x 2) (- 1/6 (/ 1 (pow x 2))))
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* -1 (* (pow x 2) (pow (- (* 1/6 (pow x 2)) 1) 2)))
(- (* -1/2 (* eps (* (pow x 3) (- (* 1/6 (pow x 2)) 1)))) (* (pow x 2) (pow (- (* 1/6 (pow x 2)) 1) 2)))
(- (* eps (- (* eps (- 1/4 (* 1/16 (pow x 4)))) (* 1/2 (* (pow x 3) (- (* 1/6 (pow x 2)) 1))))) (* (pow x 2) (pow (- (* 1/6 (pow x 2)) 1) 2)))
(- (* eps (- (* eps (- 1/4 (* 1/16 (pow x 4)))) (* 1/2 (* (pow x 3) (- (* 1/6 (pow x 2)) 1))))) (* (pow x 2) (pow (- (* 1/6 (pow x 2)) 1) 2)))
(* (pow eps 2) (- 1/4 (* 1/16 (pow x 4))))
(* (pow eps 2) (- (+ 1/4 (* -1/2 (/ (* (pow x 3) (- (* 1/6 (pow x 2)) 1)) eps))) (* 1/16 (pow x 4))))
(* (pow eps 2) (- (+ 1/4 (* -1 (/ (* (pow x 2) (pow (- (* 1/6 (pow x 2)) 1) 2)) (pow eps 2)))) (+ (* 1/16 (pow x 4)) (* 1/2 (/ (* (pow x 3) (- (* 1/6 (pow x 2)) 1)) eps)))))
(* (pow eps 2) (- (+ 1/4 (* -1 (/ (* (pow x 2) (pow (- (* 1/6 (pow x 2)) 1) 2)) (pow eps 2)))) (+ (* 1/16 (pow x 4)) (* 1/2 (/ (* (pow x 3) (- (* 1/6 (pow x 2)) 1)) eps)))))
(* (pow eps 2) (- 1/4 (* 1/16 (pow x 4))))
(* (pow eps 2) (- (+ 1/4 (* -1/2 (/ (* (pow x 3) (- (* 1/6 (pow x 2)) 1)) eps))) (* 1/16 (pow x 4))))
(* (pow eps 2) (- (+ 1/4 (* -1 (/ (- (/ (* (pow x 2) (pow (- (* 1/6 (pow x 2)) 1) 2)) eps) (* -1/2 (* (pow x 3) (- (* 1/6 (pow x 2)) 1)))) eps))) (* 1/16 (pow x 4))))
(* (pow eps 2) (- (+ 1/4 (* -1 (/ (- (/ (* (pow x 2) (pow (- (* 1/6 (pow x 2)) 1) 2)) eps) (* -1/2 (* (pow x 3) (- (* 1/6 (pow x 2)) 1)))) eps))) (* 1/16 (pow x 4))))
(* 1/4 (pow eps 2))
(+ (* -1 (pow x 2)) (* 1/4 (pow eps 2)))
(+ (* 1/4 (pow eps 2)) (* (pow x 2) (- (* 1/2 (* eps x)) 1)))
(+ (* 1/4 (pow eps 2)) (* (pow x 2) (- (* x (- (* x (- 1/3 (* 1/16 (pow eps 2)))) (* -1/2 eps))) 1)))
(* -1/36 (pow x 6))
(* (pow x 6) (- (* -1/12 (/ eps x)) 1/36))
(* (pow x 6) (- (/ 1/3 (pow x 2)) (+ 1/36 (+ (* 1/16 (/ (pow eps 2) (pow x 2))) (* 1/12 (/ eps x))))))
(* (pow x 6) (- (+ (* 1/2 (/ eps (pow x 3))) (/ 1/3 (pow x 2))) (+ 1/36 (+ (* 1/16 (/ (pow eps 2) (pow x 2))) (* 1/12 (/ eps x))))))
(* -1/36 (pow x 6))
(* (pow x 6) (- (* -1/12 (/ eps x)) 1/36))
(* (pow x 6) (- (* -1 (/ (- (* -1 (/ (- 1/3 (* 1/16 (pow eps 2))) x)) (* -1/12 eps)) x)) 1/36))
(* (pow x 6) (- (* -1 (/ (- (* -1 (/ (- (+ 1/3 (* 1/2 (/ eps x))) (* 1/16 (pow eps 2))) x)) (* -1/12 eps)) x)) 1/36))
(* -1 (* x (- (* 1/6 (pow x 2)) 1)))
(- (* -1 (* eps (+ 1/2 (* 1/4 (pow x 2))))) (* x (- (* 1/6 (pow x 2)) 1)))
(- (* -1 (* eps (+ 1/2 (* 1/4 (pow x 2))))) (* x (- (* 1/6 (pow x 2)) 1)))
(- (* -1 (* eps (+ 1/2 (* 1/4 (pow x 2))))) (* x (- (* 1/6 (pow x 2)) 1)))
(* -1 (* eps (+ 1/2 (* 1/4 (pow x 2)))))
(* eps (- (* -1 (/ (* x (- (* 1/6 (pow x 2)) 1)) eps)) (+ 1/2 (* 1/4 (pow x 2)))))
(* eps (- (* -1 (/ (* x (- (* 1/6 (pow x 2)) 1)) eps)) (+ 1/2 (* 1/4 (pow x 2)))))
(* eps (- (* -1 (/ (* x (- (* 1/6 (pow x 2)) 1)) eps)) (+ 1/2 (* 1/4 (pow x 2)))))
(* -1 (* eps (- 1/2 (* -1/4 (pow x 2)))))
(* -1 (* eps (- (+ 1/2 (/ (* x (- (* 1/6 (pow x 2)) 1)) eps)) (* -1/4 (pow x 2)))))
(* -1 (* eps (- (+ 1/2 (/ (* x (- (* 1/6 (pow x 2)) 1)) eps)) (* -1/4 (pow x 2)))))
(* -1 (* eps (- (+ 1/2 (/ (* x (- (* 1/6 (pow x 2)) 1)) eps)) (* -1/4 (pow x 2)))))
(* -1/2 eps)
(+ x (* -1/2 eps))
(+ (* -1/2 eps) (* x (+ 1 (* -1/4 (* eps x)))))
(+ (* -1/2 eps) (* x (+ 1 (* x (- (* -1/6 x) (* 1/4 eps))))))
(* -1/6 (pow x 3))
(* (pow x 3) (- (* -1/4 (/ eps x)) 1/6))
(* (pow x 3) (- (/ 1 (pow x 2)) (+ 1/6 (* 1/4 (/ eps x)))))
(* (pow x 3) (- (+ (* -1/2 (/ eps (pow x 3))) (/ 1 (pow x 2))) (+ 1/6 (* 1/4 (/ eps x)))))
(* -1/6 (pow x 3))
(* -1 (* (pow x 3) (+ 1/6 (* 1/4 (/ eps x)))))
(* -1 (* (pow x 3) (+ 1/6 (* -1 (/ (- (/ 1 x) (* 1/4 eps)) x)))))
(* -1 (* (pow x 3) (+ 1/6 (* -1 (/ (- (* -1 (/ (- (* 1/2 (/ eps x)) 1) x)) (* 1/4 eps)) x)))))
(* eps (* x (- (* 1/6 (pow x 2)) 1)))
(* eps (+ (* eps (- (* 1/2 (pow x 2)) (+ 1/2 (* 1/4 (pow x 2))))) (* x (- (* 1/6 (pow x 2)) 1))))
(* eps (+ (* eps (- (+ (* 1/2 (pow x 2)) (* eps (- (* -1 (/ (- 1/4 (* 1/16 (pow x 4))) (* x (- (* 1/6 (pow x 2)) 1)))) (/ (* (+ 1/2 (* 1/4 (pow x 2))) (- (* 1/2 (pow x 2)) (+ 1/2 (* 1/4 (pow x 2))))) (* x (- (* 1/6 (pow x 2)) 1)))))) (+ 1/2 (* 1/4 (pow x 2))))) (* x (- (* 1/6 (pow x 2)) 1))))
(* eps (+ (* eps (- (+ (* 1/2 (pow x 2)) (* eps (- (+ (* -1 (/ (* eps (* (+ 1/2 (* 1/4 (pow x 2))) (- (* -1 (/ (- 1/4 (* 1/16 (pow x 4))) (* x (- (* 1/6 (pow x 2)) 1)))) (/ (* (+ 1/2 (* 1/4 (pow x 2))) (- (* 1/2 (pow x 2)) (+ 1/2 (* 1/4 (pow x 2))))) (* x (- (* 1/6 (pow x 2)) 1)))))) (* x (- (* 1/6 (pow x 2)) 1)))) (* -1 (/ (- 1/4 (* 1/16 (pow x 4))) (* x (- (* 1/6 (pow x 2)) 1))))) (/ (* (+ 1/2 (* 1/4 (pow x 2))) (- (* 1/2 (pow x 2)) (+ 1/2 (* 1/4 (pow x 2))))) (* x (- (* 1/6 (pow x 2)) 1)))))) (+ 1/2 (* 1/4 (pow x 2))))) (* x (- (* 1/6 (pow x 2)) 1))))
(* -1 (/ (* (pow eps 2) (- 1/4 (* 1/16 (pow x 4)))) (+ 1/2 (* 1/4 (pow x 2)))))
(* (pow eps 2) (+ (* -1 (/ (- 1/4 (* 1/16 (pow x 4))) (+ 1/2 (* 1/4 (pow x 2))))) (* -1 (/ (- (* -1/2 (/ (* (pow x 3) (- (* 1/6 (pow x 2)) 1)) (+ 1/2 (* 1/4 (pow x 2))))) (/ (* x (* (- 1/4 (* 1/16 (pow x 4))) (- (* 1/6 (pow x 2)) 1))) (pow (+ 1/2 (* 1/4 (pow x 2))) 2))) eps))))
(* (pow eps 2) (+ (* -1 (/ (- 1/4 (* 1/16 (pow x 4))) (+ 1/2 (* 1/4 (pow x 2))))) (+ (* -1 (/ (- (* -1 (/ (* (pow x 2) (pow (- (* 1/6 (pow x 2)) 1) 2)) (+ 1/2 (* 1/4 (pow x 2))))) (/ (* x (* (- (* -1/2 (/ (* (pow x 3) (- (* 1/6 (pow x 2)) 1)) (+ 1/2 (* 1/4 (pow x 2))))) (/ (* x (* (- 1/4 (* 1/16 (pow x 4))) (- (* 1/6 (pow x 2)) 1))) (pow (+ 1/2 (* 1/4 (pow x 2))) 2))) (- (* 1/6 (pow x 2)) 1))) (+ 1/2 (* 1/4 (pow x 2))))) (pow eps 2))) (* -1 (/ (- (* -1/2 (/ (* (pow x 3) (- (* 1/6 (pow x 2)) 1)) (+ 1/2 (* 1/4 (pow x 2))))) (/ (* x (* (- 1/4 (* 1/16 (pow x 4))) (- (* 1/6 (pow x 2)) 1))) (pow (+ 1/2 (* 1/4 (pow x 2))) 2))) eps)))))
(* (pow eps 2) (+ (* -1 (/ (- 1/4 (* 1/16 (pow x 4))) (+ 1/2 (* 1/4 (pow x 2))))) (+ (* -1 (/ (- (* -1 (/ (* (pow x 2) (pow (- (* 1/6 (pow x 2)) 1) 2)) (+ 1/2 (* 1/4 (pow x 2))))) (/ (* x (* (- (* -1/2 (/ (* (pow x 3) (- (* 1/6 (pow x 2)) 1)) (+ 1/2 (* 1/4 (pow x 2))))) (/ (* x (* (- 1/4 (* 1/16 (pow x 4))) (- (* 1/6 (pow x 2)) 1))) (pow (+ 1/2 (* 1/4 (pow x 2))) 2))) (- (* 1/6 (pow x 2)) 1))) (+ 1/2 (* 1/4 (pow x 2))))) (pow eps 2))) (+ (* -1 (/ (- (* -1/2 (/ (* (pow x 3) (- (* 1/6 (pow x 2)) 1)) (+ 1/2 (* 1/4 (pow x 2))))) (/ (* x (* (- 1/4 (* 1/16 (pow x 4))) (- (* 1/6 (pow x 2)) 1))) (pow (+ 1/2 (* 1/4 (pow x 2))) 2))) eps)) (/ (* x (* (- (* -1 (/ (* (pow x 2) (pow (- (* 1/6 (pow x 2)) 1) 2)) (+ 1/2 (* 1/4 (pow x 2))))) (/ (* x (* (- (* -1/2 (/ (* (pow x 3) (- (* 1/6 (pow x 2)) 1)) (+ 1/2 (* 1/4 (pow x 2))))) (/ (* x (* (- 1/4 (* 1/16 (pow x 4))) (- (* 1/6 (pow x 2)) 1))) (pow (+ 1/2 (* 1/4 (pow x 2))) 2))) (- (* 1/6 (pow x 2)) 1))) (+ 1/2 (* 1/4 (pow x 2))))) (- (* 1/6 (pow x 2)) 1))) (* (pow eps 3) (+ 1/2 (* 1/4 (pow x 2)))))))))
(* -1 (/ (* (pow eps 2) (- 1/4 (* 1/16 (pow x 4)))) (- 1/2 (* -1/4 (pow x 2)))))
(* (pow eps 2) (- (+ (* -1 (/ (- 1/4 (* 1/16 (pow x 4))) (- 1/2 (* -1/4 (pow x 2))))) (* 1/2 (/ (* (pow x 3) (- (* 1/6 (pow x 2)) 1)) (* eps (- 1/2 (* -1/4 (pow x 2))))))) (* -1 (/ (* x (* (- 1/4 (* 1/16 (pow x 4))) (- (* 1/6 (pow x 2)) 1))) (* eps (pow (- 1/2 (* -1/4 (pow x 2))) 2))))))
