Metrics for 2cos (problem 3.3.5)

analyze41.0ms (0.2%)

Memory

13.4MiB live, 90.0MiB 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)

sample8.1s (47.4%)

Memory

122.5MiB live, 9 562.8MiB allocated

Samples

3.3s	25 796×	0	invalid
2.8s	5 673×	2	valid
487.0ms	2 445×	1	valid
25.0ms	138×	0	valid

Precisions

Click to see histograms. Total time spent on operations: 5.1s

ival-cos: 2.3s (44.4% of total)

const: 737.0ms (14.4% of total)

adjust: 427.0ms (8.3% of total)

ival-add: 354.0ms (6.9% of total)

ival-sub: 316.0ms (6.2% of total)

ival-mult: 295.0ms (5.8% of total)

ival-fabs: 198.0ms (3.9% of total)

ival-<=: 198.0ms (3.9% of total)

ival-<: 158.0ms (3.1% of total)

ival-and: 102.0ms (2% of total)

exact: 47.0ms (0.9% of total)

ival-assert: 13.0ms (0.3% of total)

Bogosity

preprocess29.0ms (0.2%)

Memory

6.9MiB live, 44.8MiB 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))

explain406.0ms (2.4%)

Memory

-142.7MiB live, 324.8MiB allocated

FPErrors

Click to see full error table

Ground Truth	Example	Underpredictions	Example	Subexpression
256	-	256	(-8.790399431867464e-186 2.4056217630262064e-195)	`(cos.f64 (+.f64 x eps))`
256	-	256	(-8.790399431867464e-186 2.4056217630262064e-195)	`(cos.f64 x)`
256	-	125	(-8.790399431867464e-186 2.4056217630262064e-195)	`(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))`
0	-	0	-	`eps`
0	-	0	-	`(+.f64 x eps)`
0	-	0	-	`x`

Explanations

Click to see full explanations table

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

138.0ms	360×	2	valid
18.0ms	144×	1	valid
1.0ms	8×	0	valid

Compiler

Compiled 78 to 34 computations (56.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 130.0ms

ival-cos: 93.0ms (71.8% of total)

adjust: 27.0ms (20.8% of total)

ival-sub: 6.0ms (4.6% of total)

ival-add: 3.0ms (2.3% of total)

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

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

eval0.0ms (0%)

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

prune1.0ms (0%)

Memory

1.5MiB live, 1.5MiB 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)

simplify11.0ms (0.1%)

Memory

-20.3MiB live, 18.3MiB 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)

localize89.0ms (0.5%)

Memory

28.2MiB live, 147.9MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(+.f64 x eps)
✓	accuracy	5.1%	(cos.f64 x)
✓	accuracy	3.9%	(cos.f64 (+.f64 x eps))
✓	accuracy	3.3%	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))

Samples

65.0ms	180×	2	valid
16.0ms	72×	1	valid
0.0ms	4×	0	valid

Compiler

Compiled 40 to 14 computations (65% saved)

Precisions

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

ival-cos: 46.0ms (68.6% of total)

adjust: 16.0ms (23.9% of total)

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

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

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

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

series6.0ms (0%)

Memory

-27.9MiB live, 11.6MiB 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	(+ x eps)
1.0ms	eps	@	inf	(- (cos (+ x eps)) (cos x))
0.0ms	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))

Compiler

Compiled 161 to 114 computations (29.2% saved)

rewrite273.0ms (1.6%)

Memory

3.6MiB live, 460.7MiB 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))

simplify471.0ms (2.7%)

Memory

8.3MiB live, 518.9MiB 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)

eval35.0ms (0.2%)

Memory: -5.9MiB live, 72.5MiB allocated
Compiler: Compiled 7 945 to 876 computations (89% saved)

prune40.0ms (0.2%)

Memory

-12.8MiB live, 109.5MiB 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)

simplify377.0ms (2.2%)

Memory

11.9MiB live, 519.9MiB 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)

localize227.0ms (1.3%)

Memory

-1.6MiB live, 452.2MiB allocated

Localize:

Found 17 expressions of interest:

New	Metric	Score	Program
✓	accuracy	3.9%	(cos.f64 x)
✓	accuracy	3.8%	(sin.f64 x)
✓	accuracy	3.4%	(.f64 eps (-.f64 (.f64 eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x)))
✓	accuracy	2.4%	(.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x)))
✓	accuracy	3.8%	(+.f64 x eps)
✓	accuracy	3.7%	(.f64 x (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal -1/2 binary64)))
✓	accuracy	3.2%	(-.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	1.6%	(fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal -1/2 binary64))
✓	accuracy	6.0%	(neg.f64 eps)
✓	accuracy	4.7%	(*.f64 (sin.f64 x) (neg.f64 eps))
✓	accuracy	3.8%	(sin.f64 x)
✓	accuracy	5.4%	(+.f64 (cos.f64 eps) #s(literal -1 binary64))
✓	accuracy	2.7%	(cos.f64 eps)
✓	accuracy	6.5%	(.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	5.5%	(sin.f64 (*.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64)))
✓	accuracy	3.8%	(+.f64 x eps)
✓	accuracy	3.5%	(.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))

Samples

146.0ms	184×	2	valid
32.0ms	69×	1	valid
1.0ms	3×	0	valid

Compiler

Compiled 382 to 72 computations (81.2% saved)

Precisions

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

ival-cos: 50.0ms (36% of total)

adjust: 35.0ms (25.2% of total)

ival-mult: 23.0ms (16.6% of total)

ival-add: 12.0ms (8.6% of total)

ival-sin: 7.0ms (5% of total)

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

const: 4.0ms (2.9% 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)

series42.0ms (0.2%)

Memory

22.6MiB live, 59.6MiB allocated

Counts

21 → 372

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 (sin.f64 (*.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64)))>
#<alt (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal -1/2 binary64))>
#<alt (.f64 x (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 (- (* -1/2 (* x (cos eps))) (sin eps)))) 1)>
#<alt (- (+ (cos eps) (* x (- (* x (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps))))) (sin eps)))) 1)>
#<alt (* -1/24 (pow x 13))>
#<alt (* (pow x 13) (- (* 1/2 (/ 1 (pow x 6))) 1/24))>
#<alt (* (pow x 13) (- (* 1/2 (/ 1 (pow x 6))) 1/24))>
#<alt (* (pow x 13) (- (+ (* 1/2 (/ 1 (pow x 6))) (/ (cos (+ eps x)) (pow x 13))) (+ 1/24 (/ 1 (pow x 13)))))>
#<alt (* 1/24 (pow x 13))>
#<alt (* -1 (* (pow x 13) (- (* 1/2 (/ 1 (pow x 6))) 1/24)))>
#<alt (* -1 (* (pow x 13) (- (* 1/2 (/ 1 (pow x 6))) 1/24)))>
#<alt (* -1 (* (pow x 13) (- (+ (* -1 (/ (- (cos (- eps (* -1 x))) 1) (pow x 13))) (* 1/2 (/ 1 (pow x 6)))) 1/24)))>
#<alt (- (cos x) (+ 1 (* (pow x 5) (- (* 1/24 (pow x 5)) 1/2))))>
#<alt (- (+ (cos x) (* -1 (* eps (sin x)))) (+ 1 (* (pow x 5) (- (* 1/24 (pow x 5)) 1/2))))>
#<alt (- (+ (cos x) (* eps (- (* -1/2 (* eps (cos x))) (sin x)))) (+ 1 (* (pow x 5) (- (* 1/24 (pow x 5)) 1/2))))>
#<alt (- (+ (cos x) (* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x)))) (+ 1 (* (pow x 5) (- (* 1/24 (pow x 5)) 1/2))))>
#<alt (- (cos (+ eps x)) (+ 1 (* (pow x 6) (- (* 1/24 (pow x 6)) 1/2))))>
#<alt (- (cos (+ eps x)) (+ 1 (* (pow x 6) (- (* 1/24 (pow x 6)) 1/2))))>
#<alt (- (cos (+ eps x)) (+ 1 (* (pow x 6) (- (* 1/24 (pow x 6)) 1/2))))>
#<alt (- (cos (+ eps x)) (+ 1 (* (pow x 6) (- (* 1/24 (pow x 6)) 1/2))))>
#<alt (- (cos (- x (* -1 eps))) (+ 1 (* (pow x 6) (- (* 1/24 (pow x 6)) 1/2))))>
#<alt (- (cos (- x (* -1 eps))) (+ 1 (* (pow x 6) (- (* 1/24 (pow x 6)) 1/2))))>
#<alt (- (cos (- x (* -1 eps))) (+ 1 (* (pow x 6) (- (* 1/24 (pow x 6)) 1/2))))>
#<alt (- (cos (- x (* -1 eps))) (+ 1 (* (pow x 6) (- (* 1/24 (pow x 6)) 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 (* -1/2 (pow x 8))>
#<alt (* (pow x 8) (- (* 1/24 (/ 1 (pow x 5))) 1/2))>
#<alt (* (pow x 8) (- (+ (* 1/24 (/ 1 (pow x 5))) (/ 1 (pow x 8))) 1/2))>
#<alt (* (pow x 8) (- (+ (* 1/24 (/ 1 (pow x 5))) (/ 1 (pow x 8))) 1/2))>
#<alt (* -1/2 (pow x 8))>
#<alt (* -1 (* (pow x 8) (+ 1/2 (* 1/24 (/ 1 (pow x 5))))))>
#<alt (* (pow x 8) (- (* -1 (/ (- 1/24 (/ 1 (pow x 3))) (pow x 5))) 1/2))>
#<alt (* (pow x 8) (- (* -1 (/ (- 1/24 (/ 1 (pow x 3))) (pow x 5))) 1/2))>
#<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 (* 1/2 eps)>
#<alt (* eps (+ 1/2 (* -1/48 (pow eps 2))))>
#<alt (* eps (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))>
#<alt (* eps (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))>
#<alt (sin (* 1/2 eps))>
#<alt (sin (* 1/2 eps))>
#<alt (sin (* 1/2 eps))>
#<alt (sin (* 1/2 eps))>
#<alt (sin (* 1/2 eps))>
#<alt (sin (* 1/2 eps))>
#<alt (sin (* 1/2 eps))>
#<alt (sin (* 1/2 eps))>
#<alt -1/2>
#<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 3))>
#<alt (* (pow x 3) (- 1/24 (* 1/2 (/ 1 (pow x 3)))))>
#<alt (* (pow x 3) (- 1/24 (* 1/2 (/ 1 (pow x 3)))))>
#<alt (* (pow x 3) (- 1/24 (* 1/2 (/ 1 (pow x 3)))))>
#<alt (* -1/24 (pow x 3))>
#<alt (* -1 (* (pow x 3) (+ 1/24 (* 1/2 (/ 1 (pow x 3))))))>
#<alt (* -1 (* (pow x 3) (+ 1/24 (* 1/2 (/ 1 (pow x 3))))))>
#<alt (* -1 (* (pow x 3) (+ 1/24 (* 1/2 (/ 1 (pow x 3))))))>
#<alt (* -1/2 x)>
#<alt (* x (- (* 1/24 (pow x 2)) 1/2))>
#<alt (* x (- (* 1/24 (pow x 2)) 1/2))>
#<alt (* x (- (* 1/24 (pow x 2)) 1/2))>
#<alt (* 1/24 (pow x 4))>
#<alt (* (pow x 4) (- 1/24 (* 1/2 (/ 1 (pow x 3)))))>
#<alt (* (pow x 4) (- 1/24 (* 1/2 (/ 1 (pow x 3)))))>
#<alt (* (pow x 4) (- 1/24 (* 1/2 (/ 1 (pow x 3)))))>
#<alt (* 1/24 (pow x 5))>
#<alt (* -1 (* (pow x 5) (- (* 1/2 (/ 1 (pow x 4))) 1/24)))>
#<alt (* -1 (* (pow x 5) (- (* 1/2 (/ 1 (pow x 4))) 1/24)))>
#<alt (* -1 (* (pow x 5) (- (* 1/2 (/ 1 (pow x 4))) 1/24)))>
#<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

93 calls:

Time	Variable		Point	Expression
6.0ms	eps	@	inf	(- (cos (+ x eps)) (+ (* 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	x	@	-inf	(* (* (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) -2)
1.0ms	eps	@	-inf	(- (cos (+ x eps)) (+ (* x (* x (+ (* 1/24 (* x x)) -1/2))) 1))

Compiler

Compiled 977 to 736 computations (24.7% saved)

rewrite357.0ms (2.1%)

Memory

-6.4MiB live, 381.2MiB 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	143
0	61	135
1	212	135
2	1731	135
0	8625	132

Stop Event

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

Counts

21 → 577

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

simplify836.0ms (4.9%)

Memory

0.3MiB live, 335.5MiB allocated

Algorithm

1×	egg-herbie

Rules

11 698×	`lower-fma.f64`
11 698×	`lower-fma.f32`
5 832×	`lower-*.f64`
5 832×	`lower-*.f32`
4 236×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	413	3236
1	1213	3123
2	3294	3058
0	8059	2872