(* (pow eps 2) (+ (* -1 (/ (- 1/4 (* 1/16 (pow x 4))) (- 1/2 (* -1/4 (pow x 2))))) (* -1 (/ (- (+ (* -1 (- (* 1/2 (/ (* (pow x 3) (- (* 1/6 (pow x 2)) 1)) (- 1/2 (* -1/4 (pow x 2))))) (* -1 (/ (* x (* (- 1/4 (* 1/16 (pow x 4))) (- (* 1/6 (pow x 2)) 1))) (pow (- 1/2 (* -1/4 (pow x 2))) 2))))) (* -1 (/ (* (pow x 2) (pow (- (* 1/6 (pow x 2)) 1) 2)) (* eps (- 1/2 (* -1/4 (pow x 2))))))) (* -1 (/ (* x (* (- (* 1/6 (pow x 2)) 1) (- (* 1/2 (/ (* (pow x 3) (- (* 1/6 (pow x 2)) 1)) (- 1/2 (* -1/4 (pow x 2))))) (* -1 (/ (* x (* (- 1/4 (* 1/16 (pow x 4))) (- (* 1/6 (pow x 2)) 1))) (pow (- 1/2 (* -1/4 (pow x 2))) 2)))))) (* eps (- 1/2 (* -1/4 (pow x 2))))))) eps))))
(* (pow eps 2) (+ (* -1 (/ (+ (* -1 (- (* 1/2 (/ (* (pow x 3) (- (* 1/6 (pow x 2)) 1)) (- 1/2 (* -1/4 (pow x 2))))) (* -1 (/ (* x (* (- 1/4 (* 1/16 (pow x 4))) (- (* 1/6 (pow x 2)) 1))) (pow (- 1/2 (* -1/4 (pow x 2))) 2))))) (* -1 (/ (+ (* -1 (- (* -1 (/ (* (pow x 2) (pow (- (* 1/6 (pow x 2)) 1) 2)) (- 1/2 (* -1/4 (pow x 2))))) (* -1 (/ (* x (* (- (* 1/6 (pow x 2)) 1) (- (* 1/2 (/ (* (pow x 3) (- (* 1/6 (pow x 2)) 1)) (- 1/2 (* -1/4 (pow x 2))))) (* -1 (/ (* x (* (- 1/4 (* 1/16 (pow x 4))) (- (* 1/6 (pow x 2)) 1))) (pow (- 1/2 (* -1/4 (pow x 2))) 2)))))) (- 1/2 (* -1/4 (pow x 2))))))) (/ (* x (* (- (* -1 (/ (* (pow x 2) (pow (- (* 1/6 (pow x 2)) 1) 2)) (- 1/2 (* -1/4 (pow x 2))))) (* -1 (/ (* x (* (- (* 1/6 (pow x 2)) 1) (- (* 1/2 (/ (* (pow x 3) (- (* 1/6 (pow x 2)) 1)) (- 1/2 (* -1/4 (pow x 2))))) (* -1 (/ (* x (* (- 1/4 (* 1/16 (pow x 4))) (- (* 1/6 (pow x 2)) 1))) (pow (- 1/2 (* -1/4 (pow x 2))) 2)))))) (- 1/2 (* -1/4 (pow x 2)))))) (- (* 1/6 (pow x 2)) 1))) (* eps (- 1/2 (* -1/4 (pow x 2)))))) eps))) eps)) (* -1 (/ (- 1/4 (* 1/16 (pow x 4))) (- 1/2 (* -1/4 (pow x 2)))))))
(* -1/2 (pow eps 2))
(+ (* -1 (* eps x)) (* -1/2 (pow eps 2)))
(+ (* -1/2 (pow eps 2)) (* x (- (* 1/4 (* (pow eps 2) x)) eps)))
(+ (* -1/2 (pow eps 2)) (* x (- (* x (- (* 1/6 (* eps x)) (* -1/4 (pow eps 2)))) eps)))
(* 1/6 (* eps (pow x 3)))
(* (pow x 3) (- (+ (* 1/6 eps) (* 1/2 (/ (pow eps 2) x))) (* 1/4 (/ (pow eps 2) x))))
(* (pow x 3) (- (+ (* -6 (/ (* eps (- 1/3 (* 1/16 (pow eps 2)))) (pow x 2))) (+ (* 1/6 eps) (* 1/2 (/ (pow eps 2) x)))) (+ (* -1 (/ eps (pow x 2))) (+ (* 1/4 (/ (pow eps 2) x)) (* 3/2 (/ (* eps (- (* 1/2 (pow eps 2)) (* 1/4 (pow eps 2)))) (pow x 2)))))))
(* (pow x 3) (- (+ (* -6 (/ (* eps (- 1/3 (* 1/16 (pow eps 2)))) (pow x 2))) (+ (* -3 (/ (pow eps 2) (pow x 3))) (+ (* 1/6 eps) (* 1/2 (/ (pow eps 2) x))))) (+ (* -6 (/ (- (* 1/2 (pow eps 2)) (* 1/4 (pow eps 2))) (pow x 3))) (+ (* -1 (/ eps (pow x 2))) (+ (* 1/4 (/ (pow eps 2) x)) (+ (* 1/2 (/ (pow eps 2) (pow x 3))) (+ (* 3/2 (/ (* eps (- (* -6 (* eps (- 1/3 (* 1/16 (pow eps 2))))) (+ (* -1 eps) (* 3/2 (* eps (- (* 1/2 (pow eps 2)) (* 1/4 (pow eps 2)))))))) (pow x 3))) (* 3/2 (/ (* eps (- (* 1/2 (pow eps 2)) (* 1/4 (pow eps 2)))) (pow x 2))))))))))
(* 1/6 (* eps (pow x 3)))
(* -1 (* (pow x 3) (+ (* -1 (/ (- (* 1/2 (pow eps 2)) (* 1/4 (pow eps 2))) x)) (* -1/6 eps))))
(* -1 (* (pow x 3) (+ (* -1 (/ (- (+ (* -1 (/ (- (* 6 (* eps (- 1/3 (* 1/16 (pow eps 2))))) (+ eps (* -3/2 (* eps (- (* 1/2 (pow eps 2)) (* 1/4 (pow eps 2))))))) x)) (* 1/2 (pow eps 2))) (* 1/4 (pow eps 2))) x)) (* -1/6 eps))))
(* -1 (* (pow x 3) (+ (* -1 (/ (- (+ (* -1 (/ (- (+ (* -1 (/ (- (* -3 (pow eps 2)) (+ (* -6 (- (* 1/2 (pow eps 2)) (* 1/4 (pow eps 2)))) (+ (* -3/2 (* eps (- (* 6 (* eps (- 1/3 (* 1/16 (pow eps 2))))) (+ eps (* -3/2 (* eps (- (* 1/2 (pow eps 2)) (* 1/4 (pow eps 2))))))))) (* 1/2 (pow eps 2))))) x)) (* 6 (* eps (- 1/3 (* 1/16 (pow eps 2)))))) (+ eps (* -3/2 (* eps (- (* 1/2 (pow eps 2)) (* 1/4 (pow eps 2))))))) x)) (* 1/2 (pow eps 2))) (* 1/4 (pow eps 2))) x)) (* -1/6 eps))))
(* x (- (* 1/6 (pow x 2)) 1))
(+ (* eps (- (* 1/2 (pow x 2)) (+ 1/2 (* 1/4 (pow x 2))))) (* x (- (* 1/6 (pow x 2)) 1)))
(+ (* eps (- (+ (* 1/2 (pow x 2)) (* eps (- (* -1 (/ (- 1/4 (* 1/16 (pow x 4))) (* x (- (* 1/6 (pow x 2)) 1)))) (/ (* (+ 1/2 (* 1/4 (pow x 2))) (- (* 1/2 (pow x 2)) (+ 1/2 (* 1/4 (pow x 2))))) (* x (- (* 1/6 (pow x 2)) 1)))))) (+ 1/2 (* 1/4 (pow x 2))))) (* x (- (* 1/6 (pow x 2)) 1)))
(+ (* eps (- (+ (* 1/2 (pow x 2)) (* eps (- (+ (* -1 (/ (* eps (* (+ 1/2 (* 1/4 (pow x 2))) (- (* -1 (/ (- 1/4 (* 1/16 (pow x 4))) (* x (- (* 1/6 (pow x 2)) 1)))) (/ (* (+ 1/2 (* 1/4 (pow x 2))) (- (* 1/2 (pow x 2)) (+ 1/2 (* 1/4 (pow x 2))))) (* x (- (* 1/6 (pow x 2)) 1)))))) (* x (- (* 1/6 (pow x 2)) 1)))) (* -1 (/ (- 1/4 (* 1/16 (pow x 4))) (* x (- (* 1/6 (pow x 2)) 1))))) (/ (* (+ 1/2 (* 1/4 (pow x 2))) (- (* 1/2 (pow x 2)) (+ 1/2 (* 1/4 (pow x 2))))) (* x (- (* 1/6 (pow x 2)) 1)))))) (+ 1/2 (* 1/4 (pow x 2))))) (* x (- (* 1/6 (pow x 2)) 1)))
(* -1 (/ (* eps (- 1/4 (* 1/16 (pow x 4)))) (+ 1/2 (* 1/4 (pow x 2)))))
(* eps (+ (* -1 (/ (- 1/4 (* 1/16 (pow x 4))) (+ 1/2 (* 1/4 (pow x 2))))) (* -1 (/ (- (* -1/2 (/ (* (pow x 3) (- (* 1/6 (pow x 2)) 1)) (+ 1/2 (* 1/4 (pow x 2))))) (/ (* x (* (- 1/4 (* 1/16 (pow x 4))) (- (* 1/6 (pow x 2)) 1))) (pow (+ 1/2 (* 1/4 (pow x 2))) 2))) eps))))
(* eps (+ (* -1 (/ (- 1/4 (* 1/16 (pow x 4))) (+ 1/2 (* 1/4 (pow x 2))))) (+ (* -1 (/ (- (* -1 (/ (* (pow x 2) (pow (- (* 1/6 (pow x 2)) 1) 2)) (+ 1/2 (* 1/4 (pow x 2))))) (/ (* x (* (- (* -1/2 (/ (* (pow x 3) (- (* 1/6 (pow x 2)) 1)) (+ 1/2 (* 1/4 (pow x 2))))) (/ (* x (* (- 1/4 (* 1/16 (pow x 4))) (- (* 1/6 (pow x 2)) 1))) (pow (+ 1/2 (* 1/4 (pow x 2))) 2))) (- (* 1/6 (pow x 2)) 1))) (+ 1/2 (* 1/4 (pow x 2))))) (pow eps 2))) (* -1 (/ (- (* -1/2 (/ (* (pow x 3) (- (* 1/6 (pow x 2)) 1)) (+ 1/2 (* 1/4 (pow x 2))))) (/ (* x (* (- 1/4 (* 1/16 (pow x 4))) (- (* 1/6 (pow x 2)) 1))) (pow (+ 1/2 (* 1/4 (pow x 2))) 2))) eps)))))
(* eps (+ (* -1 (/ (- 1/4 (* 1/16 (pow x 4))) (+ 1/2 (* 1/4 (pow x 2))))) (+ (* -1 (/ (- (* -1 (/ (* (pow x 2) (pow (- (* 1/6 (pow x 2)) 1) 2)) (+ 1/2 (* 1/4 (pow x 2))))) (/ (* x (* (- (* -1/2 (/ (* (pow x 3) (- (* 1/6 (pow x 2)) 1)) (+ 1/2 (* 1/4 (pow x 2))))) (/ (* x (* (- 1/4 (* 1/16 (pow x 4))) (- (* 1/6 (pow x 2)) 1))) (pow (+ 1/2 (* 1/4 (pow x 2))) 2))) (- (* 1/6 (pow x 2)) 1))) (+ 1/2 (* 1/4 (pow x 2))))) (pow eps 2))) (+ (* -1 (/ (- (* -1/2 (/ (* (pow x 3) (- (* 1/6 (pow x 2)) 1)) (+ 1/2 (* 1/4 (pow x 2))))) (/ (* x (* (- 1/4 (* 1/16 (pow x 4))) (- (* 1/6 (pow x 2)) 1))) (pow (+ 1/2 (* 1/4 (pow x 2))) 2))) eps)) (/ (* x (* (- (* -1 (/ (* (pow x 2) (pow (- (* 1/6 (pow x 2)) 1) 2)) (+ 1/2 (* 1/4 (pow x 2))))) (/ (* x (* (- (* -1/2 (/ (* (pow x 3) (- (* 1/6 (pow x 2)) 1)) (+ 1/2 (* 1/4 (pow x 2))))) (/ (* x (* (- 1/4 (* 1/16 (pow x 4))) (- (* 1/6 (pow x 2)) 1))) (pow (+ 1/2 (* 1/4 (pow x 2))) 2))) (- (* 1/6 (pow x 2)) 1))) (+ 1/2 (* 1/4 (pow x 2))))) (- (* 1/6 (pow x 2)) 1))) (* (pow eps 3) (+ 1/2 (* 1/4 (pow x 2)))))))))
(* -1 (/ (* eps (- 1/4 (* 1/16 (pow x 4)))) (- 1/2 (* -1/4 (pow x 2)))))
(* -1 (* eps (- (+ (* -1 (/ (- (* 1/2 (/ (* (pow x 3) (- (* 1/6 (pow x 2)) 1)) (- 1/2 (* -1/4 (pow x 2))))) (* -1 (/ (* x (* (- 1/4 (* 1/16 (pow x 4))) (- (* 1/6 (pow x 2)) 1))) (pow (- 1/2 (* -1/4 (pow x 2))) 2)))) eps)) (* 1/4 (/ 1 (- 1/2 (* -1/4 (pow x 2)))))) (* 1/16 (/ (pow x 4) (- 1/2 (* -1/4 (pow x 2))))))))
(* -1 (* eps (- (+ (* -1 (/ (- (+ (* -1 (/ (- (* -1 (/ (* (pow x 2) (pow (- (* 1/6 (pow x 2)) 1) 2)) (- 1/2 (* -1/4 (pow x 2))))) (* -1 (/ (* x (* (- (* 1/6 (pow x 2)) 1) (- (* 1/2 (/ (* (pow x 3) (- (* 1/6 (pow x 2)) 1)) (- 1/2 (* -1/4 (pow x 2))))) (* -1 (/ (* x (* (- 1/4 (* 1/16 (pow x 4))) (- (* 1/6 (pow x 2)) 1))) (pow (- 1/2 (* -1/4 (pow x 2))) 2)))))) (- 1/2 (* -1/4 (pow x 2)))))) eps)) (* 1/2 (/ (* (pow x 3) (- (* 1/6 (pow x 2)) 1)) (- 1/2 (* -1/4 (pow x 2)))))) (* -1 (/ (* x (* (- 1/4 (* 1/16 (pow x 4))) (- (* 1/6 (pow x 2)) 1))) (pow (- 1/2 (* -1/4 (pow x 2))) 2)))) eps)) (* 1/4 (/ 1 (- 1/2 (* -1/4 (pow x 2)))))) (* 1/16 (/ (pow x 4) (- 1/2 (* -1/4 (pow x 2))))))))
(* -1 (* eps (- (+ (* -1 (/ (- (+ (* -1 (/ (- (+ (* -1 (/ (* x (* (- (* -1 (/ (* (pow x 2) (pow (- (* 1/6 (pow x 2)) 1) 2)) (- 1/2 (* -1/4 (pow x 2))))) (* -1 (/ (* x (* (- (* 1/6 (pow x 2)) 1) (- (* 1/2 (/ (* (pow x 3) (- (* 1/6 (pow x 2)) 1)) (- 1/2 (* -1/4 (pow x 2))))) (* -1 (/ (* x (* (- 1/4 (* 1/16 (pow x 4))) (- (* 1/6 (pow x 2)) 1))) (pow (- 1/2 (* -1/4 (pow x 2))) 2)))))) (- 1/2 (* -1/4 (pow x 2)))))) (- (* 1/6 (pow x 2)) 1))) (* eps (- 1/2 (* -1/4 (pow x 2)))))) (* -1 (/ (* (pow x 2) (pow (- (* 1/6 (pow x 2)) 1) 2)) (- 1/2 (* -1/4 (pow x 2)))))) (* -1 (/ (* x (* (- (* 1/6 (pow x 2)) 1) (- (* 1/2 (/ (* (pow x 3) (- (* 1/6 (pow x 2)) 1)) (- 1/2 (* -1/4 (pow x 2))))) (* -1 (/ (* x (* (- 1/4 (* 1/16 (pow x 4))) (- (* 1/6 (pow x 2)) 1))) (pow (- 1/2 (* -1/4 (pow x 2))) 2)))))) (- 1/2 (* -1/4 (pow x 2)))))) eps)) (* 1/2 (/ (* (pow x 3) (- (* 1/6 (pow x 2)) 1)) (- 1/2 (* -1/4 (pow x 2)))))) (* -1 (/ (* x (* (- 1/4 (* 1/16 (pow x 4))) (- (* 1/6 (pow x 2)) 1))) (pow (- 1/2 (* -1/4 (pow x 2))) 2)))) eps)) (* 1/4 (/ 1 (- 1/2 (* -1/4 (pow x 2)))))) (* 1/16 (/ (pow x 4) (- 1/2 (* -1/4 (pow x 2))))))))
(* -1/2 eps)
(+ (* -1 x) (* -1/2 eps))
(+ (* -1/2 eps) (* x (- (* x (- (* 2 (/ 1 eps)) (+ (* -1/4 eps) (* 2 (/ 1 eps))))) 1)))
(+ (* -1/2 eps) (* x (- (* x (- (* -1 (* x (+ 1/3 (* -2 (/ (- (* 2 (/ 1 eps)) (+ (* -1/4 eps) (* 2 (/ 1 eps)))) eps))))) (* -1/4 eps))) 1)))
(* 1/6 (pow x 3))
(* (pow x 3) (- (+ 1/6 (* 1/2 (/ eps x))) (* 1/4 (/ eps x))))
(* (pow x 3) (- (+ 1/6 (+ (* -6 (/ (- 1/3 (* 1/16 (pow eps 2))) (pow x 2))) (+ (* 1/2 (/ eps x)) (/ 1 (pow x 2))))) (+ (* 1/4 (/ eps x)) (* 3/2 (/ (* eps (- (* 1/2 eps) (* 1/4 eps))) (pow x 2))))))
(* (pow x 3) (- (+ 1/6 (+ (* -6 (/ (- 1/3 (* 1/16 (pow eps 2))) (pow x 2))) (+ (* -3 (/ eps (pow x 3))) (+ (* 1/2 (/ eps x)) (/ 1 (pow x 2)))))) (+ (* -6 (/ (- (* 1/2 eps) (* 1/4 eps)) (pow x 3))) (+ (* 1/4 (/ eps x)) (+ (* 1/2 (/ eps (pow x 3))) (+ (* 3/2 (/ (* eps (- (* 1/2 eps) (* 1/4 eps))) (pow x 2))) (* 3/2 (/ (* eps (- (+ 1 (* -6 (- 1/3 (* 1/16 (pow eps 2))))) (* 3/2 (* eps (- (* 1/2 eps) (* 1/4 eps)))))) (pow x 3)))))))))
(* 1/6 (pow x 3))
(* -1 (* (pow x 3) (- (* -1 (/ (- (* 1/2 eps) (* 1/4 eps)) x)) 1/6)))
(* -1 (* (pow x 3) (- (* -1 (/ (- (+ (* -1 (/ (- (* 6 (- 1/3 (* 1/16 (pow eps 2)))) (+ 1 (* -3/2 (* eps (- (* 1/2 eps) (* 1/4 eps)))))) x)) (* 1/2 eps)) (* 1/4 eps)) x)) 1/6)))
(* -1 (* (pow x 3) (- (* -1 (/ (- (+ (* -1 (/ (- (+ (* -1 (/ (- (* -3 eps) (+ (* -6 (- (* 1/2 eps) (* 1/4 eps))) (+ (* -3/2 (* eps (- (* 6 (- 1/3 (* 1/16 (pow eps 2)))) (+ 1 (* -3/2 (* eps (- (* 1/2 eps) (* 1/4 eps)))))))) (* 1/2 eps)))) x)) (* 6 (- 1/3 (* 1/16 (pow eps 2))))) (+ 1 (* -3/2 (* eps (- (* 1/2 eps) (* 1/4 eps)))))) x)) (* 1/2 eps)) (* 1/4 eps)) x)) 1/6)))
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
(pow eps 3)
(pow eps 3)
(pow eps 3)
(pow eps 3)
(pow eps 3)
(pow eps 3)
(pow eps 3)
(pow eps 3)
(pow eps 3)
(pow eps 3)
(pow eps 3)
(pow eps 3)
(/ 1 (pow eps 2))
(/ 1 (pow eps 2))
(/ 1 (pow eps 2))
(/ 1 (pow eps 2))
(/ 1 (pow eps 2))
(/ 1 (pow eps 2))
(/ 1 (pow eps 2))
(/ 1 (pow eps 2))
(/ 1 (pow eps 2))
(/ 1 (pow eps 2))
(/ 1 (pow eps 2))
(/ 1 (pow eps 2))
(* -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)))))
(sin (* 1/2 eps))
(+ (sin (* 1/2 eps)) (* -1/2 (* (pow x 2) (sin (* 1/2 eps)))))
(+ (sin (* 1/2 eps)) (* (pow x 2) (+ (* -1/2 (sin (* 1/2 eps))) (* 1/24 (* (pow x 2) (sin (* 1/2 eps)))))))
(+ (sin (* 1/2 eps)) (* (pow x 2) (+ (* -1/2 (sin (* 1/2 eps))) (* (pow x 2) (+ (* -1/720 (* (pow x 2) (sin (* 1/2 eps)))) (* 1/24 (sin (* 1/2 eps))))))))
(* (cos x) (sin (* 1/2 eps)))
(* (cos x) (sin (* 1/2 eps)))
(* (cos x) (sin (* 1/2 eps)))
(* (cos x) (sin (* 1/2 eps)))
(* (cos x) (sin (* 1/2 eps)))
(* (cos x) (sin (* 1/2 eps)))
(* (cos x) (sin (* 1/2 eps)))
(* (cos x) (sin (* 1/2 eps)))
(* 1/2 (* eps (cos x)))
(* eps (+ (* -1/48 (* (pow eps 2) (cos x))) (* 1/2 (cos x))))
(* eps (+ (* 1/2 (cos x)) (* (pow eps 2) (+ (* -1/48 (cos x)) (* 1/3840 (* (pow eps 2) (cos x)))))))
(* eps (+ (* 1/2 (cos x)) (* (pow eps 2) (+ (* -1/48 (cos x)) (* (pow eps 2) (+ (* -1/645120 (* (pow eps 2) (cos x))) (* 1/3840 (cos x))))))))
(* (cos x) (sin (* 1/2 eps)))
(* (cos x) (sin (* 1/2 eps)))
(* (cos x) (sin (* 1/2 eps)))
(* (cos x) (sin (* 1/2 eps)))
(* (cos x) (sin (* 1/2 eps)))
(* (cos x) (sin (* 1/2 eps)))
(* (cos x) (sin (* 1/2 eps)))
(* (cos x) (sin (* 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)))))))))
(+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))
(+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))
(+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))
(+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))
(+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))
(+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))
(+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))
(+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin 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))))))))
(+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))
(+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))
(+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))
(+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))
(+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))
(+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))
(+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))
(+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))
(* 1/4 eps)
(+ (* 1/6 x) (* 1/4 eps))
(+ (* 1/6 x) (* 1/4 eps))
(+ (* 1/6 x) (* 1/4 eps))
(* 1/6 x)
(* x (+ 1/6 (* 1/4 (/ eps x))))
(* x (+ 1/6 (* 1/4 (/ eps x))))
(* x (+ 1/6 (* 1/4 (/ eps x))))
(* 1/6 x)
(* -1 (* x (- (* -1/4 (/ eps x)) 1/6)))
(* -1 (* x (- (* -1/4 (/ eps x)) 1/6)))
(* -1 (* x (- (* -1/4 (/ eps x)) 1/6)))
(* 1/6 x)
(+ (* 1/6 x) (* 1/4 eps))
(+ (* 1/6 x) (* 1/4 eps))
(+ (* 1/6 x) (* 1/4 eps))
(* 1/4 eps)
(* eps (+ 1/4 (* 1/6 (/ x eps))))
(* eps (+ 1/4 (* 1/6 (/ x eps))))
(* eps (+ 1/4 (* 1/6 (/ x eps))))
(* 1/4 eps)
(* -1 (* eps (- (* -1/6 (/ x eps)) 1/4)))
(* -1 (* eps (- (* -1/6 (/ x eps)) 1/4)))
(* -1 (* eps (- (* -1/6 (/ x eps)) 1/4)))
(* 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))))
(pow eps 3)
(pow eps 3)
(pow eps 3)
(pow eps 3)
(pow eps 3)
(pow eps 3)
(pow eps 3)
(pow eps 3)
(pow eps 3)
(pow eps 3)
(pow eps 3)
(pow eps 3)