Stop Event

1×	iter limit
1×	node limit

Counts

372 → 350

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 (- (* -1/2 (* x (cos eps))) (sin eps)))) 1)
(- (+ (cos eps) (* x (- (* x (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps))))) (sin eps)))) 1)
(* -1/24 (pow x 13))
(* (pow x 13) (- (* 1/2 (/ 1 (pow x 6))) 1/24))
(* (pow x 13) (- (* 1/2 (/ 1 (pow x 6))) 1/24))
(* (pow x 13) (- (+ (* 1/2 (/ 1 (pow x 6))) (/ (cos (+ eps x)) (pow x 13))) (+ 1/24 (/ 1 (pow x 13)))))
(* 1/24 (pow x 13))
(* -1 (* (pow x 13) (- (* 1/2 (/ 1 (pow x 6))) 1/24)))
(* -1 (* (pow x 13) (- (* 1/2 (/ 1 (pow x 6))) 1/24)))
(* -1 (* (pow x 13) (- (+ (* -1 (/ (- (cos (- eps (* -1 x))) 1) (pow x 13))) (* 1/2 (/ 1 (pow x 6)))) 1/24)))
(- (cos x) (+ 1 (* (pow x 5) (- (* 1/24 (pow x 5)) 1/2))))
(- (+ (cos x) (* -1 (* eps (sin x)))) (+ 1 (* (pow x 5) (- (* 1/24 (pow x 5)) 1/2))))
(- (+ (cos x) (* eps (- (* -1/2 (* eps (cos x))) (sin x)))) (+ 1 (* (pow x 5) (- (* 1/24 (pow x 5)) 1/2))))
(- (+ (cos x) (* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x)))) (+ 1 (* (pow x 5) (- (* 1/24 (pow x 5)) 1/2))))
(- (cos (+ eps x)) (+ 1 (* (pow x 6) (- (* 1/24 (pow x 6)) 1/2))))
(- (cos (+ eps x)) (+ 1 (* (pow x 6) (- (* 1/24 (pow x 6)) 1/2))))
(- (cos (+ eps x)) (+ 1 (* (pow x 6) (- (* 1/24 (pow x 6)) 1/2))))
(- (cos (+ eps x)) (+ 1 (* (pow x 6) (- (* 1/24 (pow x 6)) 1/2))))
(- (cos (- x (* -1 eps))) (+ 1 (* (pow x 6) (- (* 1/24 (pow x 6)) 1/2))))
(- (cos (- x (* -1 eps))) (+ 1 (* (pow x 6) (- (* 1/24 (pow x 6)) 1/2))))
(- (cos (- x (* -1 eps))) (+ 1 (* (pow x 6) (- (* 1/24 (pow x 6)) 1/2))))
(- (cos (- x (* -1 eps))) (+ 1 (* (pow x 6) (- (* 1/24 (pow x 6)) 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)))
(* -1/2 (pow x 8))
(* (pow x 8) (- (* 1/24 (/ 1 (pow x 5))) 1/2))
(* (pow x 8) (- (+ (* 1/24 (/ 1 (pow x 5))) (/ 1 (pow x 8))) 1/2))
(* (pow x 8) (- (+ (* 1/24 (/ 1 (pow x 5))) (/ 1 (pow x 8))) 1/2))
(* -1/2 (pow x 8))
(* -1 (* (pow x 8) (+ 1/2 (* 1/24 (/ 1 (pow x 5))))))
(* (pow x 8) (- (* -1 (/ (- 1/24 (/ 1 (pow x 3))) (pow x 5))) 1/2))
(* (pow x 8) (- (* -1 (/ (- 1/24 (/ 1 (pow x 3))) (pow x 5))) 1/2))
(* -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))
(* 1/2 eps)
(* eps (+ 1/2 (* -1/48 (pow eps 2))))
(* eps (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))
(* eps (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
-1/2
(- (* 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 3))
(* (pow x 3) (- 1/24 (* 1/2 (/ 1 (pow x 3)))))
(* (pow x 3) (- 1/24 (* 1/2 (/ 1 (pow x 3)))))
(* (pow x 3) (- 1/24 (* 1/2 (/ 1 (pow x 3)))))
(* -1/24 (pow x 3))
(* -1 (* (pow x 3) (+ 1/24 (* 1/2 (/ 1 (pow x 3))))))
(* -1 (* (pow x 3) (+ 1/24 (* 1/2 (/ 1 (pow x 3))))))
(* -1 (* (pow x 3) (+ 1/24 (* 1/2 (/ 1 (pow x 3))))))
(* -1/2 x)
(* x (- (* 1/24 (pow x 2)) 1/2))
(* x (- (* 1/24 (pow x 2)) 1/2))
(* x (- (* 1/24 (pow x 2)) 1/2))
(* 1/24 (pow x 4))
(* (pow x 4) (- 1/24 (* 1/2 (/ 1 (pow x 3)))))
(* (pow x 4) (- 1/24 (* 1/2 (/ 1 (pow x 3)))))
(* (pow x 4) (- 1/24 (* 1/2 (/ 1 (pow x 3)))))
(* 1/24 (pow x 5))
(* -1 (* (pow x 5) (- (* 1/2 (/ 1 (pow x 4))) 1/24)))
(* -1 (* (pow x 5) (- (* 1/2 (/ 1 (pow x 4))) 1/24)))
(* -1 (* (pow x 5) (- (* 1/2 (/ 1 (pow x 4))) 1/24)))
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))))
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(neg.f64 eps)
(* -1 eps)
(neg.f64 eps)
(* -1 eps)
(neg.f64 eps)
(* -1 eps)
(neg.f64 eps)
(- (cos eps) 1)
(+.f64 #s(literal -1 binary64) (cos.f64 eps))
(- (+ (cos eps) (* -1 (* x (sin eps)))) 1)
(-.f64 (cos.f64 eps) (fma.f64 x (sin.f64 eps) #s(literal 1 binary64)))
(- (+ (cos eps) (* x (- (* -1/2 (* x (cos eps))) (sin eps)))) 1)
(fma.f64 x (-.f64 (.f64 (cos.f64 eps) (.f64 x #s(literal -1/2 binary64))) (sin.f64 eps)) (+.f64 #s(literal -1 binary64) (cos.f64 eps)))
(- (+ (cos eps) (* x (- (* x (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps))))) (sin eps)))) 1)
(fma.f64 x (fma.f64 x (.f64 #s(literal -1/2 binary64) (cos.f64 eps)) (.f64 (sin.f64 eps) (fma.f64 x (*.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64)))) (+.f64 #s(literal -1 binary64) (cos.f64 eps)))
(* -1/24 (pow x 13))
(*.f64 #s(literal -1/24 binary64) (pow.f64 x #s(literal 13 binary64)))
(* (pow x 13) (- (* 1/2 (/ 1 (pow x 6))) 1/24))
(*.f64 (pow.f64 x #s(literal 13 binary64)) (+.f64 #s(literal -1/24 binary64) (/.f64 #s(literal 1/2 binary64) (pow.f64 x #s(literal 6 binary64)))))
(* (pow x 13) (- (* 1/2 (/ 1 (pow x 6))) 1/24))
(*.f64 (pow.f64 x #s(literal 13 binary64)) (+.f64 #s(literal -1/24 binary64) (/.f64 #s(literal 1/2 binary64) (pow.f64 x #s(literal 6 binary64)))))
(* (pow x 13) (- (+ (* 1/2 (/ 1 (pow x 6))) (/ (cos (+ eps x)) (pow x 13))) (+ 1/24 (/ 1 (pow x 13)))))
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(* 1/24 (pow x 13))
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(* -1 (* (pow x 13) (- (* 1/2 (/ 1 (pow x 6))) 1/24)))
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(cos eps)
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(+ (cos eps) (* -1 (* x (sin eps))))
(-.f64 (cos.f64 eps) (*.f64 x (sin.f64 eps)))
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(cos (+ eps x))
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(cos (+ eps x))
(cos.f64 (+.f64 eps x))
(cos (+ eps x))
(cos.f64 (+.f64 eps x))
(cos (+ eps x))
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(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))))
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(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)))
(fma.f64 x (/.f64 eps x) x)
(* x (+ 1 (/ eps x)))
(fma.f64 x (/.f64 eps x) x)
(* x (+ 1 (/ eps x)))
(fma.f64 x (/.f64 eps x) x)
x
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(fma.f64 x (/.f64 eps x) x)
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(fma.f64 x (/.f64 eps x) x)
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(fma.f64 x (/.f64 eps x) x)
x
(+ eps x)
(+.f64 eps x)
(+ eps x)
(+.f64 eps x)
(+ eps x)
(+.f64 eps x)
eps
(* eps (+ 1 (/ x eps)))
(fma.f64 eps (/.f64 x eps) eps)
(* eps (+ 1 (/ x eps)))
(fma.f64 eps (/.f64 x eps) eps)
(* eps (+ 1 (/ x eps)))
(fma.f64 eps (/.f64 x eps) eps)
eps
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
(fma.f64 eps (/.f64 x eps) eps)
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
(fma.f64 eps (/.f64 x eps) eps)
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
(fma.f64 eps (/.f64 x eps) eps)
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) (- (* 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))
(* -1/2 (pow x 8))
(*.f64 #s(literal -1/2 binary64) (pow.f64 x #s(literal 8 binary64)))
(* (pow x 8) (- (* 1/24 (/ 1 (pow x 5))) 1/2))
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(* (pow x 8) (- (+ (* 1/24 (/ 1 (pow x 5))) (/ 1 (pow x 8))) 1/2))
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(* -1/2 (pow x 8))
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(* -1/2 (* (pow eps 2) (cos x)))
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(* (pow eps 2) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))
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(* (pow eps 2) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))
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(* (pow eps 2) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))
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(* -1/2 (* (pow eps 2) (cos x)))
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(* (pow eps 2) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))
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(* (pow eps 2) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))
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(* (pow eps 2) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))
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(* -1/2 (pow eps 2))
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(+ (* -1/2 (pow eps 2)) (* x (+ (* -1 eps) (* x (+ (* 1/6 (* eps x)) (* 1/4 (pow eps 2)))))))
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(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
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(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
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(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
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(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
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(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
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(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
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(* 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)))
(* -1 (sin x))
(neg.f64 (sin.f64 x))
(- (* -1/2 (* eps (cos x))) (sin x))
(-.f64 (.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x))
(- (* -1/2 (* eps (cos x))) (sin x))
(-.f64 (.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x))
(- (* -1/2 (* eps (cos x))) (sin x))
(-.f64 (.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x))
(* -1/2 (* eps (cos x)))
(.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x)))
(* eps (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))
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(* eps (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))
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(* eps (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))
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(* -1/2 (* eps (cos x)))
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(* -1 (* eps (+ (* 1/2 (cos x)) (/ (sin x) eps))))
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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 (- (* 1/4 (* eps x)) 1)))
(fma.f64 eps (fma.f64 x (*.f64 x #s(literal 1/4 binary64)) #s(literal -1/2 binary64)) (neg.f64 x))
(+ (* -1/2 eps) (* x (- (* x (+ (* 1/6 x) (* 1/4 eps))) 1)))
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(- (* -1/2 (* eps (cos x))) (sin x))
(-.f64 (.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x))
(- (* -1/2 (* eps (cos x))) (sin x))
(-.f64 (.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x))
(- (* -1/2 (* eps (cos x))) (sin x))
(-.f64 (.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x))
(- (* -1/2 (* eps (cos x))) (sin x))
(-.f64 (.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x))
(- (* -1/2 (* eps (cos x))) (sin x))
(-.f64 (.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x))
(- (* -1/2 (* eps (cos x))) (sin x))
(-.f64 (.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x))
(- (* -1/2 (* eps (cos x))) (sin x))
(-.f64 (.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x))
(- (* -1/2 (* eps (cos x))) (sin x))
(-.f64 (.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.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 (* 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)
(*.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 #s(literal -1/48 binary64) (.f64 x x) #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 x x) (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))) (.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 #s(literal -1/48 binary64) (.f64 x x) #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))
(* 1/2 eps)
(*.f64 #s(literal 1/2 binary64) eps)
(* eps (+ 1/2 (* -1/48 (pow eps 2))))
(.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))
(* eps (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))
(.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 (*.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))
(* eps (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))
(.f64 eps (fma.f64 eps (.f64 eps (fma.f64 eps (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/645120 binary64)) #s(literal 1/3840 binary64))) #s(literal -1/48 binary64))) #s(literal 1/2 binary64)))
(sin (* 1/2 eps))
(sin.f64 (*.f64 #s(literal 1/2 binary64) eps))
(sin (* 1/2 eps))
(sin.f64 (*.f64 #s(literal 1/2 binary64) eps))
(sin (* 1/2 eps))
(sin.f64 (*.f64 #s(literal 1/2 binary64) eps))
(sin (* 1/2 eps))
(sin.f64 (*.f64 #s(literal 1/2 binary64) eps))
(sin (* 1/2 eps))
(sin.f64 (*.f64 #s(literal 1/2 binary64) eps))
(sin (* 1/2 eps))
(sin.f64 (*.f64 #s(literal 1/2 binary64) eps))
(sin (* 1/2 eps))
(sin.f64 (*.f64 #s(literal 1/2 binary64) eps))
(sin (* 1/2 eps))
(sin.f64 (*.f64 #s(literal 1/2 binary64) eps))
-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 3))
(.f64 #s(literal 1/24 binary64) (.f64 x (*.f64 x x)))
(* (pow x 3) (- 1/24 (* 1/2 (/ 1 (pow x 3)))))
(fma.f64 x (.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal -1/2 binary64))
(* (pow x 3) (- 1/24 (* 1/2 (/ 1 (pow x 3)))))
(fma.f64 x (.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal -1/2 binary64))
(* (pow x 3) (- 1/24 (* 1/2 (/ 1 (pow x 3)))))
(fma.f64 x (.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal -1/2 binary64))
(* -1/24 (pow x 3))
(.f64 x (.f64 (*.f64 x x) #s(literal -1/24 binary64)))
(* -1 (* (pow x 3) (+ 1/24 (* 1/2 (/ 1 (pow x 3))))))
(fma.f64 x (.f64 (.f64 x x) #s(literal -1/24 binary64)) #s(literal -1/2 binary64))
(* -1 (* (pow x 3) (+ 1/24 (* 1/2 (/ 1 (pow x 3))))))
(fma.f64 x (.f64 (.f64 x x) #s(literal -1/24 binary64)) #s(literal -1/2 binary64))
(* -1 (* (pow x 3) (+ 1/24 (* 1/2 (/ 1 (pow x 3))))))
(fma.f64 x (.f64 (.f64 x x) #s(literal -1/24 binary64)) #s(literal -1/2 binary64))
(* -1/2 x)
(*.f64 x #s(literal -1/2 binary64))
(* x (- (* 1/24 (pow x 2)) 1/2))
(.f64 x (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal -1/2 binary64)))
(* x (- (* 1/24 (pow x 2)) 1/2))
(.f64 x (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal -1/2 binary64)))
(* x (- (* 1/24 (pow x 2)) 1/2))
(.f64 x (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal -1/2 binary64)))
(* 1/24 (pow x 4))
(.f64 #s(literal 1/24 binary64) (.f64 (.f64 x x) (.f64 x x)))
(* (pow x 4) (- 1/24 (* 1/2 (/ 1 (pow x 3)))))
(.f64 (+.f64 #s(literal 1/24 binary64) (/.f64 #s(literal -1/2 binary64) (.f64 x (.f64 x x)))) (.f64 (.f64 x x) (.f64 x x)))
(* (pow x 4) (- 1/24 (* 1/2 (/ 1 (pow x 3)))))
(.f64 (+.f64 #s(literal 1/24 binary64) (/.f64 #s(literal -1/2 binary64) (.f64 x (.f64 x x)))) (.f64 (.f64 x x) (.f64 x x)))
(* (pow x 4) (- 1/24 (* 1/2 (/ 1 (pow x 3)))))
(.f64 (+.f64 #s(literal 1/24 binary64) (/.f64 #s(literal -1/2 binary64) (.f64 x (.f64 x x)))) (.f64 (.f64 x x) (.f64 x x)))
(* 1/24 (pow x 5))
(*.f64 #s(literal 1/24 binary64) (pow.f64 x #s(literal 5 binary64)))
(* -1 (* (pow x 5) (- (* 1/2 (/ 1 (pow x 4))) 1/24)))
(.f64 (pow.f64 x #s(literal 5 binary64)) (neg.f64 (+.f64 #s(literal -1/24 binary64) (/.f64 #s(literal 1/2 binary64) (.f64 (.f64 x x) (.f64 x x))))))
(* -1 (* (pow x 5) (- (* 1/2 (/ 1 (pow x 4))) 1/24)))
(.f64 (pow.f64 x #s(literal 5 binary64)) (neg.f64 (+.f64 #s(literal -1/24 binary64) (/.f64 #s(literal 1/2 binary64) (.f64 (.f64 x x) (.f64 x x))))))
(* -1 (* (pow x 5) (- (* 1/2 (/ 1 (pow x 4))) 1/24)))
(.f64 (pow.f64 x #s(literal 5 binary64)) (neg.f64 (+.f64 #s(literal -1/24 binary64) (/.f64 #s(literal 1/2 binary64) (.f64 (.f64 x x) (.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 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)

eval207.0ms (1.2%)

Memory: 10.9MiB live, 168.2MiB allocated
Compiler: Compiled 26 997 to 2 749 computations (89.8% saved)

prune190.0ms (1.1%)

Memory

-23.3MiB live, 177.6MiB allocated

Pruning

22 alts after pruning (18 fresh and 4 done)

	Pruned	Kept	Total
New	989	15	1 004
Fresh	4	3	7
Picked	2	3	5
Done	0	1	1
Total	995	22	1 017

Accuracy

100.0%

Counts

1 017 → 22

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))))
▶	98.1%	(fma.f64 x (-.f64 (.f64 x (.f64 eps (.f64 eps #s(literal 1/4 binary64)))) eps) (.f64 #s(literal -1/2 binary64) (*.f64 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 x (.f64 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))
▶	99.4%	(.f64 (.f64 (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64))) (sin.f64 (*.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)))) #s(literal -2 binary64))
▶	99.1%	(.f64 (.f64 (.f64 #s(literal 1/2 binary64) eps) (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))
	78.1%	(.f64 x (fma.f64 x (.f64 x (.f64 eps (fma.f64 (.f64 x x) #s(literal -1/120 binary64) #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 x (*.f64 x #s(literal 1/4 binary64)) #s(literal -1/2 binary64))) (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 594 to 380 computations (36% saved)

simplify745.0ms (4.3%)