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

eval198.0ms (1%)

Memory: -7.6MiB live, 475.3MiB allocated
Compiler: Compiled 64 516 to 5 454 computations (91.5% saved)

prune187.0ms (1%)

Memory

14.1MiB live, 461.6MiB allocated

Pruning

39 alts after pruning (29 fresh and 10 done)

	Pruned	Kept	Total
New	1 443	8	1 451
Fresh	3	21	24
Picked	2	3	5
Done	0	7	7
Total	1 448	39	1 487

Accuracy

100.0%

Counts

1 487 → 39

Alt Table

Click to see full alt table

Status	Accuracy	Program
	98.5%	(fma.f64 (.f64 eps (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) (.f64 eps #s(literal 1/4 binary64))) #s(literal -1 binary64))) x (.f64 eps (.f64 eps #s(literal -1/2 binary64))))
	98.9%	(fma.f64 (.f64 eps (fma.f64 #s(literal 1/4 binary64) (.f64 x x) #s(literal -1/2 binary64))) eps (*.f64 (neg.f64 (sin.f64 x)) eps))
	53.2%	(fma.f64 (cos.f64 x) (cos.f64 eps) (neg.f64 (fma.f64 (sin.f64 x) (sin.f64 eps) (cos.f64 x))))
	98.1%	(fma.f64 x (neg.f64 eps) (.f64 eps (.f64 eps #s(literal -1/2 binary64))))
	53.2%	(/.f64 (/.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))) #s(literal 2 binary64)) (.f64 (cos.f64 (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64))) (cos.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64)))))
	53.2%	(-.f64 (/.f64 (*.f64 (cos.f64 (-.f64 x eps)) (cos.f64 (+.f64 x eps))) (cos.f64 (-.f64 x eps))) (cos.f64 x))
✓	52.3%	(-.f64 (cos.f64 (+.f64 x eps)) (fma.f64 x (.f64 x (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal -1/2 binary64))) #s(literal 1 binary64)))
✓	53.2%	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
✓	51.7%	(+.f64 (cos.f64 eps) #s(literal -1 binary64))
	78.1%	(.f64 (fma.f64 (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) (.f64 x (*.f64 x x)) x) (neg.f64 eps))
	99.8%	(.f64 (fma.f64 (sin.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (cos.f64 x) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) #s(literal -2 binary64)))
	99.7%	(.f64 (.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) #s(literal -2 binary64))
	99.4%	(.f64 (.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (fma.f64 (sin.f64 (.f64 (+.f64 x x) #s(literal 1/2 binary64))) (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 eps (.f64 (cos.f64 x) (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)))))) #s(literal -2 binary64))
	99.4%	(.f64 (.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (fma.f64 eps (fma.f64 (cos.f64 x) (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)) (.f64 eps (.f64 (sin.f64 x) #s(literal -1/8 binary64)))) (sin.f64 x))) #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))
	21.8%	(.f64 (.f64 (sin.f64 (.f64 (.f64 (/.f64 (.f64 eps eps) (.f64 eps (.f64 eps (.f64 eps eps)))) (/.f64 eps (/.f64 #s(literal 1 binary64) (*.f64 eps eps)))) #s(literal 1/2 binary64))) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x))) #s(literal -2 binary64))
	5.6%	(.f64 (.f64 (sin.f64 (.f64 (.f64 (/.f64 eps (/.f64 (pow.f64 (.f64 eps (.f64 eps (.f64 eps eps))) #s(literal 3 binary64)) (.f64 (.f64 eps (.f64 eps eps)) (.f64 (.f64 eps eps) (.f64 eps (.f64 eps (.f64 eps eps))))))) (/.f64 eps (/.f64 #s(literal 1 binary64) (.f64 eps eps)))) #s(literal 1/2 binary64))) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x))) #s(literal -2 binary64))
✓	32.5%	(.f64 (.f64 (sin.f64 (.f64 (.f64 (/.f64 eps (.f64 eps (.f64 eps eps))) (/.f64 eps (/.f64 #s(literal 1 binary64) (*.f64 eps eps)))) #s(literal 1/2 binary64))) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x))) #s(literal -2 binary64))
✓	78.4%	(*.f64 (sin.f64 x) (neg.f64 eps))
	78.1%	(.f64 x (fma.f64 (.f64 x x) (.f64 eps (fma.f64 #s(literal -1/120 binary64) (.f64 x x) #s(literal 1/6 binary64))) (neg.f64 eps)))
	78.0%	(.f64 x (-.f64 (.f64 eps (.f64 #s(literal 1/6 binary64) (.f64 x x))) eps))
	77.8%	(*.f64 x (neg.f64 eps))
✓	98.3%	(.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))))
	98.3%	(.f64 eps (fma.f64 x (fma.f64 x (.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64)) (*.f64 eps #s(literal -1/2 binary64))))
	98.2%	(.f64 eps (/.f64 (fma.f64 (.f64 x x) (fma.f64 x (fma.f64 x (fma.f64 #s(literal -1/16 binary64) (.f64 eps eps) #s(literal 1/3 binary64)) (.f64 eps #s(literal 1/2 binary64))) #s(literal -1 binary64)) (.f64 #s(literal 1/4 binary64) (.f64 eps eps))) (-.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) (*.f64 eps #s(literal 1/4 binary64))) #s(literal -1 binary64))))))
	97.8%	(.f64 eps (/.f64 (fma.f64 x (neg.f64 x) (.f64 #s(literal 1/4 binary64) (.f64 eps eps))) (-.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) (.f64 eps #s(literal 1/4 binary64))) #s(literal -1 binary64))))))
	98.9%	(.f64 eps (-.f64 (.f64 eps (fma.f64 (.f64 x x) (fma.f64 x (.f64 x (fma.f64 (*.f64 x x) #s(literal 1/1440 binary64) #s(literal -1/48 binary64))) #s(literal 1/4 binary64)) #s(literal -1/2 binary64))) (sin.f64 x)))
	98.9%	(.f64 eps (-.f64 (.f64 eps (fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal -1/48 binary64)) #s(literal 1/4 binary64)) #s(literal -1/2 binary64))) (sin.f64 x)))
	98.6%	(.f64 eps (-.f64 (.f64 eps (fma.f64 x (.f64 x #s(literal 1/4 binary64)) #s(literal -1/2 binary64))) (fma.f64 (.f64 x (.f64 x x)) (fma.f64 (.f64 x x) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) x)))
	98.7%	(.f64 eps (-.f64 (.f64 eps (fma.f64 x (.f64 x #s(literal 1/4 binary64)) #s(literal -1/2 binary64))) (fma.f64 (.f64 x (.f64 x x)) (fma.f64 x (.f64 x (fma.f64 x (*.f64 x #s(literal -1/5040 binary64)) #s(literal 1/120 binary64))) #s(literal -1/6 binary64)) x)))
✓	98.9%	(.f64 eps (-.f64 (.f64 eps (fma.f64 x (*.f64 x #s(literal 1/4 binary64)) #s(literal -1/2 binary64))) (sin.f64 x)))
✓	99.1%	(.f64 eps (-.f64 (.f64 eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x)))
	98.7%	(.f64 eps (-.f64 (.f64 eps #s(literal -1/2 binary64)) (sin.f64 x)))
	97.9%	(.f64 eps (-.f64 (.f64 eps #s(literal -1/2 binary64)) x))
✓	78.0%	(.f64 eps (.f64 x (fma.f64 x (*.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64))))
	53.0%	(.f64 eps (.f64 eps (fma.f64 x (*.f64 x #s(literal 1/4 binary64)) #s(literal -1/2 binary64))))
	52.9%	(.f64 eps (.f64 eps #s(literal -1/2 binary64)))
	51.8%	(.f64 eps (.f64 #s(literal 1/4 binary64) (.f64 x (.f64 x eps))))
✓	51.6%	#s(literal 0 binary64)

Compiler

Compiled 1 763 to 738 computations (58.1% saved)

regimes45.0ms (0.2%)