Memory

10.7MiB live, 442.5MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 17 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(*.f64 #s(literal 1/2 binary64) eps)
✓	cost-diff	0	(.f64 (.f64 #s(literal 1/2 binary64) eps) (sin.f64 (*.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64))))
✓	cost-diff	320	(*.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64))
✓	cost-diff	512	(.f64 (.f64 (.f64 #s(literal 1/2 binary64) eps) (sin.f64 (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)))) #s(literal -2 binary64))
✓	cost-diff	0	(.f64 eps (.f64 eps #s(literal 1/4 binary64)))
✓	cost-diff	0	(.f64 x (.f64 eps (*.f64 eps #s(literal 1/4 binary64))))
✓	cost-diff	128	(-.f64 (.f64 x (.f64 eps (*.f64 eps #s(literal 1/4 binary64)))) eps)
✓	cost-diff	512	(fma.f64 x (-.f64 (.f64 x (.f64 eps (.f64 eps #s(literal 1/4 binary64)))) eps) (.f64 #s(literal -1/2 binary64) (*.f64 eps eps)))
✓	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 eps (fma.f64 x (.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64)))
✓	cost-diff	0	(.f64 x (.f64 eps (fma.f64 x (*.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64))))
✓	cost-diff	192	(+.f64 #s(literal 1 binary64) #s(literal -1 binary64))
✓	cost-diff	0	(.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))
✓	cost-diff	0	(.f64 (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64))) (sin.f64 (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64))))
✓	cost-diff	320	(*.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64))
✓	cost-diff	320	(.f64 (.f64 (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64))) (sin.f64 (*.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)))) #s(literal -2 binary64))

Rules

14 716×	`lower-fma.f32`
14 710×	`lower-fma.f64`
6 262×	`lower-*.f32`
6 230×	`lower-*.f64`
3 178×	`lower-+.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	34	223
0	62	223
1	117	221
2	257	220
3	514	200
4	923	197
5	2217	197
6	6889	197
0	8097	185

Stop Event

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

Calls

Call 1

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

localize522.0ms (3%)

Memory

-2.5MiB live, 156.8MiB allocated

Localize:

Found 17 expressions of interest:

New	Metric	Score	Program
✓	accuracy	19.0%	(+.f64 x (+.f64 x eps))
✓	accuracy	19.0%	(sin.f64 (*.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)))
✓	accuracy	4.2%	(+.f64 x eps)
✓	accuracy	3.8%	(.f64 (.f64 #s(literal 1/2 binary64) eps) (sin.f64 (*.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64))))
✓	accuracy	8.5%	(-.f64 (.f64 x (.f64 eps (*.f64 eps #s(literal 1/4 binary64)))) eps)
✓	accuracy	6.3%	(fma.f64 x (-.f64 (.f64 x (.f64 eps (.f64 eps #s(literal 1/4 binary64)))) eps) (.f64 #s(literal -1/2 binary64) (*.f64 eps eps)))
✓	accuracy	5.5%	(*.f64 eps #s(literal 1/4 binary64))
✓	accuracy	3.1%	(.f64 eps (.f64 eps #s(literal 1/4 binary64)))
✓	accuracy	16.9%	(*.f64 x #s(literal 1/6 binary64))
✓	accuracy	5.5%	(fma.f64 x (*.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64))
✓	accuracy	4.4%	(.f64 eps (fma.f64 x (.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64)))
✓	accuracy	3.8%	(.f64 x (.f64 eps (fma.f64 x (*.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64))))
✓	accuracy	3.5%	(+.f64 #s(literal 1 binary64) #s(literal -1 binary64))
✓	accuracy	4.2%	(+.f64 x eps)
✓	accuracy	3.9%	(.f64 (.f64 (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64))) (sin.f64 (*.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)))) #s(literal -2 binary64))
✓	accuracy	2.7%	(fma.f64 eps (*.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64))
✓	accuracy	2.7%	(.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))

Samples

332.0ms	255×	0	valid
0.0ms	1×	1	exit

Compiler

Compiled 462 to 73 computations (84.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 177.0ms

ival-mult: 161.0ms (90.9% of total)

ival-add: 6.0ms (3.4% of total)

const: 6.0ms (3.4% of total)

ival-sin: 2.0ms (1.1% of total)

ival-sub: 1.0ms (0.6% of total)

exact: 1.0ms (0.6% of total)

adjust: 0.0ms (0% of total)

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

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

series92.0ms (0.5%)

Memory

25.5MiB live, 65.0MiB allocated

Counts

21 → 396

Calls

Call 1

Inputs
#<alt (.f64 (.f64 (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 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 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64))>
#<alt (.f64 (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64))) (sin.f64 (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64))))>
#<alt (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))>
#<alt (+.f64 #s(literal 1 binary64) #s(literal -1 binary64))>
#<alt (.f64 x (.f64 eps (fma.f64 x (*.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64))))>
#<alt (.f64 eps (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 (fma.f64 x (-.f64 (.f64 x (.f64 eps (.f64 eps #s(literal 1/4 binary64)))) eps) (.f64 #s(literal -1/2 binary64) (*.f64 eps eps)))>
#<alt (-.f64 (.f64 x (.f64 eps (*.f64 eps #s(literal 1/4 binary64)))) eps)>
#<alt (.f64 x (.f64 eps (*.f64 eps #s(literal 1/4 binary64))))>
#<alt (.f64 eps (.f64 eps #s(literal 1/4 binary64)))>
#<alt (.f64 (.f64 (.f64 #s(literal 1/2 binary64) eps) (sin.f64 (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)))) #s(literal -2 binary64))>
#<alt (.f64 (.f64 #s(literal 1/2 binary64) eps) (sin.f64 (*.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64))))>
#<alt (*.f64 #s(literal 1/2 binary64) eps)>
#<alt (fma.f64 eps (*.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64))>
#<alt (+.f64 x eps)>
#<alt (*.f64 eps #s(literal 1/4 binary64))>
#<alt (sin.f64 (*.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)))>
#<alt (+.f64 x (+.f64 x eps))>