Memory

-17.8MiB live, 60.5MiB allocated

Counts

58 → 1

Calls

Call 1

Inputs
#s(literal 0 binary64)
(+.f64 #s(literal 1 binary64) #s(literal -1 binary64))
(*.f64 eps (neg.f64 x))
(*.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))
(fma.f64 x (neg.f64 eps) (.f64 eps (.f64 eps #s(literal -1/2 binary64))))
(.f64 eps (.f64 #s(literal 1/4 binary64) (.f64 x (.f64 x eps))))
(.f64 eps (.f64 eps (fma.f64 x (*.f64 x #s(literal 1/4 binary64)) #s(literal -1/2 binary64))))
(.f64 eps (.f64 x (fma.f64 x (*.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64))))
(.f64 x (.f64 eps (fma.f64 x (*.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64))))
(.f64 x (-.f64 (.f64 eps (.f64 #s(literal 1/6 binary64) (.f64 x x))) eps))
(.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 x (*.f64 x x)) x) (neg.f64 eps))
(.f64 eps (fma.f64 x (fma.f64 x (.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64)) (*.f64 eps #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))))
(.f64 x (fma.f64 (.f64 x x) (.f64 eps (fma.f64 #s(literal -1/120 binary64) (.f64 x x) #s(literal 1/6 binary64))) (neg.f64 eps)))
(fma.f64 eps (.f64 eps #s(literal -1/2 binary64)) (.f64 x (-.f64 (.f64 x (.f64 #s(literal 1/4 binary64) (*.f64 eps eps))) eps)))
(fma.f64 (.f64 eps (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) (.f64 eps #s(literal 1/4 binary64))) #s(literal -1 binary64))) x (.f64 eps (.f64 eps #s(literal -1/2 binary64))))
(fma.f64 x (fma.f64 x (.f64 eps (fma.f64 eps #s(literal 1/4 binary64) (.f64 x #s(literal 1/6 binary64)))) (neg.f64 eps)) (.f64 eps (.f64 eps #s(literal -1/2 binary64))))
(.f64 (fma.f64 (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) (.f64 x (*.f64 x x)) x) (neg.f64 eps))
(.f64 eps (-.f64 (.f64 eps (fma.f64 x (.f64 x #s(literal 1/4 binary64)) #s(literal -1/2 binary64))) (fma.f64 (.f64 x (.f64 x x)) (fma.f64 (.f64 x x) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) x)))
(.f64 eps (-.f64 (.f64 eps (fma.f64 x (.f64 x #s(literal 1/4 binary64)) #s(literal -1/2 binary64))) (fma.f64 (.f64 x (.f64 x x)) (fma.f64 x (.f64 x (fma.f64 x (*.f64 x #s(literal -1/5040 binary64)) #s(literal 1/120 binary64))) #s(literal -1/6 binary64)) x)))
(.f64 eps (/.f64 (fma.f64 x (neg.f64 x) (.f64 #s(literal 1/4 binary64) (.f64 eps eps))) (-.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) (.f64 eps #s(literal 1/4 binary64))) #s(literal -1 binary64))))))
(.f64 eps (/.f64 (fma.f64 (.f64 x x) (fma.f64 x (fma.f64 x (fma.f64 #s(literal -1/16 binary64) (.f64 eps eps) #s(literal 1/3 binary64)) (.f64 eps #s(literal 1/2 binary64))) #s(literal -1 binary64)) (.f64 #s(literal 1/4 binary64) (.f64 eps eps))) (-.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) (*.f64 eps #s(literal 1/4 binary64))) #s(literal -1 binary64))))))
(+.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 (.f64 #s(literal 1/4 binary64) (.f64 eps eps)) (.f64 (.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) (.f64 eps #s(literal 1/4 binary64))) #s(literal -1 binary64))) (.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) (.f64 eps #s(literal 1/4 binary64))) #s(literal -1 binary64))))) (-.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) (*.f64 eps #s(literal 1/4 binary64))) #s(literal -1 binary64))))))
(.f64 eps (-.f64 (.f64 eps #s(literal -1/2 binary64)) (sin.f64 x)))
(-.f64 (cos.f64 (+.f64 x eps)) (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)))
(.f64 eps (-.f64 (.f64 eps (fma.f64 x (*.f64 x #s(literal 1/4 binary64)) #s(literal -1/2 binary64))) (sin.f64 x)))
(-.f64 (cos.f64 (+.f64 x eps)) (fma.f64 x (.f64 x (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal -1/2 binary64))) #s(literal 1 binary64)))
(fma.f64 (.f64 eps (fma.f64 #s(literal 1/4 binary64) (.f64 x x) #s(literal -1/2 binary64))) eps (*.f64 (neg.f64 (sin.f64 x)) eps))
(.f64 eps (-.f64 (.f64 eps (fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal -1/48 binary64)) #s(literal 1/4 binary64)) #s(literal -1/2 binary64))) (sin.f64 x)))
(-.f64 (cos.f64 (+.f64 x eps)) (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)))
(.f64 eps (-.f64 (.f64 eps (fma.f64 (.f64 x x) (fma.f64 x (.f64 x (fma.f64 (*.f64 x x) #s(literal 1/1440 binary64) #s(literal -1/48 binary64))) #s(literal 1/4 binary64)) #s(literal -1/2 binary64))) (sin.f64 x)))
(-.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 (fma.f64 eps #s(literal 1/2 binary64) x))) #s(literal -2 binary64))
(.f64 (.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) #s(literal -2 binary64))
(fma.f64 (.f64 (cos.f64 x) (.f64 eps #s(literal -1/2 binary64))) eps (neg.f64 (*.f64 eps (sin.f64 x))))
(.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 (.f64 (/.f64 eps (.f64 eps (.f64 eps eps))) (/.f64 eps (/.f64 #s(literal 1 binary64) (*.f64 eps eps)))) #s(literal 1/2 binary64))) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x))) #s(literal -2 binary64))
(.f64 (.f64 (sin.f64 (.f64 (.f64 (/.f64 eps (.f64 eps (.f64 eps eps))) (/.f64 eps (/.f64 #s(literal 1 binary64) (.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 (/.f64 (.f64 eps eps) (.f64 eps (.f64 eps (.f64 eps eps)))) (/.f64 eps (/.f64 #s(literal 1 binary64) (*.f64 eps eps)))) #s(literal 1/2 binary64))) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x))) #s(literal -2 binary64))
(.f64 (.f64 (sin.f64 (.f64 (.f64 (/.f64 (.f64 eps eps) (.f64 eps (.f64 eps (.f64 eps eps)))) (/.f64 eps (/.f64 #s(literal 1 binary64) (.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 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))))
(-.f64 (/.f64 (*.f64 (cos.f64 (-.f64 x eps)) (cos.f64 (+.f64 x eps))) (cos.f64 (-.f64 x eps))) (cos.f64 x))
(.f64 (.f64 (sin.f64 (.f64 (.f64 (/.f64 eps (/.f64 (pow.f64 (.f64 eps (.f64 eps (.f64 eps eps))) #s(literal 3 binary64)) (.f64 (.f64 eps (.f64 eps eps)) (.f64 (.f64 eps eps) (.f64 eps (.f64 eps (.f64 eps eps))))))) (/.f64 eps (/.f64 #s(literal 1 binary64) (.f64 eps eps)))) #s(literal 1/2 binary64))) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x))) #s(literal -2 binary64))
(.f64 (.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (fma.f64 eps (fma.f64 (cos.f64 x) (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)) (.f64 eps (.f64 (sin.f64 x) #s(literal -1/8 binary64)))) (sin.f64 x))) #s(literal -2 binary64))
(.f64 (.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (fma.f64 (sin.f64 (.f64 (+.f64 x x) #s(literal 1/2 binary64))) (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 eps (.f64 (cos.f64 x) (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)))))) #s(literal -2 binary64))
(/.f64 (/.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))) #s(literal 2 binary64)) (.f64 (cos.f64 (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64))) (cos.f64 (.f64 (+.f64 eps #s(literal 0 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))))
(.f64 (fma.f64 (sin.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (cos.f64 x) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) #s(literal -2 binary64)))
(.f64 (.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (fma.f64 (sin.f64 (.f64 (+.f64 x x) #s(literal 1/2 binary64))) (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (cos.f64 x) (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))))) #s(literal -2 binary64))
(.f64 (.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (fma.f64 (sin.f64 (.f64 (+.f64 x x) #s(literal 1/2 binary64))) (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (cos.f64 (.f64 (+.f64 x x) #s(literal 1/2 binary64))) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))))) #s(literal -2 binary64))

Outputs

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

Calls

3 calls:

16.0ms	x
14.0ms	eps
12.0ms	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))

Results

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

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes42.0ms (0.2%)

Memory

3.2MiB live, 41.3MiB allocated

Counts

55 → 1

Calls

Call 1

Inputs
#s(literal 0 binary64)
(+.f64 #s(literal 1 binary64) #s(literal -1 binary64))
(*.f64 eps (neg.f64 x))
(*.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))
(fma.f64 x (neg.f64 eps) (.f64 eps (.f64 eps #s(literal -1/2 binary64))))
(.f64 eps (.f64 #s(literal 1/4 binary64) (.f64 x (.f64 x eps))))
(.f64 eps (.f64 eps (fma.f64 x (*.f64 x #s(literal 1/4 binary64)) #s(literal -1/2 binary64))))
(.f64 eps (.f64 x (fma.f64 x (*.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64))))
(.f64 x (.f64 eps (fma.f64 x (*.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64))))
(.f64 x (-.f64 (.f64 eps (.f64 #s(literal 1/6 binary64) (.f64 x x))) eps))
(.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 x (*.f64 x x)) x) (neg.f64 eps))
(.f64 eps (fma.f64 x (fma.f64 x (.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64)) (*.f64 eps #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))))
(.f64 x (fma.f64 (.f64 x x) (.f64 eps (fma.f64 #s(literal -1/120 binary64) (.f64 x x) #s(literal 1/6 binary64))) (neg.f64 eps)))
(fma.f64 eps (.f64 eps #s(literal -1/2 binary64)) (.f64 x (-.f64 (.f64 x (.f64 #s(literal 1/4 binary64) (*.f64 eps eps))) eps)))
(fma.f64 (.f64 eps (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) (.f64 eps #s(literal 1/4 binary64))) #s(literal -1 binary64))) x (.f64 eps (.f64 eps #s(literal -1/2 binary64))))
(fma.f64 x (fma.f64 x (.f64 eps (fma.f64 eps #s(literal 1/4 binary64) (.f64 x #s(literal 1/6 binary64)))) (neg.f64 eps)) (.f64 eps (.f64 eps #s(literal -1/2 binary64))))
(.f64 (fma.f64 (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) (.f64 x (*.f64 x x)) x) (neg.f64 eps))
(.f64 eps (-.f64 (.f64 eps (fma.f64 x (.f64 x #s(literal 1/4 binary64)) #s(literal -1/2 binary64))) (fma.f64 (.f64 x (.f64 x x)) (fma.f64 (.f64 x x) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) x)))
(.f64 eps (-.f64 (.f64 eps (fma.f64 x (.f64 x #s(literal 1/4 binary64)) #s(literal -1/2 binary64))) (fma.f64 (.f64 x (.f64 x x)) (fma.f64 x (.f64 x (fma.f64 x (*.f64 x #s(literal -1/5040 binary64)) #s(literal 1/120 binary64))) #s(literal -1/6 binary64)) x)))
(.f64 eps (/.f64 (fma.f64 x (neg.f64 x) (.f64 #s(literal 1/4 binary64) (.f64 eps eps))) (-.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) (.f64 eps #s(literal 1/4 binary64))) #s(literal -1 binary64))))))
(.f64 eps (/.f64 (fma.f64 (.f64 x x) (fma.f64 x (fma.f64 x (fma.f64 #s(literal -1/16 binary64) (.f64 eps eps) #s(literal 1/3 binary64)) (.f64 eps #s(literal 1/2 binary64))) #s(literal -1 binary64)) (.f64 #s(literal 1/4 binary64) (.f64 eps eps))) (-.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) (*.f64 eps #s(literal 1/4 binary64))) #s(literal -1 binary64))))))
(+.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 (.f64 #s(literal 1/4 binary64) (.f64 eps eps)) (.f64 (.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) (.f64 eps #s(literal 1/4 binary64))) #s(literal -1 binary64))) (.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) (.f64 eps #s(literal 1/4 binary64))) #s(literal -1 binary64))))) (-.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) (*.f64 eps #s(literal 1/4 binary64))) #s(literal -1 binary64))))))
(.f64 eps (-.f64 (.f64 eps #s(literal -1/2 binary64)) (sin.f64 x)))
(-.f64 (cos.f64 (+.f64 x eps)) (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)))
(.f64 eps (-.f64 (.f64 eps (fma.f64 x (*.f64 x #s(literal 1/4 binary64)) #s(literal -1/2 binary64))) (sin.f64 x)))
(-.f64 (cos.f64 (+.f64 x eps)) (fma.f64 x (.f64 x (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal -1/2 binary64))) #s(literal 1 binary64)))
(fma.f64 (.f64 eps (fma.f64 #s(literal 1/4 binary64) (.f64 x x) #s(literal -1/2 binary64))) eps (*.f64 (neg.f64 (sin.f64 x)) eps))
(.f64 eps (-.f64 (.f64 eps (fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal -1/48 binary64)) #s(literal 1/4 binary64)) #s(literal -1/2 binary64))) (sin.f64 x)))
(-.f64 (cos.f64 (+.f64 x eps)) (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)))
(.f64 eps (-.f64 (.f64 eps (fma.f64 (.f64 x x) (fma.f64 x (.f64 x (fma.f64 (*.f64 x x) #s(literal 1/1440 binary64) #s(literal -1/48 binary64))) #s(literal 1/4 binary64)) #s(literal -1/2 binary64))) (sin.f64 x)))
(-.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 (fma.f64 eps #s(literal 1/2 binary64) x))) #s(literal -2 binary64))
(.f64 (.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) #s(literal -2 binary64))
(fma.f64 (.f64 (cos.f64 x) (.f64 eps #s(literal -1/2 binary64))) eps (neg.f64 (*.f64 eps (sin.f64 x))))
(.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 (.f64 (/.f64 eps (.f64 eps (.f64 eps eps))) (/.f64 eps (/.f64 #s(literal 1 binary64) (*.f64 eps eps)))) #s(literal 1/2 binary64))) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x))) #s(literal -2 binary64))
(.f64 (.f64 (sin.f64 (.f64 (.f64 (/.f64 eps (.f64 eps (.f64 eps eps))) (/.f64 eps (/.f64 #s(literal 1 binary64) (.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 (/.f64 (.f64 eps eps) (.f64 eps (.f64 eps (.f64 eps eps)))) (/.f64 eps (/.f64 #s(literal 1 binary64) (*.f64 eps eps)))) #s(literal 1/2 binary64))) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x))) #s(literal -2 binary64))
(.f64 (.f64 (sin.f64 (.f64 (.f64 (/.f64 (.f64 eps eps) (.f64 eps (.f64 eps (.f64 eps eps)))) (/.f64 eps (/.f64 #s(literal 1 binary64) (.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 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))))
(-.f64 (/.f64 (*.f64 (cos.f64 (-.f64 x eps)) (cos.f64 (+.f64 x eps))) (cos.f64 (-.f64 x eps))) (cos.f64 x))
(.f64 (.f64 (sin.f64 (.f64 (.f64 (/.f64 eps (/.f64 (pow.f64 (.f64 eps (.f64 eps (.f64 eps eps))) #s(literal 3 binary64)) (.f64 (.f64 eps (.f64 eps eps)) (.f64 (.f64 eps eps) (.f64 eps (.f64 eps (.f64 eps eps))))))) (/.f64 eps (/.f64 #s(literal 1 binary64) (.f64 eps eps)))) #s(literal 1/2 binary64))) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x))) #s(literal -2 binary64))
(.f64 (.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (fma.f64 eps (fma.f64 (cos.f64 x) (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)) (.f64 eps (.f64 (sin.f64 x) #s(literal -1/8 binary64)))) (sin.f64 x))) #s(literal -2 binary64))
(.f64 (.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (fma.f64 (sin.f64 (.f64 (+.f64 x x) #s(literal 1/2 binary64))) (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 eps (.f64 (cos.f64 x) (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)))))) #s(literal -2 binary64))
(/.f64 (/.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))) #s(literal 2 binary64)) (.f64 (cos.f64 (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64))) (cos.f64 (.f64 (+.f64 eps #s(literal 0 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))))

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:

15.0ms	eps
14.0ms	x
11.0ms	(-.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)

regimes30.0ms (0.2%)

Memory

-9.0MiB live, 34.5MiB allocated

Counts

38 → 1

Calls

Call 1

Inputs
#s(literal 0 binary64)
(+.f64 #s(literal 1 binary64) #s(literal -1 binary64))
(*.f64 eps (neg.f64 x))
(*.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))
(fma.f64 x (neg.f64 eps) (.f64 eps (.f64 eps #s(literal -1/2 binary64))))
(.f64 eps (.f64 #s(literal 1/4 binary64) (.f64 x (.f64 x eps))))
(.f64 eps (.f64 eps (fma.f64 x (*.f64 x #s(literal 1/4 binary64)) #s(literal -1/2 binary64))))
(.f64 eps (.f64 x (fma.f64 x (*.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64))))
(.f64 x (.f64 eps (fma.f64 x (*.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64))))
(.f64 x (-.f64 (.f64 eps (.f64 #s(literal 1/6 binary64) (.f64 x x))) eps))
(.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 x (*.f64 x x)) x) (neg.f64 eps))
(.f64 eps (fma.f64 x (fma.f64 x (.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64)) (*.f64 eps #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))))
(.f64 x (fma.f64 (.f64 x x) (.f64 eps (fma.f64 #s(literal -1/120 binary64) (.f64 x x) #s(literal 1/6 binary64))) (neg.f64 eps)))
(fma.f64 eps (.f64 eps #s(literal -1/2 binary64)) (.f64 x (-.f64 (.f64 x (.f64 #s(literal 1/4 binary64) (*.f64 eps eps))) eps)))
(fma.f64 (.f64 eps (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) (.f64 eps #s(literal 1/4 binary64))) #s(literal -1 binary64))) x (.f64 eps (.f64 eps #s(literal -1/2 binary64))))
(fma.f64 x (fma.f64 x (.f64 eps (fma.f64 eps #s(literal 1/4 binary64) (.f64 x #s(literal 1/6 binary64)))) (neg.f64 eps)) (.f64 eps (.f64 eps #s(literal -1/2 binary64))))
(.f64 (fma.f64 (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) (.f64 x (*.f64 x x)) x) (neg.f64 eps))
(.f64 eps (-.f64 (.f64 eps (fma.f64 x (.f64 x #s(literal 1/4 binary64)) #s(literal -1/2 binary64))) (fma.f64 (.f64 x (.f64 x x)) (fma.f64 (.f64 x x) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) x)))
(.f64 eps (-.f64 (.f64 eps (fma.f64 x (.f64 x #s(literal 1/4 binary64)) #s(literal -1/2 binary64))) (fma.f64 (.f64 x (.f64 x x)) (fma.f64 x (.f64 x (fma.f64 x (*.f64 x #s(literal -1/5040 binary64)) #s(literal 1/120 binary64))) #s(literal -1/6 binary64)) x)))
(.f64 eps (/.f64 (fma.f64 x (neg.f64 x) (.f64 #s(literal 1/4 binary64) (.f64 eps eps))) (-.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) (.f64 eps #s(literal 1/4 binary64))) #s(literal -1 binary64))))))
(.f64 eps (/.f64 (fma.f64 (.f64 x x) (fma.f64 x (fma.f64 x (fma.f64 #s(literal -1/16 binary64) (.f64 eps eps) #s(literal 1/3 binary64)) (.f64 eps #s(literal 1/2 binary64))) #s(literal -1 binary64)) (.f64 #s(literal 1/4 binary64) (.f64 eps eps))) (-.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) (*.f64 eps #s(literal 1/4 binary64))) #s(literal -1 binary64))))))
(+.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 (.f64 #s(literal 1/4 binary64) (.f64 eps eps)) (.f64 (.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) (.f64 eps #s(literal 1/4 binary64))) #s(literal -1 binary64))) (.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) (.f64 eps #s(literal 1/4 binary64))) #s(literal -1 binary64))))) (-.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) (*.f64 eps #s(literal 1/4 binary64))) #s(literal -1 binary64))))))
(.f64 eps (-.f64 (.f64 eps #s(literal -1/2 binary64)) (sin.f64 x)))
(-.f64 (cos.f64 (+.f64 x eps)) (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)))
(.f64 eps (-.f64 (.f64 eps (fma.f64 x (*.f64 x #s(literal 1/4 binary64)) #s(literal -1/2 binary64))) (sin.f64 x)))
(-.f64 (cos.f64 (+.f64 x eps)) (fma.f64 x (.f64 x (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal -1/2 binary64))) #s(literal 1 binary64)))
(fma.f64 (.f64 eps (fma.f64 #s(literal 1/4 binary64) (.f64 x x) #s(literal -1/2 binary64))) eps (*.f64 (neg.f64 (sin.f64 x)) eps))
(.f64 eps (-.f64 (.f64 eps (fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal -1/48 binary64)) #s(literal 1/4 binary64)) #s(literal -1/2 binary64))) (sin.f64 x)))
(-.f64 (cos.f64 (+.f64 x eps)) (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)))
(.f64 eps (-.f64 (.f64 eps (fma.f64 (.f64 x x) (fma.f64 x (.f64 x (fma.f64 (*.f64 x x) #s(literal 1/1440 binary64) #s(literal -1/48 binary64))) #s(literal 1/4 binary64)) #s(literal -1/2 binary64))) (sin.f64 x)))
(-.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 eps (-.f64 (.f64 eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x)))

Calls

3 calls:

11.0ms	eps
10.0ms	x
8.0ms	(-.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)

regimes28.0ms (0.1%)

Memory

23.2MiB live, 23.2MiB allocated

Counts

37 → 1

Calls

Call 1

Inputs
#s(literal 0 binary64)
(+.f64 #s(literal 1 binary64) #s(literal -1 binary64))
(*.f64 eps (neg.f64 x))
(*.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))
(fma.f64 x (neg.f64 eps) (.f64 eps (.f64 eps #s(literal -1/2 binary64))))
(.f64 eps (.f64 #s(literal 1/4 binary64) (.f64 x (.f64 x eps))))
(.f64 eps (.f64 eps (fma.f64 x (*.f64 x #s(literal 1/4 binary64)) #s(literal -1/2 binary64))))
(.f64 eps (.f64 x (fma.f64 x (*.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64))))
(.f64 x (.f64 eps (fma.f64 x (*.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64))))
(.f64 x (-.f64 (.f64 eps (.f64 #s(literal 1/6 binary64) (.f64 x x))) eps))
(.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 x (*.f64 x x)) x) (neg.f64 eps))
(.f64 eps (fma.f64 x (fma.f64 x (.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64)) (*.f64 eps #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))))
(.f64 x (fma.f64 (.f64 x x) (.f64 eps (fma.f64 #s(literal -1/120 binary64) (.f64 x x) #s(literal 1/6 binary64))) (neg.f64 eps)))
(fma.f64 eps (.f64 eps #s(literal -1/2 binary64)) (.f64 x (-.f64 (.f64 x (.f64 #s(literal 1/4 binary64) (*.f64 eps eps))) eps)))
(fma.f64 (.f64 eps (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) (.f64 eps #s(literal 1/4 binary64))) #s(literal -1 binary64))) x (.f64 eps (.f64 eps #s(literal -1/2 binary64))))
(fma.f64 x (fma.f64 x (.f64 eps (fma.f64 eps #s(literal 1/4 binary64) (.f64 x #s(literal 1/6 binary64)))) (neg.f64 eps)) (.f64 eps (.f64 eps #s(literal -1/2 binary64))))
(.f64 (fma.f64 (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) (.f64 x (*.f64 x x)) x) (neg.f64 eps))
(.f64 eps (-.f64 (.f64 eps (fma.f64 x (.f64 x #s(literal 1/4 binary64)) #s(literal -1/2 binary64))) (fma.f64 (.f64 x (.f64 x x)) (fma.f64 (.f64 x x) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) x)))
(.f64 eps (-.f64 (.f64 eps (fma.f64 x (.f64 x #s(literal 1/4 binary64)) #s(literal -1/2 binary64))) (fma.f64 (.f64 x (.f64 x x)) (fma.f64 x (.f64 x (fma.f64 x (*.f64 x #s(literal -1/5040 binary64)) #s(literal 1/120 binary64))) #s(literal -1/6 binary64)) x)))
(.f64 eps (/.f64 (fma.f64 x (neg.f64 x) (.f64 #s(literal 1/4 binary64) (.f64 eps eps))) (-.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) (.f64 eps #s(literal 1/4 binary64))) #s(literal -1 binary64))))))
(.f64 eps (/.f64 (fma.f64 (.f64 x x) (fma.f64 x (fma.f64 x (fma.f64 #s(literal -1/16 binary64) (.f64 eps eps) #s(literal 1/3 binary64)) (.f64 eps #s(literal 1/2 binary64))) #s(literal -1 binary64)) (.f64 #s(literal 1/4 binary64) (.f64 eps eps))) (-.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) (*.f64 eps #s(literal 1/4 binary64))) #s(literal -1 binary64))))))
(+.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 (.f64 #s(literal 1/4 binary64) (.f64 eps eps)) (.f64 (.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) (.f64 eps #s(literal 1/4 binary64))) #s(literal -1 binary64))) (.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) (.f64 eps #s(literal 1/4 binary64))) #s(literal -1 binary64))))) (-.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) (*.f64 eps #s(literal 1/4 binary64))) #s(literal -1 binary64))))))
(.f64 eps (-.f64 (.f64 eps #s(literal -1/2 binary64)) (sin.f64 x)))
(-.f64 (cos.f64 (+.f64 x eps)) (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)))
(.f64 eps (-.f64 (.f64 eps (fma.f64 x (*.f64 x #s(literal 1/4 binary64)) #s(literal -1/2 binary64))) (sin.f64 x)))
(-.f64 (cos.f64 (+.f64 x eps)) (fma.f64 x (.f64 x (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal -1/2 binary64))) #s(literal 1 binary64)))
(fma.f64 (.f64 eps (fma.f64 #s(literal 1/4 binary64) (.f64 x x) #s(literal -1/2 binary64))) eps (*.f64 (neg.f64 (sin.f64 x)) eps))
(.f64 eps (-.f64 (.f64 eps (fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal -1/48 binary64)) #s(literal 1/4 binary64)) #s(literal -1/2 binary64))) (sin.f64 x)))
(-.f64 (cos.f64 (+.f64 x eps)) (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)))
(.f64 eps (-.f64 (.f64 eps (fma.f64 (.f64 x x) (fma.f64 x (.f64 x (fma.f64 (*.f64 x x) #s(literal 1/1440 binary64) #s(literal -1/48 binary64))) #s(literal 1/4 binary64)) #s(literal -1/2 binary64))) (sin.f64 x)))
(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))

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

Calls

3 calls:

10.0ms	x
9.0ms	eps
8.0ms	(-.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)

regimes28.0ms (0.1%)