Outputs
#<alt (* -1 (* eps (sin x)))>
#<alt (* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))>
#<alt (* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* 1/8 (* eps (sin x)))))))>
#<alt (* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/48 (* eps (cos x))) (* 1/8 (sin x))))))))>
#<alt (* 1/24 (* (pow eps 5) (sin (* 1/2 (+ eps (* 2 x))))))>
#<alt (* (pow eps 5) (+ (* -1 (/ (sin (* 1/2 (+ eps (* 2 x)))) (pow eps 4))) (* 1/24 (sin (* 1/2 (+ eps (* 2 x)))))))>
#<alt (* (pow eps 5) (+ (* -1 (/ (sin (* 1/2 (+ eps (* 2 x)))) (pow eps 4))) (* 1/24 (sin (* 1/2 (+ eps (* 2 x)))))))>
#<alt (* (pow eps 5) (+ (* -1 (/ (sin (* 1/2 (+ eps (* 2 x)))) (pow eps 4))) (* 1/24 (sin (* 1/2 (+ eps (* 2 x)))))))>
#<alt (* 1/24 (* (pow eps 3) (sin (* 1/2 (- (* 2 x) (* -1 eps))))))>
#<alt (* -1 (* (pow eps 3) (+ (* -1/24 (sin (* 1/2 (- (* 2 x) (* -1 eps))))) (/ (sin (* 1/2 (- (* 2 x) (* -1 eps)))) (pow eps 2)))))>
#<alt (* -1 (* (pow eps 3) (+ (* -1/24 (sin (* 1/2 (- (* 2 x) (* -1 eps))))) (/ (sin (* 1/2 (- (* 2 x) (* -1 eps)))) (pow eps 2)))))>
#<alt (* -1 (* (pow eps 3) (+ (* -1/24 (sin (* 1/2 (- (* 2 x) (* -1 eps))))) (/ (sin (* 1/2 (- (* 2 x) (* -1 eps)))) (pow eps 2)))))>
#<alt (* -2 (* eps (* (sin (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 4))))))>
#<alt (+ (* -2 (* eps (* x (* (cos (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 4))))))) (* -2 (* eps (* (sin (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 4)))))))>
#<alt (+ (* -2 (* eps (* (sin (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 4)))))) (* x (+ (* -2 (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 4)))))) (* eps (* x (* (sin (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 4)))))))))>
#<alt (+ (* -2 (* eps (* (sin (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 4)))))) (* x (+ (* -2 (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 4)))))) (* x (+ (* 1/3 (* eps (* x (* (cos (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 4))))))) (* eps (* (sin (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 4))))))))))>
#<alt (* -2 (* eps (* (sin (* 1/2 (+ eps (* 2 x)))) (+ 1/2 (* -1/48 (pow eps 4))))))>
#<alt (* -2 (* eps (* (sin (* 1/2 (+ eps (* 2 x)))) (+ 1/2 (* -1/48 (pow eps 4))))))>
#<alt (* -2 (* eps (* (sin (* 1/2 (+ eps (* 2 x)))) (+ 1/2 (* -1/48 (pow eps 4))))))>
#<alt (* -2 (* eps (* (sin (* 1/2 (+ eps (* 2 x)))) (+ 1/2 (* -1/48 (pow eps 4))))))>
#<alt (* -2 (* eps (* (sin (* 1/2 (- eps (* -2 x)))) (+ 1/2 (* -1/48 (pow eps 4))))))>
#<alt (* -2 (* eps (* (sin (* 1/2 (- eps (* -2 x)))) (+ 1/2 (* -1/48 (pow eps 4))))))>
#<alt (* -2 (* eps (* (sin (* 1/2 (- eps (* -2 x)))) (+ 1/2 (* -1/48 (pow eps 4))))))>
#<alt (* -2 (* eps (* (sin (* 1/2 (- eps (* -2 x)))) (+ 1/2 (* -1/48 (pow eps 4))))))>
#<alt (* 1/2 eps)>
#<alt (+ x (* 1/2 eps))>
#<alt (+ x (* 1/2 eps))>
#<alt (+ x (* 1/2 eps))>
#<alt x>
#<alt (* x (+ 1 (* 1/2 (/ eps x))))>
#<alt (* x (+ 1 (* 1/2 (/ eps x))))>
#<alt (* x (+ 1 (* 1/2 (/ eps x))))>
#<alt x>
#<alt (* -1 (* x (- (* -1/2 (/ eps x)) 1)))>
#<alt (* -1 (* x (- (* -1/2 (/ eps x)) 1)))>
#<alt (* -1 (* x (- (* -1/2 (/ eps x)) 1)))>
#<alt x>
#<alt (+ x (* 1/2 eps))>
#<alt (+ x (* 1/2 eps))>
#<alt (+ x (* 1/2 eps))>
#<alt (* 1/2 eps)>
#<alt (* eps (+ 1/2 (/ x eps)))>
#<alt (* eps (+ 1/2 (/ x eps)))>
#<alt (* eps (+ 1/2 (/ x eps)))>
#<alt (* 1/2 eps)>
#<alt (* -1 (* eps (- (* -1 (/ x eps)) 1/2)))>
#<alt (* -1 (* eps (- (* -1 (/ x eps)) 1/2)))>
#<alt (* -1 (* eps (- (* -1 (/ x eps)) 1/2)))>
#<alt (* 1/2 (* eps (sin x)))>
#<alt (* eps (+ (* 1/4 (* eps (cos x))) (* 1/2 (sin x))))>
#<alt (* eps (+ (* 1/2 (sin x)) (* eps (+ (* -1/16 (* eps (sin x))) (* 1/4 (cos x))))))>
#<alt (* eps (+ (* 1/2 (sin x)) (* eps (+ (* 1/4 (cos x)) (* eps (+ (* -1/16 (sin x)) (* eps (+ (* -1/48 (sin x)) (* -1/96 (cos x))))))))))>
#<alt (* -1/48 (* (pow eps 4) (sin (* 1/2 (+ eps (* 2 x))))))>
#<alt (* (pow eps 4) (+ (* -1/48 (sin (* 1/2 (+ eps (* 2 x))))) (* 1/2 (/ (sin (* 1/2 (+ eps (* 2 x)))) (pow eps 3)))))>
#<alt (* (pow eps 4) (+ (* -1/48 (sin (* 1/2 (+ eps (* 2 x))))) (* 1/2 (/ (sin (* 1/2 (+ eps (* 2 x)))) (pow eps 3)))))>
#<alt (* (pow eps 4) (+ (* -1/48 (sin (* 1/2 (+ eps (* 2 x))))) (* 1/2 (/ (sin (* 1/2 (+ eps (* 2 x)))) (pow eps 3)))))>
#<alt (* -1/48 (* (pow eps 5) (sin (* 1/2 (- (* 2 x) (* -1 eps))))))>
#<alt (* -1 (* (pow eps 5) (+ (* -1/2 (/ (sin (* 1/2 (- (* 2 x) (* -1 eps)))) (pow eps 4))) (* 1/48 (sin (* 1/2 (- (* 2 x) (* -1 eps))))))))>
#<alt (* -1 (* (pow eps 5) (+ (* -1/2 (/ (sin (* 1/2 (- (* 2 x) (* -1 eps)))) (pow eps 4))) (* 1/48 (sin (* 1/2 (- (* 2 x) (* -1 eps))))))))>
#<alt (* -1 (* (pow eps 5) (+ (* -1/2 (/ (sin (* 1/2 (- (* 2 x) (* -1 eps)))) (pow eps 4))) (* 1/48 (sin (* 1/2 (- (* 2 x) (* -1 eps))))))))>
#<alt (* eps (* (sin (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 3)))))>
#<alt (+ (* eps (* x (* (cos (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 3)))))) (* eps (* (sin (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 3))))))>
#<alt (+ (* eps (* (sin (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 3))))) (* x (+ (* -1/2 (* eps (* x (* (sin (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 3))))))) (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 3))))))))>
#<alt (+ (* eps (* (sin (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 3))))) (* x (+ (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 3))))) (* x (+ (* -1/2 (* eps (* (sin (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 3)))))) (* -1/6 (* eps (* x (* (cos (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 3))))))))))))>
#<alt (* eps (* (sin (* 1/2 (+ eps (* 2 x)))) (+ 1/2 (* -1/48 (pow eps 3)))))>
#<alt (* eps (* (sin (* 1/2 (+ eps (* 2 x)))) (+ 1/2 (* -1/48 (pow eps 3)))))>
#<alt (* eps (* (sin (* 1/2 (+ eps (* 2 x)))) (+ 1/2 (* -1/48 (pow eps 3)))))>
#<alt (* eps (* (sin (* 1/2 (+ eps (* 2 x)))) (+ 1/2 (* -1/48 (pow eps 3)))))>
#<alt (* eps (* (sin (* 1/2 (- eps (* -2 x)))) (+ 1/2 (* -1/48 (pow eps 3)))))>
#<alt (* eps (* (sin (* 1/2 (- eps (* -2 x)))) (+ 1/2 (* -1/48 (pow eps 3)))))>
#<alt (* eps (* (sin (* 1/2 (- eps (* -2 x)))) (+ 1/2 (* -1/48 (pow eps 3)))))>
#<alt (* eps (* (sin (* 1/2 (- eps (* -2 x)))) (+ 1/2 (* -1/48 (pow eps 3)))))>
#<alt (* 1/2 eps)>
#<alt (* eps (+ 1/2 (* -1/48 (pow eps 3))))>
#<alt (* eps (+ 1/2 (* -1/48 (pow eps 3))))>
#<alt (* eps (+ 1/2 (* -1/48 (pow eps 3))))>
#<alt (* -1/48 (pow eps 5))>
#<alt (* (pow eps 5) (- (* 1/2 (/ 1 (pow eps 4))) 1/48))>
#<alt (* (pow eps 5) (- (* 1/2 (/ 1 (pow eps 4))) 1/48))>
#<alt (* (pow eps 5) (- (* 1/2 (/ 1 (pow eps 4))) 1/48))>
#<alt (* 1/48 (pow eps 6))>
#<alt (* (pow eps 6) (+ 1/48 (* 1/2 (/ 1 (pow eps 5)))))>
#<alt (* (pow eps 6) (+ 1/48 (* 1/2 (/ 1 (pow eps 5)))))>
#<alt (* (pow eps 6) (+ 1/48 (* 1/2 (/ 1 (pow eps 5)))))>
#<alt (* -1 (* eps x))>
#<alt (* x (+ (* -1 eps) (* 1/6 (* eps (pow x 3)))))>
#<alt (* x (+ (* -1 eps) (* 1/6 (* eps (pow x 3)))))>
#<alt (* x (+ (* -1 eps) (* 1/6 (* eps (pow x 3)))))>
#<alt (* 1/6 (* eps (pow x 5)))>
#<alt (* (pow x 5) (+ (* -1 (/ eps (pow x 4))) (* 1/6 eps)))>
#<alt (* (pow x 5) (+ (* -1 (/ eps (pow x 4))) (* 1/6 eps)))>
#<alt (* (pow x 5) (+ (* -1 (/ eps (pow x 4))) (* 1/6 eps)))>
#<alt (* -1/6 (* eps (pow x 6)))>
#<alt (* (pow x 6) (+ (* -1 (/ eps (pow x 5))) (* -1/6 eps)))>
#<alt (* (pow x 6) (+ (* -1 (/ eps (pow x 5))) (* -1/6 eps)))>
#<alt (* (pow x 6) (+ (* -1 (/ eps (pow x 5))) (* -1/6 eps)))>
#<alt (* eps (* x (- (* 1/6 (pow x 3)) 1)))>
#<alt (* eps (* x (- (* 1/6 (pow x 3)) 1)))>
#<alt (* eps (* x (- (* 1/6 (pow x 3)) 1)))>
#<alt (* eps (* x (- (* 1/6 (pow x 3)) 1)))>
#<alt (* eps (* x (- (* 1/6 (pow x 3)) 1)))>
#<alt (* eps (* x (- (* 1/6 (pow x 3)) 1)))>
#<alt (* eps (* x (- (* 1/6 (pow x 3)) 1)))>
#<alt (* eps (* x (- (* 1/6 (pow x 3)) 1)))>
#<alt (* eps (* x (- (* 1/6 (pow x 4)) 1)))>
#<alt (* eps (* x (- (* 1/6 (pow x 4)) 1)))>
#<alt (* eps (* x (- (* 1/6 (pow x 4)) 1)))>
#<alt (* eps (* x (- (* 1/6 (pow x 4)) 1)))>
#<alt (* eps (- (* 1/6 (pow x 3)) 1))>
#<alt (* eps (- (* 1/6 (pow x 3)) 1))>
#<alt (* eps (- (* 1/6 (pow x 3)) 1))>
#<alt (* eps (- (* 1/6 (pow x 3)) 1))>
#<alt (* eps (- (* 1/6 (pow x 3)) 1))>
#<alt (* eps (- (* 1/6 (pow x 3)) 1))>
#<alt (* eps (- (* 1/6 (pow x 3)) 1))>
#<alt (* eps (- (* 1/6 (pow x 3)) 1))>
#<alt (* eps (- (* 1/6 (pow x 4)) 1))>
#<alt (* eps (- (* 1/6 (pow x 4)) 1))>
#<alt (* eps (- (* 1/6 (pow x 4)) 1))>
#<alt (* eps (- (* 1/6 (pow x 4)) 1))>
#<alt (* -1 eps)>
#<alt (+ (* -1 eps) (* 1/6 (* eps (pow x 3))))>
#<alt (+ (* -1 eps) (* 1/6 (* eps (pow x 3))))>
#<alt (+ (* -1 eps) (* 1/6 (* eps (pow x 3))))>
#<alt (* 1/6 (* eps (pow x 4)))>
#<alt (* (pow x 4) (+ (* -1 (/ eps (pow x 4))) (* 1/6 eps)))>
#<alt (* (pow x 4) (+ (* -1 (/ eps (pow x 4))) (* 1/6 eps)))>
#<alt (* (pow x 4) (+ (* -1 (/ eps (pow x 4))) (* 1/6 eps)))>
#<alt (* 1/6 (* eps (pow x 4)))>
#<alt (* (pow x 4) (+ (* -1 (/ eps (pow x 4))) (* 1/6 eps)))>
#<alt (* (pow x 4) (+ (* -1 (/ eps (pow x 4))) (* 1/6 eps)))>
#<alt (* (pow x 4) (+ (* -1 (/ eps (pow x 4))) (* 1/6 eps)))>
#<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 3))>
#<alt (* (pow x 3) (- 1/6 (/ 1 (pow x 3))))>
#<alt (* (pow x 3) (- 1/6 (/ 1 (pow x 3))))>
#<alt (* (pow x 3) (- 1/6 (/ 1 (pow x 3))))>
#<alt (* -1/6 (pow x 3))>
#<alt (* -1 (* (pow x 3) (+ 1/6 (/ 1 (pow x 3)))))>
#<alt (* -1 (* (pow x 3) (+ 1/6 (/ 1 (pow x 3)))))>
#<alt (* -1 (* (pow x 3) (+ 1/6 (/ 1 (pow x 3)))))>
#<alt (* 1/6 x)>
#<alt (* 1/6 x)>
#<alt (* 1/6 x)>
#<alt (* 1/6 x)>
#<alt x>
#<alt x>
#<alt x>
#<alt x>
#<alt (* -1 x)>
#<alt (* -1 x)>
#<alt (* -1 x)>
#<alt (* -1 x)>
#<alt (* -1/2 (pow eps 3))>
#<alt (+ (* -1 (* eps x)) (* -1/2 (pow eps 3)))>
#<alt (+ (* -1/2 (pow eps 3)) (* x (+ (* -1 eps) (* 1/4 (* (pow eps 3) x)))))>
#<alt (+ (* -1/2 (pow eps 3)) (* x (+ (* -1 eps) (* 1/4 (* (pow eps 3) x)))))>
#<alt (* 1/4 (* (pow eps 3) (pow x 3)))>
#<alt (* (pow x 3) (- (* 1/4 (pow eps 3)) (/ 1 (pow x 2))))>
#<alt (* (pow x 3) (- (+ (* -1/2 (/ (pow eps 3) (pow x 3))) (* 1/4 (pow eps 3))) (/ 1 (pow x 2))))>
#<alt (* (pow x 3) (- (+ (* -1/2 (/ (pow eps 3) (pow x 3))) (* 1/4 (pow eps 3))) (/ 1 (pow x 2))))>
#<alt (* 1/4 (* (pow eps 4) (pow x 2)))>
#<alt (* (pow x 2) (+ (* -1 (/ eps x)) (* 1/4 (pow eps 4))))>
#<alt (* (pow x 2) (+ (* -1 (/ (+ eps (* 1/2 (/ (pow eps 4) x))) x)) (* 1/4 (pow eps 4))))>
#<alt (* (pow x 2) (+ (* -1 (/ (+ eps (* 1/2 (/ (pow eps 4) x))) x)) (* 1/4 (pow eps 4))))>
#<alt (* -1 (* eps x))>
#<alt (* eps (+ (* -1 x) (* (pow eps 2) (- (* 1/4 (pow x 2)) 1/2))))>
#<alt (* eps (+ (* -1 x) (* (pow eps 2) (- (* 1/4 (pow x 2)) 1/2))))>
#<alt (* eps (+ (* -1 x) (* (pow eps 2) (- (* 1/4 (pow x 2)) 1/2))))>
#<alt (* (pow eps 3) (- (* 1/4 (pow x 2)) 1/2))>
#<alt (* (pow eps 3) (- (+ (* -1 (/ x (pow eps 2))) (* 1/4 (pow x 2))) 1/2))>
#<alt (* (pow eps 3) (- (+ (* -1 (/ x (pow eps 2))) (* 1/4 (pow x 2))) 1/2))>
#<alt (* (pow eps 3) (- (+ (* -1 (/ x (pow eps 2))) (* 1/4 (pow x 2))) 1/2))>
#<alt (* -1 (* (pow eps 3) (- (* 1/4 (pow x 2)) 1/2)))>
#<alt (* -1 (* (pow eps 3) (- (+ (* 1/4 (pow x 2)) (/ x (pow eps 2))) 1/2)))>
#<alt (* -1 (* (pow eps 3) (- (+ (* 1/4 (pow x 2)) (/ x (pow eps 2))) 1/2)))>
#<alt (* -1 (* (pow eps 3) (- (+ (* 1/4 (pow x 2)) (/ x (pow eps 2))) 1/2)))>
#<alt (* -1 eps)>
#<alt (- (* 1/4 (* (pow eps 3) x)) eps)>
#<alt (- (* 1/4 (* (pow eps 3) x)) eps)>
#<alt (- (* 1/4 (* (pow eps 3) x)) eps)>
#<alt (* 1/4 (* (pow eps 3) x))>
#<alt (* x (+ (* -1 (/ eps x)) (* 1/4 (pow eps 3))))>
#<alt (* x (+ (* -1 (/ eps x)) (* 1/4 (pow eps 3))))>
#<alt (* x (+ (* -1 (/ eps x)) (* 1/4 (pow eps 3))))>
#<alt (* 1/4 (* (pow eps 3) x))>
#<alt (* -1 (* x (+ (* -1/4 (pow eps 3)) (/ eps x))))>
#<alt (* -1 (* x (+ (* -1/4 (pow eps 3)) (/ eps x))))>
#<alt (* -1 (* x (+ (* -1/4 (pow eps 3)) (/ eps x))))>
#<alt (* -1 eps)>
#<alt (* eps (- (* 1/4 (* (pow eps 2) x)) 1))>
#<alt (* eps (- (* 1/4 (* (pow eps 2) x)) 1))>
#<alt (* eps (- (* 1/4 (* (pow eps 2) x)) 1))>
#<alt (* 1/4 (* (pow eps 3) x))>
#<alt (* (pow eps 3) (- (* 1/4 x) (/ 1 (pow eps 2))))>
#<alt (* (pow eps 3) (- (* 1/4 x) (/ 1 (pow eps 2))))>
#<alt (* (pow eps 3) (- (* 1/4 x) (/ 1 (pow eps 2))))>
#<alt (* -1/4 (* (pow eps 3) x))>
#<alt (* -1 (* (pow eps 3) (+ (* 1/4 x) (/ 1 (pow eps 2)))))>
#<alt (* -1 (* (pow eps 3) (+ (* 1/4 x) (/ 1 (pow eps 2)))))>
#<alt (* -1 (* (pow eps 3) (+ (* 1/4 x) (/ 1 (pow eps 2)))))>
#<alt (* 1/4 (* (pow eps 3) x))>
#<alt (* 1/4 (* (pow eps 3) x))>
#<alt (* 1/4 (* (pow eps 3) x))>
#<alt (* 1/4 (* (pow eps 3) x))>
#<alt (* 1/4 (* (pow eps 3) x))>
#<alt (* 1/4 (* (pow eps 3) x))>
#<alt (* 1/4 (* (pow eps 3) x))>
#<alt (* 1/4 (* (pow eps 3) x))>
#<alt (* 1/4 (* (pow eps 3) x))>
#<alt (* 1/4 (* (pow eps 3) x))>
#<alt (* 1/4 (* (pow eps 3) x))>
#<alt (* 1/4 (* (pow eps 3) x))>
#<alt (* 1/4 (* (pow eps 3) x))>
#<alt (* 1/4 (* (pow eps 3) x))>
#<alt (* 1/4 (* (pow eps 3) x))>
#<alt (* 1/4 (* (pow eps 3) x))>
#<alt (* 1/4 (* (pow eps 3) x))>
#<alt (* 1/4 (* (pow eps 3) x))>
#<alt (* 1/4 (* (pow eps 3) x))>
#<alt (* 1/4 (* (pow eps 3) x))>
#<alt (* -1/4 (* (pow eps 3) x))>
#<alt (* -1/4 (* (pow eps 3) x))>
#<alt (* -1/4 (* (pow eps 3) x))>
#<alt (* -1/4 (* (pow eps 3) x))>
#<alt (* 1/4 (pow eps 2))>
#<alt (* 1/4 (pow eps 2))>
#<alt (* 1/4 (pow eps 2))>
#<alt (* 1/4 (pow eps 2))>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (* -1 (* eps (sin x)))>
#<alt (* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))>
#<alt (* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* 1/8 (* eps (sin x)))))))>
#<alt (* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/48 (* eps (cos x))) (* 1/8 (sin x))))))))>
#<alt (* -1 (* eps (sin (* 1/2 (+ eps (* 2 x))))))>
#<alt (* -1 (* eps (sin (* 1/2 (+ eps (* 2 x))))))>
#<alt (* -1 (* eps (sin (* 1/2 (+ eps (* 2 x))))))>
#<alt (* -1 (* eps (sin (* 1/2 (+ eps (* 2 x))))))>
#<alt (* -1 (* eps (sin (* 1/2 (- (* 2 x) (* -1 eps))))))>
#<alt (* -1 (* eps (sin (* 1/2 (- (* 2 x) (* -1 eps))))))>
#<alt (* -1 (* eps (sin (* 1/2 (- (* 2 x) (* -1 eps))))))>
#<alt (* -1 (* eps (sin (* 1/2 (- (* 2 x) (* -1 eps))))))>
#<alt (* -1 (* eps (sin (* 1/2 eps))))>
#<alt (+ (* -1 (* eps (sin (* 1/2 eps)))) (* -1 (* eps (* x (cos (* 1/2 eps))))))>
#<alt (+ (* -1 (* eps (sin (* 1/2 eps)))) (* x (+ (* -1 (* eps (cos (* 1/2 eps)))) (* 1/2 (* eps (* x (sin (* 1/2 eps))))))))>
#<alt (+ (* -1 (* eps (sin (* 1/2 eps)))) (* x (+ (* -1 (* eps (cos (* 1/2 eps)))) (* x (+ (* 1/6 (* eps (* x (cos (* 1/2 eps))))) (* 1/2 (* eps (sin (* 1/2 eps)))))))))>
#<alt (* -1 (* eps (sin (* 1/2 (+ eps (* 2 x))))))>
#<alt (* -1 (* eps (sin (* 1/2 (+ eps (* 2 x))))))>
#<alt (* -1 (* eps (sin (* 1/2 (+ eps (* 2 x))))))>
#<alt (* -1 (* eps (sin (* 1/2 (+ eps (* 2 x))))))>
#<alt (* -1 (* eps (sin (* 1/2 (- eps (* -2 x))))))>
#<alt (* -1 (* eps (sin (* 1/2 (- eps (* -2 x))))))>
#<alt (* -1 (* eps (sin (* 1/2 (- eps (* -2 x))))))>
#<alt (* -1 (* 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 (+ (* -1/16 (* eps (sin x))) (* 1/4 (cos x))))))>
#<alt (* eps (+ (* 1/2 (sin x)) (* eps (+ (* 1/4 (cos x)) (* eps (+ (* -1/16 (sin x)) (* -1/96 (* eps (cos x)))))))))>
#<alt (* 1/2 (* eps (sin (* 1/2 (+ eps (* 2 x))))))>
#<alt (* 1/2 (* eps (sin (* 1/2 (+ eps (* 2 x))))))>
#<alt (* 1/2 (* eps (sin (* 1/2 (+ eps (* 2 x))))))>
#<alt (* 1/2 (* eps (sin (* 1/2 (+ eps (* 2 x))))))>
#<alt (* 1/2 (* eps (sin (* 1/2 (- (* 2 x) (* -1 eps))))))>
#<alt (* 1/2 (* eps (sin (* 1/2 (- (* 2 x) (* -1 eps))))))>
#<alt (* 1/2 (* eps (sin (* 1/2 (- (* 2 x) (* -1 eps))))))>
#<alt (* 1/2 (* eps (sin (* 1/2 (- (* 2 x) (* -1 eps))))))>
#<alt (* 1/2 (* eps (sin (* 1/2 eps))))>
#<alt (+ (* 1/2 (* eps (sin (* 1/2 eps)))) (* 1/2 (* eps (* x (cos (* 1/2 eps))))))>
#<alt (+ (* 1/2 (* eps (sin (* 1/2 eps)))) (* x (+ (* -1/4 (* eps (* x (sin (* 1/2 eps))))) (* 1/2 (* eps (cos (* 1/2 eps)))))))>
#<alt (+ (* 1/2 (* eps (sin (* 1/2 eps)))) (* x (+ (* 1/2 (* eps (cos (* 1/2 eps)))) (* x (+ (* -1/4 (* eps (sin (* 1/2 eps)))) (* -1/12 (* eps (* x (cos (* 1/2 eps))))))))))>
#<alt (* 1/2 (* eps (sin (* 1/2 (+ eps (* 2 x))))))>
#<alt (* 1/2 (* eps (sin (* 1/2 (+ eps (* 2 x))))))>
#<alt (* 1/2 (* eps (sin (* 1/2 (+ eps (* 2 x))))))>
#<alt (* 1/2 (* eps (sin (* 1/2 (+ eps (* 2 x))))))>
#<alt (* 1/2 (* eps (sin (* 1/2 (- eps (* -2 x))))))>
#<alt (* 1/2 (* eps (sin (* 1/2 (- eps (* -2 x))))))>
#<alt (* 1/2 (* eps (sin (* 1/2 (- eps (* -2 x))))))>
#<alt (* 1/2 (* eps (sin (* 1/2 (- eps (* -2 x))))))>
#<alt (* 1/2 eps)>
#<alt (* 1/2 eps)>
#<alt (* 1/2 eps)>
#<alt (* 1/2 eps)>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt (* -1 eps)>
#<alt (* -1 eps)>
#<alt (* -1 eps)>
#<alt (* -1 eps)>
#<alt 1/2>
#<alt (+ 1/2 (* -1/48 (pow eps 3)))>
#<alt (+ 1/2 (* -1/48 (pow eps 3)))>
#<alt (+ 1/2 (* -1/48 (pow eps 3)))>
#<alt (* -1/48 (pow eps 4))>
#<alt (* (pow eps 4) (- (* 1/2 (/ 1 (pow eps 4))) 1/48))>
#<alt (* (pow eps 4) (- (* 1/2 (/ 1 (pow eps 4))) 1/48))>
#<alt (* (pow eps 4) (- (* 1/2 (/ 1 (pow eps 4))) 1/48))>
#<alt (* -1/48 (pow eps 4))>
#<alt (* (pow eps 4) (- (* 1/2 (/ 1 (pow eps 4))) 1/48))>
#<alt (* (pow eps 4) (- (* 1/2 (/ 1 (pow eps 4))) 1/48))>
#<alt (* (pow eps 4) (- (* 1/2 (/ 1 (pow eps 4))) 1/48))>
#<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 (* 1/4 eps)>
#<alt (* 1/4 eps)>
#<alt (* 1/4 eps)>
#<alt (* 1/4 eps)>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt (* -1 eps)>
#<alt (* -1 eps)>
#<alt (* -1 eps)>
#<alt (* -1 eps)>
#<alt (sin (* 1/2 eps))>
#<alt (+ (sin (* 1/2 eps)) (* x (cos (* 1/2 eps))))>
#<alt (+ (sin (* 1/2 eps)) (* x (+ (cos (* 1/2 eps)) (* -1/2 (* x (sin (* 1/2 eps)))))))>
#<alt (+ (sin (* 1/2 eps)) (* x (+ (cos (* 1/2 eps)) (* x (+ (* -1/2 (sin (* 1/2 eps))) (* -1/6 (* x (cos (* 1/2 eps)))))))))>
#<alt (sin (* 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 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)))>

Calls

99 calls:

Time	Variable		Point	Expression
38.0ms	eps	@	-inf	(* x (* eps (+ (* x (* x 1/6)) -1)))
6.0ms	x	@	inf	(* (* eps (+ (* eps (* eps -1/48)) 1/2)) (sin (* (+ x (+ x eps)) 1/2)))
2.0ms	x	@	inf	(* (* (* eps (+ (* eps (* eps -1/48)) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) -2)
1.0ms	eps	@	inf	(* (* (* eps (+ (* eps (* eps -1/48)) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) -2)
1.0ms	x	@	-inf	(* x (* eps (+ (* x (* x 1/6)) -1)))

Compiler

Compiled 1 232 to 931 computations (24.4% saved)

rewrite595.0ms (3.5%)

Memory

-12.2MiB live, 393.1MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

8 018×	`lower-fma.f32`
8 012×	`lower-fma.f64`
5 316×	`lower-*.f32`
5 284×	`lower-*.f64`
4 114×	`lower-/.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	34	170
0	62	170
1	186	168
2	1212	167
0	8629	160

Stop Event

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

Counts

21 → 533

Calls

Call 1

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

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

simplify350.0ms (2%)

Memory

6.2MiB live, 686.0MiB allocated

Algorithm

1×	egg-herbie

Rules

12 600×	`lower-fma.f64`
12 600×	`lower-fma.f32`
7 648×	`lower-*.f64`
7 648×	`lower-*.f32`
3 572×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	420	4200
1	1309	3899
2	4088	3827
0	8083	3542