Memory

-17.6MiB live, 19.6MiB allocated

Counts

32 → 1

Calls

Call 1

Inputs
#s(literal 0 binary64)
(+.f64 #s(literal 1 binary64) #s(literal -1 binary64))
(*.f64 eps (neg.f64 x))
(*.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))
(fma.f64 x (neg.f64 eps) (.f64 eps (.f64 eps #s(literal -1/2 binary64))))
(.f64 eps (.f64 #s(literal 1/4 binary64) (.f64 x (.f64 x eps))))
(.f64 eps (.f64 eps (fma.f64 x (*.f64 x #s(literal 1/4 binary64)) #s(literal -1/2 binary64))))
(.f64 eps (.f64 x (fma.f64 x (*.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64))))
(.f64 x (.f64 eps (fma.f64 x (*.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64))))
(.f64 x (-.f64 (.f64 eps (.f64 #s(literal 1/6 binary64) (.f64 x x))) eps))
(.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 x (*.f64 x x)) x) (neg.f64 eps))
(.f64 eps (fma.f64 x (fma.f64 x (.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64)) (*.f64 eps #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))))
(.f64 x (fma.f64 (.f64 x x) (.f64 eps (fma.f64 #s(literal -1/120 binary64) (.f64 x x) #s(literal 1/6 binary64))) (neg.f64 eps)))
(fma.f64 eps (.f64 eps #s(literal -1/2 binary64)) (.f64 x (-.f64 (.f64 x (.f64 #s(literal 1/4 binary64) (*.f64 eps eps))) eps)))
(fma.f64 (.f64 eps (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) (.f64 eps #s(literal 1/4 binary64))) #s(literal -1 binary64))) x (.f64 eps (.f64 eps #s(literal -1/2 binary64))))
(fma.f64 x (fma.f64 x (.f64 eps (fma.f64 eps #s(literal 1/4 binary64) (.f64 x #s(literal 1/6 binary64)))) (neg.f64 eps)) (.f64 eps (.f64 eps #s(literal -1/2 binary64))))
(.f64 (fma.f64 (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) (.f64 x (*.f64 x x)) x) (neg.f64 eps))
(.f64 eps (-.f64 (.f64 eps (fma.f64 x (.f64 x #s(literal 1/4 binary64)) #s(literal -1/2 binary64))) (fma.f64 (.f64 x (.f64 x x)) (fma.f64 (.f64 x x) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) x)))
(.f64 eps (-.f64 (.f64 eps (fma.f64 x (.f64 x #s(literal 1/4 binary64)) #s(literal -1/2 binary64))) (fma.f64 (.f64 x (.f64 x x)) (fma.f64 x (.f64 x (fma.f64 x (*.f64 x #s(literal -1/5040 binary64)) #s(literal 1/120 binary64))) #s(literal -1/6 binary64)) x)))
(.f64 eps (/.f64 (fma.f64 x (neg.f64 x) (.f64 #s(literal 1/4 binary64) (.f64 eps eps))) (-.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) (.f64 eps #s(literal 1/4 binary64))) #s(literal -1 binary64))))))
(.f64 eps (/.f64 (fma.f64 (.f64 x x) (fma.f64 x (fma.f64 x (fma.f64 #s(literal -1/16 binary64) (.f64 eps eps) #s(literal 1/3 binary64)) (.f64 eps #s(literal 1/2 binary64))) #s(literal -1 binary64)) (.f64 #s(literal 1/4 binary64) (.f64 eps eps))) (-.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) (*.f64 eps #s(literal 1/4 binary64))) #s(literal -1 binary64))))))
(+.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 (.f64 #s(literal 1/4 binary64) (.f64 eps eps)) (.f64 (.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) (.f64 eps #s(literal 1/4 binary64))) #s(literal -1 binary64))) (.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) (.f64 eps #s(literal 1/4 binary64))) #s(literal -1 binary64))))) (-.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) (*.f64 eps #s(literal 1/4 binary64))) #s(literal -1 binary64))))))
(.f64 eps (-.f64 (.f64 eps #s(literal -1/2 binary64)) (sin.f64 x)))
(-.f64 (cos.f64 (+.f64 x eps)) (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)))
(.f64 eps (-.f64 (.f64 eps (fma.f64 x (*.f64 x #s(literal 1/4 binary64)) #s(literal -1/2 binary64))) (sin.f64 x)))
(-.f64 (cos.f64 (+.f64 x eps)) (fma.f64 x (.f64 x (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal -1/2 binary64))) #s(literal 1 binary64)))

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

Calls

3 calls:

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

regimes23.0ms (0.1%)

Memory

20.5MiB live, 20.5MiB allocated

Counts

30 → 1

Calls

Call 1

Inputs
#s(literal 0 binary64)
(+.f64 #s(literal 1 binary64) #s(literal -1 binary64))
(*.f64 eps (neg.f64 x))
(*.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))
(fma.f64 x (neg.f64 eps) (.f64 eps (.f64 eps #s(literal -1/2 binary64))))
(.f64 eps (.f64 #s(literal 1/4 binary64) (.f64 x (.f64 x eps))))
(.f64 eps (.f64 eps (fma.f64 x (*.f64 x #s(literal 1/4 binary64)) #s(literal -1/2 binary64))))
(.f64 eps (.f64 x (fma.f64 x (*.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64))))
(.f64 x (.f64 eps (fma.f64 x (*.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64))))
(.f64 x (-.f64 (.f64 eps (.f64 #s(literal 1/6 binary64) (.f64 x x))) eps))
(.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 x (*.f64 x x)) x) (neg.f64 eps))
(.f64 eps (fma.f64 x (fma.f64 x (.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64)) (*.f64 eps #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))))
(.f64 x (fma.f64 (.f64 x x) (.f64 eps (fma.f64 #s(literal -1/120 binary64) (.f64 x x) #s(literal 1/6 binary64))) (neg.f64 eps)))
(fma.f64 eps (.f64 eps #s(literal -1/2 binary64)) (.f64 x (-.f64 (.f64 x (.f64 #s(literal 1/4 binary64) (*.f64 eps eps))) eps)))
(fma.f64 (.f64 eps (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) (.f64 eps #s(literal 1/4 binary64))) #s(literal -1 binary64))) x (.f64 eps (.f64 eps #s(literal -1/2 binary64))))
(fma.f64 x (fma.f64 x (.f64 eps (fma.f64 eps #s(literal 1/4 binary64) (.f64 x #s(literal 1/6 binary64)))) (neg.f64 eps)) (.f64 eps (.f64 eps #s(literal -1/2 binary64))))
(.f64 (fma.f64 (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) (.f64 x (*.f64 x x)) x) (neg.f64 eps))
(.f64 eps (-.f64 (.f64 eps (fma.f64 x (.f64 x #s(literal 1/4 binary64)) #s(literal -1/2 binary64))) (fma.f64 (.f64 x (.f64 x x)) (fma.f64 (.f64 x x) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) x)))
(.f64 eps (-.f64 (.f64 eps (fma.f64 x (.f64 x #s(literal 1/4 binary64)) #s(literal -1/2 binary64))) (fma.f64 (.f64 x (.f64 x x)) (fma.f64 x (.f64 x (fma.f64 x (*.f64 x #s(literal -1/5040 binary64)) #s(literal 1/120 binary64))) #s(literal -1/6 binary64)) x)))
(.f64 eps (/.f64 (fma.f64 x (neg.f64 x) (.f64 #s(literal 1/4 binary64) (.f64 eps eps))) (-.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) (.f64 eps #s(literal 1/4 binary64))) #s(literal -1 binary64))))))
(.f64 eps (/.f64 (fma.f64 (.f64 x x) (fma.f64 x (fma.f64 x (fma.f64 #s(literal -1/16 binary64) (.f64 eps eps) #s(literal 1/3 binary64)) (.f64 eps #s(literal 1/2 binary64))) #s(literal -1 binary64)) (.f64 #s(literal 1/4 binary64) (.f64 eps eps))) (-.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) (*.f64 eps #s(literal 1/4 binary64))) #s(literal -1 binary64))))))
(+.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 (.f64 #s(literal 1/4 binary64) (.f64 eps eps)) (.f64 (.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) (.f64 eps #s(literal 1/4 binary64))) #s(literal -1 binary64))) (.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) (.f64 eps #s(literal 1/4 binary64))) #s(literal -1 binary64))))) (-.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) (*.f64 eps #s(literal 1/4 binary64))) #s(literal -1 binary64))))))
(.f64 eps (-.f64 (.f64 eps #s(literal -1/2 binary64)) (sin.f64 x)))
(-.f64 (cos.f64 (+.f64 x eps)) (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)))

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

Calls

3 calls:

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

Results

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

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes26.0ms (0.1%)

Memory

-8.7MiB live, 28.7MiB allocated

Counts

28 → 1

Calls

Call 1

Inputs
#s(literal 0 binary64)
(+.f64 #s(literal 1 binary64) #s(literal -1 binary64))
(*.f64 eps (neg.f64 x))
(*.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))
(fma.f64 x (neg.f64 eps) (.f64 eps (.f64 eps #s(literal -1/2 binary64))))
(.f64 eps (.f64 #s(literal 1/4 binary64) (.f64 x (.f64 x eps))))
(.f64 eps (.f64 eps (fma.f64 x (*.f64 x #s(literal 1/4 binary64)) #s(literal -1/2 binary64))))
(.f64 eps (.f64 x (fma.f64 x (*.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64))))
(.f64 x (.f64 eps (fma.f64 x (*.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64))))
(.f64 x (-.f64 (.f64 eps (.f64 #s(literal 1/6 binary64) (.f64 x x))) eps))
(.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 x (*.f64 x x)) x) (neg.f64 eps))
(.f64 eps (fma.f64 x (fma.f64 x (.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64)) (*.f64 eps #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))))
(.f64 x (fma.f64 (.f64 x x) (.f64 eps (fma.f64 #s(literal -1/120 binary64) (.f64 x x) #s(literal 1/6 binary64))) (neg.f64 eps)))
(fma.f64 eps (.f64 eps #s(literal -1/2 binary64)) (.f64 x (-.f64 (.f64 x (.f64 #s(literal 1/4 binary64) (*.f64 eps eps))) eps)))
(fma.f64 (.f64 eps (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) (.f64 eps #s(literal 1/4 binary64))) #s(literal -1 binary64))) x (.f64 eps (.f64 eps #s(literal -1/2 binary64))))
(fma.f64 x (fma.f64 x (.f64 eps (fma.f64 eps #s(literal 1/4 binary64) (.f64 x #s(literal 1/6 binary64)))) (neg.f64 eps)) (.f64 eps (.f64 eps #s(literal -1/2 binary64))))
(.f64 (fma.f64 (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) (.f64 x (*.f64 x x)) x) (neg.f64 eps))
(.f64 eps (-.f64 (.f64 eps (fma.f64 x (.f64 x #s(literal 1/4 binary64)) #s(literal -1/2 binary64))) (fma.f64 (.f64 x (.f64 x x)) (fma.f64 (.f64 x x) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) x)))
(.f64 eps (-.f64 (.f64 eps (fma.f64 x (.f64 x #s(literal 1/4 binary64)) #s(literal -1/2 binary64))) (fma.f64 (.f64 x (.f64 x x)) (fma.f64 x (.f64 x (fma.f64 x (*.f64 x #s(literal -1/5040 binary64)) #s(literal 1/120 binary64))) #s(literal -1/6 binary64)) x)))
(.f64 eps (/.f64 (fma.f64 x (neg.f64 x) (.f64 #s(literal 1/4 binary64) (.f64 eps eps))) (-.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) (.f64 eps #s(literal 1/4 binary64))) #s(literal -1 binary64))))))
(.f64 eps (/.f64 (fma.f64 (.f64 x x) (fma.f64 x (fma.f64 x (fma.f64 #s(literal -1/16 binary64) (.f64 eps eps) #s(literal 1/3 binary64)) (.f64 eps #s(literal 1/2 binary64))) #s(literal -1 binary64)) (.f64 #s(literal 1/4 binary64) (.f64 eps eps))) (-.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) (*.f64 eps #s(literal 1/4 binary64))) #s(literal -1 binary64))))))
(+.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 (.f64 #s(literal 1/4 binary64) (.f64 eps eps)) (.f64 (.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) (.f64 eps #s(literal 1/4 binary64))) #s(literal -1 binary64))) (.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) (.f64 eps #s(literal 1/4 binary64))) #s(literal -1 binary64))))) (-.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) (*.f64 eps #s(literal 1/4 binary64))) #s(literal -1 binary64))))))

Outputs

(*.f64 eps (-.f64 (*.f64 eps (fma.f64 x (*.f64 x #s(literal 1/4 binary64)) #s(literal -1/2 binary64))) (fma.f64 (*.f64 x (*.f64 x x)) (fma.f64 x (*.f64 x (fma.f64 x (*.f64 x #s(literal -1/5040 binary64)) #s(literal 1/120 binary64))) #s(literal -1/6 binary64)) x)))

Calls

3 calls:

10.0ms	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
7.0ms	eps
7.0ms	x

Results

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

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes19.0ms (0.1%)

Memory

-6.7MiB live, 32.4MiB allocated

Counts

21 → 1

Calls

Call 1

Inputs
#s(literal 0 binary64)
(+.f64 #s(literal 1 binary64) #s(literal -1 binary64))
(*.f64 eps (neg.f64 x))
(*.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))
(fma.f64 x (neg.f64 eps) (.f64 eps (.f64 eps #s(literal -1/2 binary64))))
(.f64 eps (.f64 #s(literal 1/4 binary64) (.f64 x (.f64 x eps))))
(.f64 eps (.f64 eps (fma.f64 x (*.f64 x #s(literal 1/4 binary64)) #s(literal -1/2 binary64))))
(.f64 eps (.f64 x (fma.f64 x (*.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64))))
(.f64 x (.f64 eps (fma.f64 x (*.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64))))
(.f64 x (-.f64 (.f64 eps (.f64 #s(literal 1/6 binary64) (.f64 x x))) eps))
(.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 x (*.f64 x x)) x) (neg.f64 eps))
(.f64 eps (fma.f64 x (fma.f64 x (.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64)) (*.f64 eps #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))))
(.f64 x (fma.f64 (.f64 x x) (.f64 eps (fma.f64 #s(literal -1/120 binary64) (.f64 x x) #s(literal 1/6 binary64))) (neg.f64 eps)))
(fma.f64 eps (.f64 eps #s(literal -1/2 binary64)) (.f64 x (-.f64 (.f64 x (.f64 #s(literal 1/4 binary64) (*.f64 eps eps))) eps)))
(fma.f64 (.f64 eps (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) (.f64 eps #s(literal 1/4 binary64))) #s(literal -1 binary64))) x (.f64 eps (.f64 eps #s(literal -1/2 binary64))))
(fma.f64 x (fma.f64 x (.f64 eps (fma.f64 eps #s(literal 1/4 binary64) (.f64 x #s(literal 1/6 binary64)))) (neg.f64 eps)) (.f64 eps (.f64 eps #s(literal -1/2 binary64))))
(.f64 (fma.f64 (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) (.f64 x (*.f64 x x)) x) (neg.f64 eps))
(.f64 eps (-.f64 (.f64 eps (fma.f64 x (.f64 x #s(literal 1/4 binary64)) #s(literal -1/2 binary64))) (fma.f64 (.f64 x (.f64 x x)) (fma.f64 (.f64 x x) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) x)))

Outputs

(*.f64 eps (-.f64 (*.f64 eps (fma.f64 x (*.f64 x #s(literal 1/4 binary64)) #s(literal -1/2 binary64))) (fma.f64 (*.f64 x (*.f64 x x)) (fma.f64 (*.f64 x x) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) x)))

Calls

3 calls:

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

Results

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

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes17.0ms (0.1%)

Memory

-11.9MiB live, 34.2MiB allocated

Counts

20 → 1

Calls

Call 1

Inputs
#s(literal 0 binary64)
(+.f64 #s(literal 1 binary64) #s(literal -1 binary64))
(*.f64 eps (neg.f64 x))
(*.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))
(fma.f64 x (neg.f64 eps) (.f64 eps (.f64 eps #s(literal -1/2 binary64))))
(.f64 eps (.f64 #s(literal 1/4 binary64) (.f64 x (.f64 x eps))))
(.f64 eps (.f64 eps (fma.f64 x (*.f64 x #s(literal 1/4 binary64)) #s(literal -1/2 binary64))))
(.f64 eps (.f64 x (fma.f64 x (*.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64))))
(.f64 x (.f64 eps (fma.f64 x (*.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64))))
(.f64 x (-.f64 (.f64 eps (.f64 #s(literal 1/6 binary64) (.f64 x x))) eps))
(.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 x (*.f64 x x)) x) (neg.f64 eps))
(.f64 eps (fma.f64 x (fma.f64 x (.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64)) (*.f64 eps #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))))
(.f64 x (fma.f64 (.f64 x x) (.f64 eps (fma.f64 #s(literal -1/120 binary64) (.f64 x x) #s(literal 1/6 binary64))) (neg.f64 eps)))
(fma.f64 eps (.f64 eps #s(literal -1/2 binary64)) (.f64 x (-.f64 (.f64 x (.f64 #s(literal 1/4 binary64) (*.f64 eps eps))) eps)))
(fma.f64 (.f64 eps (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) (.f64 eps #s(literal 1/4 binary64))) #s(literal -1 binary64))) x (.f64 eps (.f64 eps #s(literal -1/2 binary64))))
(fma.f64 x (fma.f64 x (.f64 eps (fma.f64 eps #s(literal 1/4 binary64) (.f64 x #s(literal 1/6 binary64)))) (neg.f64 eps)) (.f64 eps (.f64 eps #s(literal -1/2 binary64))))
(.f64 (fma.f64 (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) (.f64 x (*.f64 x x)) x) (neg.f64 eps))

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

Calls

3 calls:

7.0ms	eps
6.0ms	x
4.0ms	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))

Results

Accuracy	Segments	Branch
98.5%	1	`eps`
98.5%	1	`(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))`
98.5%	1	`x`

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes15.0ms (0.1%)

Memory

9.7MiB live, 9.7MiB 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 x (neg.f64 eps))
(.f64 eps (.f64 eps #s(literal -1/2 binary64)))
(.f64 eps (-.f64 (.f64 eps #s(literal -1/2 binary64)) x))
(fma.f64 x (neg.f64 eps) (.f64 eps (.f64 eps #s(literal -1/2 binary64))))
(.f64 eps (.f64 #s(literal 1/4 binary64) (.f64 x (.f64 x eps))))
(.f64 eps (.f64 eps (fma.f64 x (*.f64 x #s(literal 1/4 binary64)) #s(literal -1/2 binary64))))
(.f64 eps (.f64 x (fma.f64 x (*.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64))))
(.f64 x (.f64 eps (fma.f64 x (*.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64))))
(.f64 x (-.f64 (.f64 eps (.f64 #s(literal 1/6 binary64) (.f64 x x))) eps))
(.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 x (*.f64 x x)) x) (neg.f64 eps))
(.f64 eps (fma.f64 x (fma.f64 x (.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64)) (*.f64 eps #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))))
(.f64 x (fma.f64 (.f64 x x) (.f64 eps (fma.f64 #s(literal -1/120 binary64) (.f64 x x) #s(literal 1/6 binary64))) (neg.f64 eps)))
(fma.f64 eps (.f64 eps #s(literal -1/2 binary64)) (.f64 x (-.f64 (.f64 x (.f64 #s(literal 1/4 binary64) (*.f64 eps eps))) eps)))

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:

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

Results

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

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes12.0ms (0.1%)

Memory

7.8MiB live, 7.8MiB allocated

Counts

14 → 1

Calls

Call 1

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

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

Calls

3 calls:

4.0ms	eps
4.0ms	x
3.0ms	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))

Results

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

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes12.0ms (0.1%)

Memory

7.5MiB live, 7.5MiB allocated

Counts

13 → 1

Calls

Call 1

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

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

Calls

3 calls:

4.0ms	x
4.0ms	eps
3.0ms	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))

Results

Accuracy	Segments	Branch
98.1%	1	`x`
98.1%	1	`eps`
98.1%	1	`(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))`

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes7.0ms (0%)

Memory

-34.4MiB live, 5.4MiB allocated

Counts

6 → 1

Calls

Call 1

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

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

Calls

3 calls:

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

Results

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

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes6.0ms (0%)

Memory

5.5MiB live, 5.5MiB 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 x (neg.f64 eps))
(.f64 eps (.f64 eps #s(literal -1/2 binary64)))

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

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
77.8%	1	`x`
77.8%	1	`eps`
77.8%	1	`(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))`

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes4.0ms (0%)

Memory

4.3MiB live, 4.3MiB 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
51.6%	1	`eps`
51.6%	1	`x`
51.6%	1	`(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))`

Compiler

Compiled 15 to 10 computations (33.3% saved)

simplify9.0ms (0%)

Memory

5.4MiB live, 5.4MiB allocated

Algorithm

1×	egg-herbie

Rules

76×	`*-commutative_binary64`
26×	`+-commutative_binary64`
26×	`sub-neg_binary64`
14×	`neg-sub0_binary64`
14×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	77	201
1	125	201
2	151	201
3	165	201
4	169	201

Stop Event

1×

saturated

Calls

Call 1

Inputs
(.f64 (fma.f64 (sin.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (cos.f64 x) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) #s(literal -2 binary64)))
(.f64 (.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 eps (-.f64 (.f64 eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x)))
(fma.f64 (.f64 eps (fma.f64 #s(literal 1/4 binary64) (.f64 x x) #s(literal -1/2 binary64))) eps (*.f64 (neg.f64 (sin.f64 x)) eps))
(.f64 eps (-.f64 (.f64 eps (fma.f64 x (*.f64 x #s(literal 1/4 binary64)) #s(literal -1/2 binary64))) (sin.f64 x)))
(.f64 eps (-.f64 (.f64 eps #s(literal -1/2 binary64)) (sin.f64 x)))
(.f64 eps (-.f64 (.f64 eps (fma.f64 x (.f64 x #s(literal 1/4 binary64)) #s(literal -1/2 binary64))) (fma.f64 (.f64 x (.f64 x x)) (fma.f64 x (.f64 x (fma.f64 x (*.f64 x #s(literal -1/5040 binary64)) #s(literal 1/120 binary64))) #s(literal -1/6 binary64)) x)))
(.f64 eps (-.f64 (.f64 eps (fma.f64 x (.f64 x #s(literal 1/4 binary64)) #s(literal -1/2 binary64))) (fma.f64 (.f64 x (.f64 x x)) (fma.f64 (.f64 x x) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) x)))
(fma.f64 (.f64 eps (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) (.f64 eps #s(literal 1/4 binary64))) #s(literal -1 binary64))) x (.f64 eps (.f64 eps #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))))
(.f64 eps (fma.f64 x (fma.f64 x (.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 (fma.f64 (sin.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (cos.f64 x) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) #s(literal -2 binary64)))
(.f64 (.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 eps #s(literal 1/2 binary64))) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))))
(.f64 eps (-.f64 (.f64 eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x)))
(.f64 eps (-.f64 (.f64 eps (*.f64 (cos.f64 x) #s(literal -1/2 binary64))) (sin.f64 x)))
(fma.f64 (.f64 eps (fma.f64 #s(literal 1/4 binary64) (.f64 x x) #s(literal -1/2 binary64))) eps (*.f64 (neg.f64 (sin.f64 x)) eps))
(fma.f64 (.f64 eps (fma.f64 #s(literal 1/4 binary64) (.f64 x x) #s(literal -1/2 binary64))) eps (neg.f64 (*.f64 (sin.f64 x) eps)))
(.f64 eps (-.f64 (.f64 eps (fma.f64 x (*.f64 x #s(literal 1/4 binary64)) #s(literal -1/2 binary64))) (sin.f64 x)))
(.f64 eps (-.f64 (.f64 eps #s(literal -1/2 binary64)) (sin.f64 x)))
(.f64 eps (-.f64 (.f64 eps (fma.f64 x (.f64 x #s(literal 1/4 binary64)) #s(literal -1/2 binary64))) (fma.f64 (.f64 x (.f64 x x)) (fma.f64 x (.f64 x (fma.f64 x (*.f64 x #s(literal -1/5040 binary64)) #s(literal 1/120 binary64))) #s(literal -1/6 binary64)) x)))
(.f64 eps (-.f64 (.f64 eps (fma.f64 x (.f64 x #s(literal 1/4 binary64)) #s(literal -1/2 binary64))) (fma.f64 (.f64 x (.f64 x x)) (fma.f64 (.f64 x x) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) x)))
(fma.f64 (.f64 eps (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) (.f64 eps #s(literal 1/4 binary64))) #s(literal -1 binary64))) x (.f64 eps (.f64 eps #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))))
(.f64 eps (fma.f64 x (fma.f64 x (.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)

soundness1.4s (7.2%)

Memory

-1.1MiB live, 38.5MiB allocated

Rules

15 816×	`lower-fma.f64`
15 816×	`lower-fma.f32`
14 158×	`lower-fma.f64`
14 158×	`lower-fma.f32`
12 362×	`lower-fma.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	34	142
0	61	136
1	212	136
2	1731	136
0	8625	131
0	717	7645
1	2424	7411
0	8325	6785
0	6	16
0	10	16
1	54	16
2	380	16
3	4694	16
0	8209	16
0	421	4855
1	1350	4682
2	4084	4648
0	8122	4331
0	50	261
0	95	239
1	323	145
2	3070	135
0	9461	135
0	105	498
1	277	495
2	609	495
3	2398	494
4	7880	494
0	8026	474
0	393	3454
1	1186	3321
2	3177	3276
3	7671	3276
0	8249	3063

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×	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 648 to 381 computations (41.2% saved)

preprocess97.0ms (0.5%)

Memory: -0.3MiB live, 79.1MiB allocated
Compiler: Compiled 492 to 212 computations (56.9% 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%)

sample9.6s (50.7%)

preprocess32.0ms (0.2%)

explain243.0ms (1.3%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify9.0ms (0%)

localize137.0ms (0.7%)

series4.0ms (0%)

rewrite294.0ms (1.5%)

simplify384.0ms (2%)

eval37.0ms (0.2%)

prune45.0ms (0.2%)

simplify362.0ms (1.9%)

localize232.0ms (1.2%)

series34.0ms (0.2%)

rewrite367.0ms (1.9%)

simplify403.0ms (2.1%)

eval130.0ms (0.7%)

prune118.0ms (0.6%)

simplify481.0ms (2.5%)

localize160.0ms (0.8%)

series36.0ms (0.2%)

rewrite385.0ms (2%)

simplify524.0ms (2.8%)

eval312.0ms (1.6%)

prune508.0ms (2.7%)

simplify817.0ms (4.3%)

localize249.0ms (1.3%)

series29.0ms (0.2%)

rewrite440.0ms (2.3%)

simplify383.0ms (2%)

eval198.0ms (1%)

prune187.0ms (1%)

regimes45.0ms (0.2%)

regimes42.0ms (0.2%)

regimes30.0ms (0.2%)

regimes28.0ms (0.1%)

regimes28.0ms (0.1%)

regimes23.0ms (0.1%)

regimes26.0ms (0.1%)

regimes19.0ms (0.1%)

regimes17.0ms (0.1%)

regimes15.0ms (0.1%)

regimes12.0ms (0.1%)

regimes12.0ms (0.1%)

regimes7.0ms (0%)

regimes6.0ms (0%)

regimes4.0ms (0%)

simplify9.0ms (0%)

soundness1.4s (7.2%)

preprocess97.0ms (0.5%)

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