Stop Event

1×	iter limit
1×	node limit

Counts

396 → 372

Calls

Call 1

Inputs
(* -1 (* eps (sin x)))
(* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))
(* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* 1/8 (* eps (sin x)))))))
(* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/48 (* eps (cos x))) (* 1/8 (sin x))))))))
(* 1/24 (* (pow eps 5) (sin (* 1/2 (+ eps (* 2 x))))))
(* (pow eps 5) (+ (* -1 (/ (sin (* 1/2 (+ eps (* 2 x)))) (pow eps 4))) (* 1/24 (sin (* 1/2 (+ eps (* 2 x)))))))
(* (pow eps 5) (+ (* -1 (/ (sin (* 1/2 (+ eps (* 2 x)))) (pow eps 4))) (* 1/24 (sin (* 1/2 (+ eps (* 2 x)))))))
(* (pow eps 5) (+ (* -1 (/ (sin (* 1/2 (+ eps (* 2 x)))) (pow eps 4))) (* 1/24 (sin (* 1/2 (+ eps (* 2 x)))))))
(* 1/24 (* (pow eps 3) (sin (* 1/2 (- (* 2 x) (* -1 eps))))))
(* -1 (* (pow eps 3) (+ (* -1/24 (sin (* 1/2 (- (* 2 x) (* -1 eps))))) (/ (sin (* 1/2 (- (* 2 x) (* -1 eps)))) (pow eps 2)))))
(* -1 (* (pow eps 3) (+ (* -1/24 (sin (* 1/2 (- (* 2 x) (* -1 eps))))) (/ (sin (* 1/2 (- (* 2 x) (* -1 eps)))) (pow eps 2)))))
(* -1 (* (pow eps 3) (+ (* -1/24 (sin (* 1/2 (- (* 2 x) (* -1 eps))))) (/ (sin (* 1/2 (- (* 2 x) (* -1 eps)))) (pow eps 2)))))
(* -2 (* eps (* (sin (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 4))))))
(+ (* -2 (* eps (* x (* (cos (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 4))))))) (* -2 (* eps (* (sin (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 4)))))))
(+ (* -2 (* eps (* (sin (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 4)))))) (* x (+ (* -2 (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 4)))))) (* eps (* x (* (sin (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 4)))))))))
(+ (* -2 (* eps (* (sin (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 4)))))) (* x (+ (* -2 (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 4)))))) (* x (+ (* 1/3 (* eps (* x (* (cos (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 4))))))) (* eps (* (sin (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 4))))))))))
(* -2 (* eps (* (sin (* 1/2 (+ eps (* 2 x)))) (+ 1/2 (* -1/48 (pow eps 4))))))
(* -2 (* eps (* (sin (* 1/2 (+ eps (* 2 x)))) (+ 1/2 (* -1/48 (pow eps 4))))))
(* -2 (* eps (* (sin (* 1/2 (+ eps (* 2 x)))) (+ 1/2 (* -1/48 (pow eps 4))))))
(* -2 (* eps (* (sin (* 1/2 (+ eps (* 2 x)))) (+ 1/2 (* -1/48 (pow eps 4))))))
(* -2 (* eps (* (sin (* 1/2 (- eps (* -2 x)))) (+ 1/2 (* -1/48 (pow eps 4))))))
(* -2 (* eps (* (sin (* 1/2 (- eps (* -2 x)))) (+ 1/2 (* -1/48 (pow eps 4))))))
(* -2 (* eps (* (sin (* 1/2 (- eps (* -2 x)))) (+ 1/2 (* -1/48 (pow eps 4))))))
(* -2 (* eps (* (sin (* 1/2 (- eps (* -2 x)))) (+ 1/2 (* -1/48 (pow eps 4))))))
(* 1/2 eps)
(+ x (* 1/2 eps))
(+ x (* 1/2 eps))
(+ x (* 1/2 eps))
x
(* x (+ 1 (* 1/2 (/ eps x))))
(* x (+ 1 (* 1/2 (/ eps x))))
(* x (+ 1 (* 1/2 (/ eps x))))
x
(* -1 (* x (- (* -1/2 (/ eps x)) 1)))
(* -1 (* x (- (* -1/2 (/ eps x)) 1)))
(* -1 (* x (- (* -1/2 (/ eps x)) 1)))
x
(+ x (* 1/2 eps))
(+ x (* 1/2 eps))
(+ x (* 1/2 eps))
(* 1/2 eps)
(* eps (+ 1/2 (/ x eps)))
(* eps (+ 1/2 (/ x eps)))
(* eps (+ 1/2 (/ x eps)))
(* 1/2 eps)
(* -1 (* eps (- (* -1 (/ x eps)) 1/2)))
(* -1 (* eps (- (* -1 (/ x eps)) 1/2)))
(* -1 (* eps (- (* -1 (/ x eps)) 1/2)))
(* 1/2 (* eps (sin x)))
(* eps (+ (* 1/4 (* eps (cos x))) (* 1/2 (sin x))))
(* eps (+ (* 1/2 (sin x)) (* eps (+ (* -1/16 (* eps (sin x))) (* 1/4 (cos x))))))
(* eps (+ (* 1/2 (sin x)) (* eps (+ (* 1/4 (cos x)) (* eps (+ (* -1/16 (sin x)) (* eps (+ (* -1/48 (sin x)) (* -1/96 (cos x))))))))))
(* -1/48 (* (pow eps 4) (sin (* 1/2 (+ eps (* 2 x))))))
(* (pow eps 4) (+ (* -1/48 (sin (* 1/2 (+ eps (* 2 x))))) (* 1/2 (/ (sin (* 1/2 (+ eps (* 2 x)))) (pow eps 3)))))
(* (pow eps 4) (+ (* -1/48 (sin (* 1/2 (+ eps (* 2 x))))) (* 1/2 (/ (sin (* 1/2 (+ eps (* 2 x)))) (pow eps 3)))))
(* (pow eps 4) (+ (* -1/48 (sin (* 1/2 (+ eps (* 2 x))))) (* 1/2 (/ (sin (* 1/2 (+ eps (* 2 x)))) (pow eps 3)))))
(* -1/48 (* (pow eps 5) (sin (* 1/2 (- (* 2 x) (* -1 eps))))))
(* -1 (* (pow eps 5) (+ (* -1/2 (/ (sin (* 1/2 (- (* 2 x) (* -1 eps)))) (pow eps 4))) (* 1/48 (sin (* 1/2 (- (* 2 x) (* -1 eps))))))))
(* -1 (* (pow eps 5) (+ (* -1/2 (/ (sin (* 1/2 (- (* 2 x) (* -1 eps)))) (pow eps 4))) (* 1/48 (sin (* 1/2 (- (* 2 x) (* -1 eps))))))))
(* -1 (* (pow eps 5) (+ (* -1/2 (/ (sin (* 1/2 (- (* 2 x) (* -1 eps)))) (pow eps 4))) (* 1/48 (sin (* 1/2 (- (* 2 x) (* -1 eps))))))))
(* eps (* (sin (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 3)))))
(+ (* eps (* x (* (cos (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 3)))))) (* eps (* (sin (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 3))))))
(+ (* eps (* (sin (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 3))))) (* x (+ (* -1/2 (* eps (* x (* (sin (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 3))))))) (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 3))))))))
(+ (* eps (* (sin (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 3))))) (* x (+ (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 3))))) (* x (+ (* -1/2 (* eps (* (sin (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 3)))))) (* -1/6 (* eps (* x (* (cos (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 3))))))))))))
(* eps (* (sin (* 1/2 (+ eps (* 2 x)))) (+ 1/2 (* -1/48 (pow eps 3)))))
(* eps (* (sin (* 1/2 (+ eps (* 2 x)))) (+ 1/2 (* -1/48 (pow eps 3)))))
(* eps (* (sin (* 1/2 (+ eps (* 2 x)))) (+ 1/2 (* -1/48 (pow eps 3)))))
(* eps (* (sin (* 1/2 (+ eps (* 2 x)))) (+ 1/2 (* -1/48 (pow eps 3)))))
(* eps (* (sin (* 1/2 (- eps (* -2 x)))) (+ 1/2 (* -1/48 (pow eps 3)))))
(* eps (* (sin (* 1/2 (- eps (* -2 x)))) (+ 1/2 (* -1/48 (pow eps 3)))))
(* eps (* (sin (* 1/2 (- eps (* -2 x)))) (+ 1/2 (* -1/48 (pow eps 3)))))
(* eps (* (sin (* 1/2 (- eps (* -2 x)))) (+ 1/2 (* -1/48 (pow eps 3)))))
(* 1/2 eps)
(* eps (+ 1/2 (* -1/48 (pow eps 3))))
(* eps (+ 1/2 (* -1/48 (pow eps 3))))
(* eps (+ 1/2 (* -1/48 (pow eps 3))))
(* -1/48 (pow eps 5))
(* (pow eps 5) (- (* 1/2 (/ 1 (pow eps 4))) 1/48))
(* (pow eps 5) (- (* 1/2 (/ 1 (pow eps 4))) 1/48))
(* (pow eps 5) (- (* 1/2 (/ 1 (pow eps 4))) 1/48))
(* 1/48 (pow eps 6))
(* (pow eps 6) (+ 1/48 (* 1/2 (/ 1 (pow eps 5)))))
(* (pow eps 6) (+ 1/48 (* 1/2 (/ 1 (pow eps 5)))))
(* (pow eps 6) (+ 1/48 (* 1/2 (/ 1 (pow eps 5)))))
(* -1 (* eps x))
(* x (+ (* -1 eps) (* 1/6 (* eps (pow x 3)))))
(* x (+ (* -1 eps) (* 1/6 (* eps (pow x 3)))))
(* x (+ (* -1 eps) (* 1/6 (* eps (pow x 3)))))
(* 1/6 (* eps (pow x 5)))
(* (pow x 5) (+ (* -1 (/ eps (pow x 4))) (* 1/6 eps)))
(* (pow x 5) (+ (* -1 (/ eps (pow x 4))) (* 1/6 eps)))
(* (pow x 5) (+ (* -1 (/ eps (pow x 4))) (* 1/6 eps)))
(* -1/6 (* eps (pow x 6)))
(* (pow x 6) (+ (* -1 (/ eps (pow x 5))) (* -1/6 eps)))
(* (pow x 6) (+ (* -1 (/ eps (pow x 5))) (* -1/6 eps)))
(* (pow x 6) (+ (* -1 (/ eps (pow x 5))) (* -1/6 eps)))
(* eps (* x (- (* 1/6 (pow x 3)) 1)))
(* eps (* x (- (* 1/6 (pow x 3)) 1)))
(* eps (* x (- (* 1/6 (pow x 3)) 1)))
(* eps (* x (- (* 1/6 (pow x 3)) 1)))
(* eps (* x (- (* 1/6 (pow x 3)) 1)))
(* eps (* x (- (* 1/6 (pow x 3)) 1)))
(* eps (* x (- (* 1/6 (pow x 3)) 1)))
(* eps (* x (- (* 1/6 (pow x 3)) 1)))
(* eps (* x (- (* 1/6 (pow x 4)) 1)))
(* eps (* x (- (* 1/6 (pow x 4)) 1)))
(* eps (* x (- (* 1/6 (pow x 4)) 1)))
(* eps (* x (- (* 1/6 (pow x 4)) 1)))
(* eps (- (* 1/6 (pow x 3)) 1))
(* eps (- (* 1/6 (pow x 3)) 1))
(* eps (- (* 1/6 (pow x 3)) 1))
(* eps (- (* 1/6 (pow x 3)) 1))
(* eps (- (* 1/6 (pow x 3)) 1))
(* eps (- (* 1/6 (pow x 3)) 1))
(* eps (- (* 1/6 (pow x 3)) 1))
(* eps (- (* 1/6 (pow x 3)) 1))
(* eps (- (* 1/6 (pow x 4)) 1))
(* eps (- (* 1/6 (pow x 4)) 1))
(* eps (- (* 1/6 (pow x 4)) 1))
(* eps (- (* 1/6 (pow x 4)) 1))
(* -1 eps)
(+ (* -1 eps) (* 1/6 (* eps (pow x 3))))
(+ (* -1 eps) (* 1/6 (* eps (pow x 3))))
(+ (* -1 eps) (* 1/6 (* eps (pow x 3))))
(* 1/6 (* eps (pow x 4)))
(* (pow x 4) (+ (* -1 (/ eps (pow x 4))) (* 1/6 eps)))
(* (pow x 4) (+ (* -1 (/ eps (pow x 4))) (* 1/6 eps)))
(* (pow x 4) (+ (* -1 (/ eps (pow x 4))) (* 1/6 eps)))
(* 1/6 (* eps (pow x 4)))
(* (pow x 4) (+ (* -1 (/ eps (pow x 4))) (* 1/6 eps)))
(* (pow x 4) (+ (* -1 (/ eps (pow x 4))) (* 1/6 eps)))
(* (pow x 4) (+ (* -1 (/ eps (pow x 4))) (* 1/6 eps)))
-1
(- (* 1/6 (pow x 2)) 1)
(- (* 1/6 (pow x 2)) 1)
(- (* 1/6 (pow x 2)) 1)
(* 1/6 (pow x 3))
(* (pow x 3) (- 1/6 (/ 1 (pow x 3))))
(* (pow x 3) (- 1/6 (/ 1 (pow x 3))))
(* (pow x 3) (- 1/6 (/ 1 (pow x 3))))
(* -1/6 (pow x 3))
(* -1 (* (pow x 3) (+ 1/6 (/ 1 (pow x 3)))))
(* -1 (* (pow x 3) (+ 1/6 (/ 1 (pow x 3)))))
(* -1 (* (pow x 3) (+ 1/6 (/ 1 (pow x 3)))))
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
x
x
x
x
(* -1 x)
(* -1 x)
(* -1 x)
(* -1 x)
(* -1/2 (pow eps 3))
(+ (* -1 (* eps x)) (* -1/2 (pow eps 3)))
(+ (* -1/2 (pow eps 3)) (* x (+ (* -1 eps) (* 1/4 (* (pow eps 3) x)))))
(+ (* -1/2 (pow eps 3)) (* x (+ (* -1 eps) (* 1/4 (* (pow eps 3) x)))))
(* 1/4 (* (pow eps 3) (pow x 3)))
(* (pow x 3) (- (* 1/4 (pow eps 3)) (/ 1 (pow x 2))))
(* (pow x 3) (- (+ (* -1/2 (/ (pow eps 3) (pow x 3))) (* 1/4 (pow eps 3))) (/ 1 (pow x 2))))
(* (pow x 3) (- (+ (* -1/2 (/ (pow eps 3) (pow x 3))) (* 1/4 (pow eps 3))) (/ 1 (pow x 2))))
(* 1/4 (* (pow eps 4) (pow x 2)))
(* (pow x 2) (+ (* -1 (/ eps x)) (* 1/4 (pow eps 4))))
(* (pow x 2) (+ (* -1 (/ (+ eps (* 1/2 (/ (pow eps 4) x))) x)) (* 1/4 (pow eps 4))))
(* (pow x 2) (+ (* -1 (/ (+ eps (* 1/2 (/ (pow eps 4) x))) x)) (* 1/4 (pow eps 4))))
(* -1 (* eps x))
(* eps (+ (* -1 x) (* (pow eps 2) (- (* 1/4 (pow x 2)) 1/2))))
(* eps (+ (* -1 x) (* (pow eps 2) (- (* 1/4 (pow x 2)) 1/2))))
(* eps (+ (* -1 x) (* (pow eps 2) (- (* 1/4 (pow x 2)) 1/2))))
(* (pow eps 3) (- (* 1/4 (pow x 2)) 1/2))
(* (pow eps 3) (- (+ (* -1 (/ x (pow eps 2))) (* 1/4 (pow x 2))) 1/2))
(* (pow eps 3) (- (+ (* -1 (/ x (pow eps 2))) (* 1/4 (pow x 2))) 1/2))
(* (pow eps 3) (- (+ (* -1 (/ x (pow eps 2))) (* 1/4 (pow x 2))) 1/2))
(* -1 (* (pow eps 3) (- (* 1/4 (pow x 2)) 1/2)))
(* -1 (* (pow eps 3) (- (+ (* 1/4 (pow x 2)) (/ x (pow eps 2))) 1/2)))
(* -1 (* (pow eps 3) (- (+ (* 1/4 (pow x 2)) (/ x (pow eps 2))) 1/2)))
(* -1 (* (pow eps 3) (- (+ (* 1/4 (pow x 2)) (/ x (pow eps 2))) 1/2)))
(* -1 eps)
(- (* 1/4 (* (pow eps 3) x)) eps)
(- (* 1/4 (* (pow eps 3) x)) eps)
(- (* 1/4 (* (pow eps 3) x)) eps)
(* 1/4 (* (pow eps 3) x))
(* x (+ (* -1 (/ eps x)) (* 1/4 (pow eps 3))))
(* x (+ (* -1 (/ eps x)) (* 1/4 (pow eps 3))))
(* x (+ (* -1 (/ eps x)) (* 1/4 (pow eps 3))))
(* 1/4 (* (pow eps 3) x))
(* -1 (* x (+ (* -1/4 (pow eps 3)) (/ eps x))))
(* -1 (* x (+ (* -1/4 (pow eps 3)) (/ eps x))))
(* -1 (* x (+ (* -1/4 (pow eps 3)) (/ eps x))))
(* -1 eps)
(* eps (- (* 1/4 (* (pow eps 2) x)) 1))
(* eps (- (* 1/4 (* (pow eps 2) x)) 1))
(* eps (- (* 1/4 (* (pow eps 2) x)) 1))
(* 1/4 (* (pow eps 3) x))
(* (pow eps 3) (- (* 1/4 x) (/ 1 (pow eps 2))))
(* (pow eps 3) (- (* 1/4 x) (/ 1 (pow eps 2))))
(* (pow eps 3) (- (* 1/4 x) (/ 1 (pow eps 2))))
(* -1/4 (* (pow eps 3) x))
(* -1 (* (pow eps 3) (+ (* 1/4 x) (/ 1 (pow eps 2)))))
(* -1 (* (pow eps 3) (+ (* 1/4 x) (/ 1 (pow eps 2)))))
(* -1 (* (pow eps 3) (+ (* 1/4 x) (/ 1 (pow eps 2)))))
(* 1/4 (* (pow eps 3) x))
(* 1/4 (* (pow eps 3) x))
(* 1/4 (* (pow eps 3) x))
(* 1/4 (* (pow eps 3) x))
(* 1/4 (* (pow eps 3) x))
(* 1/4 (* (pow eps 3) x))
(* 1/4 (* (pow eps 3) x))
(* 1/4 (* (pow eps 3) x))
(* 1/4 (* (pow eps 3) x))
(* 1/4 (* (pow eps 3) x))
(* 1/4 (* (pow eps 3) x))
(* 1/4 (* (pow eps 3) x))
(* 1/4 (* (pow eps 3) x))
(* 1/4 (* (pow eps 3) x))
(* 1/4 (* (pow eps 3) x))
(* 1/4 (* (pow eps 3) x))
(* 1/4 (* (pow eps 3) x))
(* 1/4 (* (pow eps 3) x))
(* 1/4 (* (pow eps 3) x))
(* 1/4 (* (pow eps 3) x))
(* -1/4 (* (pow eps 3) x))
(* -1/4 (* (pow eps 3) x))
(* -1/4 (* (pow eps 3) x))
(* -1/4 (* (pow eps 3) x))
(* 1/4 (pow eps 2))
(* 1/4 (pow eps 2))
(* 1/4 (pow eps 2))
(* 1/4 (pow eps 2))
(pow eps 2)
(pow eps 2)
(pow eps 2)
(pow eps 2)
(pow eps 2)
(pow eps 2)
(pow eps 2)
(pow eps 2)
(* -1 (* eps (sin x)))
(* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))
(* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* 1/8 (* eps (sin x)))))))
(* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/48 (* eps (cos x))) (* 1/8 (sin x))))))))
(* -1 (* eps (sin (* 1/2 (+ eps (* 2 x))))))
(* -1 (* eps (sin (* 1/2 (+ eps (* 2 x))))))
(* -1 (* eps (sin (* 1/2 (+ eps (* 2 x))))))
(* -1 (* eps (sin (* 1/2 (+ eps (* 2 x))))))
(* -1 (* eps (sin (* 1/2 (- (* 2 x) (* -1 eps))))))
(* -1 (* eps (sin (* 1/2 (- (* 2 x) (* -1 eps))))))
(* -1 (* eps (sin (* 1/2 (- (* 2 x) (* -1 eps))))))
(* -1 (* eps (sin (* 1/2 (- (* 2 x) (* -1 eps))))))
(* -1 (* eps (sin (* 1/2 eps))))
(+ (* -1 (* eps (sin (* 1/2 eps)))) (* -1 (* eps (* x (cos (* 1/2 eps))))))
(+ (* -1 (* eps (sin (* 1/2 eps)))) (* x (+ (* -1 (* eps (cos (* 1/2 eps)))) (* 1/2 (* eps (* x (sin (* 1/2 eps))))))))
(+ (* -1 (* eps (sin (* 1/2 eps)))) (* x (+ (* -1 (* eps (cos (* 1/2 eps)))) (* x (+ (* 1/6 (* eps (* x (cos (* 1/2 eps))))) (* 1/2 (* eps (sin (* 1/2 eps)))))))))
(* -1 (* eps (sin (* 1/2 (+ eps (* 2 x))))))
(* -1 (* eps (sin (* 1/2 (+ eps (* 2 x))))))
(* -1 (* eps (sin (* 1/2 (+ eps (* 2 x))))))
(* -1 (* eps (sin (* 1/2 (+ eps (* 2 x))))))
(* -1 (* eps (sin (* 1/2 (- eps (* -2 x))))))
(* -1 (* eps (sin (* 1/2 (- eps (* -2 x))))))
(* -1 (* eps (sin (* 1/2 (- eps (* -2 x))))))
(* -1 (* 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 (+ (* -1/16 (* eps (sin x))) (* 1/4 (cos x))))))
(* eps (+ (* 1/2 (sin x)) (* eps (+ (* 1/4 (cos x)) (* eps (+ (* -1/16 (sin x)) (* -1/96 (* eps (cos x)))))))))
(* 1/2 (* eps (sin (* 1/2 (+ eps (* 2 x))))))
(* 1/2 (* eps (sin (* 1/2 (+ eps (* 2 x))))))
(* 1/2 (* eps (sin (* 1/2 (+ eps (* 2 x))))))
(* 1/2 (* eps (sin (* 1/2 (+ eps (* 2 x))))))
(* 1/2 (* eps (sin (* 1/2 (- (* 2 x) (* -1 eps))))))
(* 1/2 (* eps (sin (* 1/2 (- (* 2 x) (* -1 eps))))))
(* 1/2 (* eps (sin (* 1/2 (- (* 2 x) (* -1 eps))))))
(* 1/2 (* eps (sin (* 1/2 (- (* 2 x) (* -1 eps))))))
(* 1/2 (* eps (sin (* 1/2 eps))))
(+ (* 1/2 (* eps (sin (* 1/2 eps)))) (* 1/2 (* eps (* x (cos (* 1/2 eps))))))
(+ (* 1/2 (* eps (sin (* 1/2 eps)))) (* x (+ (* -1/4 (* eps (* x (sin (* 1/2 eps))))) (* 1/2 (* eps (cos (* 1/2 eps)))))))
(+ (* 1/2 (* eps (sin (* 1/2 eps)))) (* x (+ (* 1/2 (* eps (cos (* 1/2 eps)))) (* x (+ (* -1/4 (* eps (sin (* 1/2 eps)))) (* -1/12 (* eps (* x (cos (* 1/2 eps))))))))))
(* 1/2 (* eps (sin (* 1/2 (+ eps (* 2 x))))))
(* 1/2 (* eps (sin (* 1/2 (+ eps (* 2 x))))))
(* 1/2 (* eps (sin (* 1/2 (+ eps (* 2 x))))))
(* 1/2 (* eps (sin (* 1/2 (+ eps (* 2 x))))))
(* 1/2 (* eps (sin (* 1/2 (- eps (* -2 x))))))
(* 1/2 (* eps (sin (* 1/2 (- eps (* -2 x))))))
(* 1/2 (* eps (sin (* 1/2 (- eps (* -2 x))))))
(* 1/2 (* eps (sin (* 1/2 (- eps (* -2 x))))))
(* 1/2 eps)
(* 1/2 eps)
(* 1/2 eps)
(* 1/2 eps)
eps
eps
eps
eps
(* -1 eps)
(* -1 eps)
(* -1 eps)
(* -1 eps)
1/2
(+ 1/2 (* -1/48 (pow eps 3)))
(+ 1/2 (* -1/48 (pow eps 3)))
(+ 1/2 (* -1/48 (pow eps 3)))
(* -1/48 (pow eps 4))
(* (pow eps 4) (- (* 1/2 (/ 1 (pow eps 4))) 1/48))
(* (pow eps 4) (- (* 1/2 (/ 1 (pow eps 4))) 1/48))
(* (pow eps 4) (- (* 1/2 (/ 1 (pow eps 4))) 1/48))
(* -1/48 (pow eps 4))
(* (pow eps 4) (- (* 1/2 (/ 1 (pow eps 4))) 1/48))
(* (pow eps 4) (- (* 1/2 (/ 1 (pow eps 4))) 1/48))
(* (pow eps 4) (- (* 1/2 (/ 1 (pow eps 4))) 1/48))
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)))
(* 1/4 eps)
(* 1/4 eps)
(* 1/4 eps)
(* 1/4 eps)
eps
eps
eps
eps
(* -1 eps)
(* -1 eps)
(* -1 eps)
(* -1 eps)
(sin (* 1/2 eps))
(+ (sin (* 1/2 eps)) (* x (cos (* 1/2 eps))))
(+ (sin (* 1/2 eps)) (* x (+ (cos (* 1/2 eps)) (* -1/2 (* x (sin (* 1/2 eps)))))))
(+ (sin (* 1/2 eps)) (* x (+ (cos (* 1/2 eps)) (* x (+ (* -1/2 (sin (* 1/2 eps))) (* -1/6 (* x (cos (* 1/2 eps)))))))))
(sin (* 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))))
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)))

Outputs
(* -1 (* eps (sin x)))
(neg.f64 (*.f64 eps (sin.f64 x)))
(* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))
(.f64 eps (-.f64 (.f64 #s(literal -1/2 binary64) (*.f64 eps (cos.f64 x))) (sin.f64 x)))
(* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* 1/8 (* eps (sin x)))))))
(.f64 eps (-.f64 (.f64 eps (fma.f64 eps (.f64 (sin.f64 x) #s(literal 1/8 binary64)) (.f64 #s(literal -1/2 binary64) (cos.f64 x)))) (sin.f64 x)))
(* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/48 (* eps (cos x))) (* 1/8 (sin 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 1/8 binary64))) (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (neg.f64 (sin.f64 x))))
(* 1/24 (* (pow eps 5) (sin (* 1/2 (+ eps (* 2 x))))))
(.f64 (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (.f64 #s(literal 1/24 binary64) (pow.f64 eps #s(literal 5 binary64))))
(* (pow eps 5) (+ (* -1 (/ (sin (* 1/2 (+ eps (* 2 x)))) (pow eps 4))) (* 1/24 (sin (* 1/2 (+ eps (* 2 x)))))))
(.f64 (pow.f64 eps #s(literal 5 binary64)) (-.f64 (.f64 #s(literal 1/24 binary64) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x))) (/.f64 (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (.f64 (.f64 eps (*.f64 eps eps)) eps))))
(* (pow eps 5) (+ (* -1 (/ (sin (* 1/2 (+ eps (* 2 x)))) (pow eps 4))) (* 1/24 (sin (* 1/2 (+ eps (* 2 x)))))))
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(sin.f64 x)
(+ (sin x) (* 1/2 (* eps (cos x))))
(fma.f64 (*.f64 eps (cos.f64 x)) #s(literal 1/2 binary64) (sin.f64 x))
(+ (sin x) (* eps (+ (* -1/8 (* eps (sin x))) (* 1/2 (cos x)))))
(fma.f64 eps (fma.f64 eps (.f64 (sin.f64 x) #s(literal -1/8 binary64)) (.f64 (cos.f64 x) #s(literal 1/2 binary64))) (sin.f64 x))
(+ (sin x) (* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/8 (sin x)) (* -1/48 (* eps (cos x))))))))
(fma.f64 eps (fma.f64 eps (fma.f64 (.f64 eps (cos.f64 x)) #s(literal -1/48 binary64) (.f64 (sin.f64 x) #s(literal -1/8 binary64))) (*.f64 (cos.f64 x) #s(literal 1/2 binary64))) (sin.f64 x))
(sin (* 1/2 (+ eps (* 2 x))))
(sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x))
(sin (* 1/2 (+ eps (* 2 x))))
(sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x))
(sin (* 1/2 (+ eps (* 2 x))))
(sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x))
(sin (* 1/2 (+ eps (* 2 x))))
(sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x))
(sin (* 1/2 (- (* 2 x) (* -1 eps))))
(sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x))
(sin (* 1/2 (- (* 2 x) (* -1 eps))))
(sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x))
(sin (* 1/2 (- (* 2 x) (* -1 eps))))
(sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x))
(sin (* 1/2 (- (* 2 x) (* -1 eps))))
(sin.f64 (fma.f64 eps #s(literal 1/2 binary64) 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 #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 #s(literal 2 binary64) (/.f64 x eps)) eps)
(* eps (+ 1 (* 2 (/ x eps))))
(fma.f64 eps (*.f64 #s(literal 2 binary64) (/.f64 x eps)) eps)
(* eps (+ 1 (* 2 (/ x eps))))
(fma.f64 eps (*.f64 #s(literal 2 binary64) (/.f64 x eps)) eps)
eps
(* -1 (* eps (- (* -2 (/ x eps)) 1)))
(fma.f64 eps (*.f64 #s(literal 2 binary64) (/.f64 x eps)) eps)
(* -1 (* eps (- (* -2 (/ x eps)) 1)))
(fma.f64 eps (*.f64 #s(literal 2 binary64) (/.f64 x eps)) eps)
(* -1 (* eps (- (* -2 (/ x eps)) 1)))
(fma.f64 eps (*.f64 #s(literal 2 binary64) (/.f64 x eps)) eps)

eval135.0ms (0.8%)

Memory: -5.4MiB live, 303.7MiB allocated
Compiler: Compiled 32 614 to 3 126 computations (90.4% saved)

prune124.0ms (0.7%)

Memory

5.3MiB live, 295.3MiB allocated

Pruning

23 alts after pruning (19 fresh and 4 done)

	Pruned	Kept	Total
New	1 136	10	1 146
Fresh	4	9	13
Picked	5	0	5
Done	0	4	4
Total	1 145	23	1 168

Accuracy

100.0%

Counts

1 168 → 23

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))))
	98.1%	(fma.f64 x (-.f64 (.f64 x (.f64 eps (neg.f64 eps))) eps) (.f64 #s(literal -1/2 binary64) (.f64 eps eps)))
▶	98.1%	(fma.f64 x (neg.f64 eps) (.f64 #s(literal -1/2 binary64) (.f64 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))
	78.1%	(.f64 (fma.f64 (fma.f64 (.f64 x x) (fma.f64 x (.f64 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))
▶	99.4%	(.f64 (.f64 (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 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 (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64))) (fma.f64 eps (fma.f64 eps (fma.f64 (.f64 eps (cos.f64 x)) #s(literal -1/48 binary64) (.f64 (sin.f64 x) #s(literal -1/8 binary64))) (*.f64 (cos.f64 x) #s(literal 1/2 binary64))) (sin.f64 x))) #s(literal -2 binary64))
▶	99.4%	(.f64 (.f64 (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64))) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x))) #s(literal -2 binary64))
	78.0%	(.f64 (.f64 x (fma.f64 x (*.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64))) eps)
	99.1%	(*.f64 (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (neg.f64 eps))
✓	78.4%	(*.f64 (sin.f64 x) (neg.f64 eps))
	78.0%	(.f64 x (fma.f64 (.f64 x (*.f64 x #s(literal 1/6 binary64))) eps (neg.f64 eps)))
	78.1%	(.f64 x (fma.f64 x (.f64 x (.f64 eps (fma.f64 (.f64 x x) #s(literal -1/120 binary64) #s(literal 1/6 binary64)))) (neg.f64 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))))
	97.9%	(.f64 eps (-.f64 (.f64 eps #s(literal -1/2 binary64)) x))
	52.9%	(.f64 eps (.f64 eps #s(literal -1/2 binary64)))
▶	51.6%	#s(literal 0 binary64)

Compiler

Compiled 678 to 418 computations (38.3% saved)

simplify419.0ms (2.4%)

Memory

-5.0MiB live, 745.4MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 16 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(fma.f64 eps (*.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64))
✓	cost-diff	0	(.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))
✓	cost-diff	0	(.f64 (.f64 eps (fma.f64 eps (*.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64))) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))
✓	cost-diff	192	(.f64 (.f64 (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64))) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x))) #s(literal -2 binary64))
✓	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	0	(*.f64 eps eps)
✓	cost-diff	0	(.f64 #s(literal -1/2 binary64) (.f64 eps eps))
✓	cost-diff	0	(neg.f64 eps)
✓	cost-diff	320	(fma.f64 x (neg.f64 eps) (.f64 #s(literal -1/2 binary64) (.f64 eps eps)))
✓	cost-diff	0	(.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))
✓	cost-diff	0	(.f64 (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64))) (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	192	(.f64 (.f64 (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 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	512	(*.f64 (+.f64 x x) #s(literal 1/2 binary64))

Rules

20 822×	`lower-fma.f32`
20 808×	`lower-fma.f64`
6 210×	`lower-*.f32`
6 182×	`lower-*.f64`
3 046×	`lower-+.f32`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	38	291
0	72	307
1	144	279
2	383	249
3	1117	245
4	3945	243
5	5913	243
0	8286	243

Stop Event

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

Calls

Call 1

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

localize127.0ms (0.7%)

Memory

-9.4MiB live, 192.3MiB allocated

Localize:

Found 16 expressions of interest:

New	Metric	Score	Program
✓	accuracy	4.5%	(sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x))
✓	accuracy	4.1%	(.f64 (.f64 eps (fma.f64 eps (*.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64))) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))
✓	accuracy	3.1%	(fma.f64 eps (*.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64))
✓	accuracy	3.1%	(.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))
✓	accuracy	5.6%	(*.f64 x #s(literal 1/6 binary64))
✓	accuracy	4.6%	(fma.f64 x (fma.f64 eps #s(literal 1/4 binary64) (*.f64 x #s(literal 1/6 binary64))) #s(literal -1 binary64))
✓	accuracy	4.5%	(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	4.1%	(.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	52.9%	(fma.f64 x (neg.f64 eps) (.f64 #s(literal -1/2 binary64) (.f64 eps eps)))
✓	accuracy	6.7%	(neg.f64 eps)
✓	accuracy	5.7%	(.f64 #s(literal -1/2 binary64) (.f64 eps eps))
✓	accuracy	5.7%	(*.f64 eps eps)
✓	accuracy	4.2%	(.f64 (.f64 (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 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	4.2%	(.f64 (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 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))))))
✓	accuracy	3.1%	(fma.f64 eps (*.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64))
✓	accuracy	3.1%	(.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))

Samples

76.0ms	251×	0	valid
2.0ms	2×	5	exit
2.0ms	3×	1	valid

Compiler

Compiled 611 to 84 computations (86.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 57.0ms

ival-mult: 27.0ms (47.6% of total)

ival-add: 11.0ms (19.4% of total)

const: 7.0ms (12.3% of total)

ival-sin: 5.0ms (8.8% of total)

ival-cos: 3.0ms (5.3% of total)

adjust: 1.0ms (1.8% of total)

exact: 1.0ms (1.8% of total)

ival-neg: 1.0ms (1.8% of total)

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

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

series65.0ms (0.4%)

Memory

-5.7MiB live, 31.9MiB allocated

Counts

17 → 324

Calls

Call 1

Inputs
#<alt (*.f64 (+.f64 x x) #s(literal 1/2 binary64))>
#<alt (.f64 (.f64 (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64))) (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 (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 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 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))>
#<alt (fma.f64 x (neg.f64 eps) (.f64 #s(literal -1/2 binary64) (.f64 eps eps)))>
#<alt (neg.f64 eps)>
#<alt (.f64 #s(literal -1/2 binary64) (.f64 eps eps))>
#<alt (*.f64 eps eps)>
#<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 (.f64 (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64))) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x))) #s(literal -2 binary64))>
#<alt (.f64 (.f64 eps (fma.f64 eps (*.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64))) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))>
#<alt (fma.f64 eps (*.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64))>
#<alt (*.f64 x #s(literal 1/6 binary64))>
#<alt (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x))>

Outputs
#<alt x>
#<alt x>
#<alt x>
#<alt x>
#<alt x>
#<alt x>
#<alt x>
#<alt x>
#<alt (* -1 x)>
#<alt (* -1 x)>
#<alt (* -1 x)>
#<alt (* -1 x)>
#<alt (* -1 (* eps (sin x)))>
#<alt (* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))>
#<alt (* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* 1/8 (* eps (sin x)))))))>
#<alt (* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/48 (* eps (cos x))) (* 1/8 (sin x))))))))>
#<alt (* 1/24 (* (pow eps 15) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))>
#<alt (* 1/24 (* (pow eps 15) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))>
#<alt (* 1/24 (* (pow eps 15) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))>
#<alt (* (pow eps 15) (+ (* -1 (/ (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))) (pow eps 14))) (* 1/24 (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))))>
#<alt (* 1/24 (* (pow eps 3) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))>
#<alt (* -1 (* (pow eps 3) (+ (* -1/24 (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))) (+ (/ (* (cos x) (sin (* 1/2 eps))) (pow eps 2)) (/ (* (cos (* 1/2 eps)) (sin x)) (pow eps 2))))))>
#<alt (* -1 (* (pow eps 3) (+ (* -1/24 (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))) (+ (/ (* (cos x) (sin (* 1/2 eps))) (pow eps 2)) (/ (* (cos (* 1/2 eps)) (sin x)) (pow eps 2))))))>
#<alt (* -1 (* (pow eps 3) (+ (* -1/24 (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))) (+ (/ (* (cos x) (sin (* 1/2 eps))) (pow eps 2)) (/ (* (cos (* 1/2 eps)) (sin x)) (pow eps 2))))))>
#<alt (* -2 (* eps (* (sin (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 5))))))>
#<alt (+ (* -2 (* eps (* x (* (cos (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 5))))))) (* -2 (* eps (* (sin (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 5)))))))>
#<alt (+ (* -2 (* eps (* (sin (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 5)))))) (* x (+ (* -2 (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 5)))))) (* eps (* x (* (sin (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 5)))))))))>
#<alt (+ (* -2 (* eps (* (sin (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 5)))))) (* x (+ (* -2 (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 5)))))) (* x (+ (* 1/3 (* eps (* x (* (cos (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 5))))))) (* eps (* (sin (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 5))))))))))>
#<alt (* -2 (* eps (* (+ 1/2 (* -1/48 (pow eps 5))) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))))>
#<alt (* -2 (* eps (* (+ 1/2 (* -1/48 (pow eps 5))) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))))>
#<alt (* -2 (* eps (* (+ 1/2 (* -1/48 (pow eps 5))) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))))>
#<alt (* -2 (* eps (* (+ 1/2 (* -1/48 (pow eps 5))) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))))>
#<alt (* -2 (* eps (* (+ 1/2 (* -1/48 (pow eps 5))) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))))>
#<alt (* -2 (* eps (* (+ 1/2 (* -1/48 (pow eps 5))) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))))>
#<alt (* -2 (* eps (* (+ 1/2 (* -1/48 (pow eps 5))) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))))>
#<alt (* -2 (* eps (* (+ 1/2 (* -1/48 (pow eps 5))) (+ (* (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 (+ (* -1/16 (* eps (sin x))) (* 1/4 (cos x))))))>
#<alt (* eps (+ (* 1/2 (sin x)) (* eps (+ (* 1/4 (cos x)) (* eps (+ (* -1/16 (sin x)) (* -1/96 (* eps (cos x)))))))))>
#<alt (* -1/48 (* (pow eps 14) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))>
#<alt (* -1/48 (* (pow eps 14) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))>
#<alt (* -1/48 (* (pow eps 14) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))>
#<alt (* (pow eps 14) (+ (* -1/48 (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))) (* 1/2 (/ (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))) (pow eps 13)))))>
#<alt (* 1/48 (* (pow eps 16) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))>
#<alt (* 1/48 (* (pow eps 16) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))>
#<alt (* 1/48 (* (pow eps 16) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))>
#<alt (* (pow eps 16) (+ (* 1/48 (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))) (* 1/2 (/ (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))) (pow eps 15)))))>
#<alt (* eps (* (sin (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 4)))))>
#<alt (+ (* eps (* x (* (cos (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 4)))))) (* eps (* (sin (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 4))))))>
#<alt (+ (* eps (* (sin (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 4))))) (* x (+ (* -1/2 (* eps (* x (* (sin (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 4))))))) (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 4))))))))>
#<alt (+ (* eps (* (sin (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 4))))) (* x (+ (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 4))))) (* x (+ (* -1/2 (* eps (* (sin (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 4)))))) (* -1/6 (* eps (* x (* (cos (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 4))))))))))))>
#<alt (* eps (* (+ 1/2 (* -1/48 (pow eps 4))) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))>
#<alt (* eps (* (+ 1/2 (* -1/48 (pow eps 4))) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))>
#<alt (* eps (* (+ 1/2 (* -1/48 (pow eps 4))) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))>
#<alt (* eps (* (+ 1/2 (* -1/48 (pow eps 4))) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))>
#<alt (* eps (* (+ 1/2 (* -1/48 (pow eps 4))) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))>
#<alt (* eps (* (+ 1/2 (* -1/48 (pow eps 4))) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))>
#<alt (* eps (* (+ 1/2 (* -1/48 (pow eps 4))) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))>
#<alt (* eps (* (+ 1/2 (* -1/48 (pow eps 4))) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))>
#<alt (* 1/2 eps)>
#<alt (* eps (+ 1/2 (* -1/48 (pow eps 3))))>
#<alt (* eps (+ 1/2 (* -1/48 (pow eps 3))))>
#<alt (* eps (+ 1/2 (* -1/48 (pow eps 3))))>
#<alt (* -1/48 (pow eps 5))>
#<alt (* (pow eps 5) (- (* 1/2 (/ 1 (pow eps 4))) 1/48))>
#<alt (* (pow eps 5) (- (* 1/2 (/ 1 (pow eps 4))) 1/48))>
#<alt (* (pow eps 5) (- (* 1/2 (/ 1 (pow eps 4))) 1/48))>
#<alt (* 1/48 (pow eps 6))>
#<alt (* (pow eps 6) (+ 1/48 (* 1/2 (/ 1 (pow eps 5)))))>
#<alt (* (pow eps 6) (+ 1/48 (* 1/2 (/ 1 (pow eps 5)))))>
#<alt (* (pow eps 6) (+ 1/48 (* 1/2 (/ 1 (pow eps 5)))))>
#<alt (* -1/2 (pow eps 6))>
#<alt (+ (* -1 (* eps x)) (* -1/2 (pow eps 6)))>
#<alt (+ (* -1 (* eps x)) (* -1/2 (pow eps 6)))>
#<alt (+ (* -1 (* eps x)) (* -1/2 (pow eps 6)))>
#<alt (* -1 x)>
#<alt (* x (- (* -1/2 (/ (pow eps 6) x)) 1))>
#<alt (* x (- (* -1/2 (/ (pow eps 6) x)) 1))>
#<alt (* x (- (* -1/2 (/ (pow eps 6) x)) 1))>
#<alt (* -1 x)>
#<alt (* -1 (* x (+ 1 (* 1/2 (/ (pow eps 3) x)))))>
#<alt (* -1 (* x (+ 1 (* 1/2 (/ (pow eps 3) x)))))>
#<alt (* -1 (* x (+ 1 (* 1/2 (/ (pow eps 3) x)))))>
#<alt (* -1 (* eps x))>
#<alt (* eps (+ (* -1 x) (* -1/2 (pow eps 5))))>
#<alt (* eps (+ (* -1 x) (* -1/2 (pow eps 5))))>
#<alt (* eps (+ (* -1 x) (* -1/2 (pow eps 5))))>
#<alt (* -1/2 (pow eps 7))>
#<alt (* (pow eps 7) (- (* -1 (/ x (pow eps 6))) 1/2))>
#<alt (* (pow eps 7) (- (* -1 (/ x (pow eps 6))) 1/2))>
#<alt (* (pow eps 7) (- (* -1 (/ x (pow eps 6))) 1/2))>
#<alt (* 1/2 (pow eps 5))>
#<alt (* -1 (* (pow eps 5) (- (/ x (pow eps 4)) 1/2)))>
#<alt (* -1 (* (pow eps 5) (- (/ x (pow eps 4)) 1/2)))>
#<alt (* -1 (* (pow eps 5) (- (/ x (pow eps 4)) 1/2)))>
#<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 (* -1/2 (pow eps 2))>
#<alt (* -1/2 (pow eps 2))>
#<alt (* -1/2 (pow eps 2))>
#<alt (* -1/2 (pow eps 2))>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (* eps (* x (- (* 1/6 (pow x 2)) 1)))>
#<alt (* eps (+ (* eps (- (* 1/4 (pow x 2)) 1/2)) (* x (- (* 1/6 (pow x 2)) 1))))>
#<alt (* eps (+ (* eps (- (* 1/4 (pow x 2)) 1/2)) (* x (- (* 1/6 (pow x 2)) 1))))>
#<alt (* eps (+ (* eps (- (* 1/4 (pow x 2)) 1/2)) (* x (- (* 1/6 (pow x 2)) 1))))>
#<alt (* (pow eps 2) (- (* 1/4 (pow x 2)) 1/2))>
#<alt (* (pow eps 2) (- (+ (* 1/4 (pow x 2)) (/ (* x (- (* 1/6 (pow x 2)) 1)) eps)) 1/2))>
#<alt (* (pow eps 2) (- (+ (* 1/4 (pow x 2)) (/ (* x (- (* 1/6 (pow x 2)) 1)) eps)) 1/2))>
#<alt (* (pow eps 2) (- (+ (* 1/4 (pow x 2)) (/ (* x (- (* 1/6 (pow x 2)) 1)) eps)) 1/2))>
#<alt (* -1 (* (pow eps 2) (+ 1/2 (* -1/4 (pow x 2)))))>
#<alt (* (pow eps 2) (+ (* -1 (+ 1/2 (* -1/4 (pow x 2)))) (/ (* x (- (* 1/6 (pow x 2)) 1)) eps)))>
#<alt (* (pow eps 2) (+ (* -1 (+ 1/2 (* -1/4 (pow x 2)))) (/ (* x (- (* 1/6 (pow x 2)) 1)) eps)))>
#<alt (* (pow eps 2) (+ (* -1 (+ 1/2 (* -1/4 (pow x 2)))) (/ (* x (- (* 1/6 (pow x 2)) 1)) eps)))>
#<alt (* -1/2 (pow eps 2))>
#<alt (+ (* -1 (* eps x)) (* -1/2 (pow eps 2)))>
#<alt (+ (* -1/2 (pow eps 2)) (* x (+ (* -1 eps) (* 1/4 (* (pow eps 2) x)))))>
#<alt (+ (* -1/2 (pow eps 2)) (* x (+ (* -1 eps) (* x (+ (* 1/6 (* eps x)) (* 1/4 (pow eps 2)))))))>
#<alt (* 1/6 (* eps (pow x 11)))>
#<alt (* (pow x 11) (+ (* 1/6 eps) (* 1/4 (/ (pow eps 2) (pow x 6)))))>
#<alt (* (pow x 11) (+ (* -1 (/ eps (pow x 10))) (+ (* 1/6 eps) (* 1/4 (/ (pow eps 2) (pow x 6))))))>
#<alt (* (pow x 11) (+ (* -1 (/ eps (pow x 10))) (+ (* -1/2 (/ (pow eps 2) (pow x 11))) (+ (* 1/6 eps) (* 1/4 (/ (pow eps 2) (pow x 6)))))))>
#<alt (* 1/6 (* eps (pow x 3)))>
#<alt (* -1 (* (pow x 3) (+ (* -1/4 (/ (pow eps 2) x)) (* -1/6 eps))))>
#<alt (* -1 (* (pow x 3) (+ (* -1 (/ (+ (* -1 (/ eps x)) (* 1/4 (pow eps 2))) x)) (* -1/6 eps))))>
#<alt (* -1 (* (pow x 3) (+ (* -1 (/ (+ (* -1 (/ (+ eps (* 1/2 (/ (pow eps 2) x))) x)) (* 1/4 (pow eps 2))) x)) (* -1/6 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 (* 1/6 (pow x 11))>
#<alt (* (pow x 11) (+ 1/6 (* 1/4 (/ 1 (pow x 6)))))>
#<alt (* (pow x 11) (- (+ 1/6 (* 1/4 (/ 1 (pow x 6)))) (/ 1 (pow x 10))))>
#<alt (* (pow x 11) (- (+ 1/6 (+ (* -1/2 (/ eps (pow x 11))) (* 1/4 (/ 1 (pow x 6))))) (/ 1 (pow x 10))))>
#<alt (* 1/6 (pow x 3))>
#<alt (* -1 (* (pow x 3) (- (* -1/4 (/ eps x)) 1/6)))>
#<alt (* -1 (* (pow x 3) (- (* -1 (/ (- (* 1/4 eps) (/ 1 x)) x)) 1/6)))>
#<alt (* -1 (* (pow x 3) (- (* -1 (/ (+ (* -1 (/ (+ 1 (* 1/2 (/ eps x))) x)) (* 1/4 eps)) x)) 1/6)))>
#<alt (* x (- (* 1/6 (pow x 2)) 1))>
#<alt (+ (* eps (- (* 1/4 (pow x 2)) 1/2)) (* x (- (* 1/6 (pow x 2)) 1)))>
#<alt (+ (* eps (- (* 1/4 (pow x 2)) 1/2)) (* x (- (* 1/6 (pow x 2)) 1)))>
#<alt (+ (* eps (- (* 1/4 (pow x 2)) 1/2)) (* x (- (* 1/6 (pow x 2)) 1)))>
#<alt (* eps (- (* 1/4 (pow x 2)) 1/2))>
#<alt (* eps (- (+ (* 1/4 (pow x 2)) (/ (* x (- (* 1/6 (pow x 2)) 1)) eps)) 1/2))>
#<alt (* eps (- (+ (* 1/4 (pow x 2)) (/ (* x (- (* 1/6 (pow x 2)) 1)) eps)) 1/2))>
#<alt (* eps (- (+ (* 1/4 (pow x 2)) (/ (* x (- (* 1/6 (pow x 2)) 1)) eps)) 1/2))>
#<alt (* -1 (* eps (+ 1/2 (* -1/4 (pow x 2)))))>
#<alt (* -1 (* eps (+ 1/2 (+ (* -1 (/ (* x (- (* 1/6 (pow x 2)) 1)) eps)) (* -1/4 (pow x 2))))))>
#<alt (* -1 (* eps (+ 1/2 (+ (* -1 (/ (* x (- (* 1/6 (pow x 2)) 1)) eps)) (* -1/4 (pow x 2))))))>
#<alt (* -1 (* eps (+ 1/2 (+ (* -1 (/ (* x (- (* 1/6 (pow x 2)) 1)) eps)) (* -1/4 (pow x 2))))))>
#<alt -1>
#<alt (- (* 1/4 (* eps x)) 1)>
#<alt (- (* x (+ (* 1/6 x) (* 1/4 eps))) 1)>
#<alt (- (* x (+ (* 1/6 x) (* 1/4 eps))) 1)>
#<alt (* 1/6 (pow x 6))>
#<alt (* (pow x 6) (+ 1/6 (* 1/4 (/ 1 (pow x 5)))))>
#<alt (* (pow x 6) (- (+ 1/6 (* 1/4 (/ 1 (pow x 5)))) (/ 1 (pow x 6))))>
#<alt (* (pow x 6) (- (+ 1/6 (* 1/4 (/ 1 (pow x 5)))) (/ 1 (pow x 6))))>
#<alt (* 1/6 (pow x 2))>
#<alt (* (pow x 2) (+ 1/6 (* 1/4 (/ eps x))))>
#<alt (* (pow x 2) (+ 1/6 (* -1 (/ (+ (* -1/4 eps) (/ 1 x)) x))))>
#<alt (* (pow x 2) (+ 1/6 (* -1 (/ (+ (* -1/4 eps) (/ 1 x)) x))))>
#<alt (- (* 1/6 (pow x 2)) 1)>
#<alt (- (+ (* 1/6 (pow x 2)) (* 1/4 (* eps x))) 1)>
#<alt (- (+ (* 1/6 (pow x 2)) (* 1/4 (* eps x))) 1)>
#<alt (- (+ (* 1/6 (pow x 2)) (* 1/4 (* eps x))) 1)>
#<alt (* 1/4 (* eps x))>
#<alt (* eps (- (+ (* 1/6 (/ (pow x 2) eps)) (* 1/4 x)) (/ 1 eps)))>
#<alt (* eps (- (+ (* 1/6 (/ (pow x 2) eps)) (* 1/4 x)) (/ 1 eps)))>
#<alt (* eps (- (+ (* 1/6 (/ (pow x 2) eps)) (* 1/4 x)) (/ 1 eps)))>
#<alt (* 1/4 (* eps x))>
#<alt (* -1 (* eps (+ (* -1 (/ (- (* 1/6 (pow x 2)) 1) eps)) (* -1/4 x))))>
#<alt (* -1 (* eps (+ (* -1 (/ (- (* 1/6 (pow x 2)) 1) eps)) (* -1/4 x))))>
#<alt (* -1 (* eps (+ (* -1 (/ (- (* 1/6 (pow x 2)) 1) eps)) (* -1/4 x))))>
#<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 (* 1/4 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 (* eps (sin x)))>
#<alt (* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))>
#<alt (* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* 1/8 (* eps (sin x)))))))>
#<alt (* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/48 (* eps (cos x))) (* 1/8 (sin x))))))))>
#<alt (* 1/24 (* (pow eps 11) (sin (+ x (* 1/2 eps)))))>
#<alt (* 1/24 (* (pow eps 11) (sin (+ x (* 1/2 eps)))))>
#<alt (* (pow eps 11) (+ (* -1 (/ (sin (+ x (* 1/2 eps))) (pow eps 10))) (* 1/24 (sin (+ x (* 1/2 eps))))))>
#<alt (* (pow eps 11) (+ (* -1 (/ (sin (+ x (* 1/2 eps))) (pow eps 10))) (* 1/24 (sin (+ x (* 1/2 eps))))))>
#<alt (* 1/24 (* (pow eps 3) (sin (- x (* -1/2 eps)))))>
#<alt (* -1 (* (pow eps 3) (+ (* -1/24 (sin (- x (* -1/2 eps)))) (/ (sin (- x (* -1/2 eps))) (pow eps 2)))))>
#<alt (* -1 (* (pow eps 3) (+ (* -1/24 (sin (- x (* -1/2 eps)))) (/ (sin (- x (* -1/2 eps))) (pow eps 2)))))>
#<alt (* -1 (* (pow eps 3) (+ (* -1/24 (sin (- x (* -1/2 eps)))) (/ (sin (- x (* -1/2 eps))) (pow eps 2)))))>
#<alt (* -2 (* eps (* (sin (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 8))))))>
#<alt (+ (* -2 (* eps (* x (* (cos (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 8))))))) (* -2 (* eps (* (sin (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 8)))))))>
#<alt (+ (* -2 (* eps (* (sin (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 8)))))) (* x (+ (* -2 (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 8)))))) (* eps (* x (* (sin (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 8)))))))))>
#<alt (+ (* -2 (* eps (* (sin (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 8)))))) (* x (+ (* -2 (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 8)))))) (* x (+ (* 1/3 (* eps (* x (* (cos (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 8))))))) (* eps (* (sin (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 8))))))))))>
#<alt (* -2 (* eps (* (sin (+ x (* 1/2 eps))) (+ 1/2 (* -1/48 (pow eps 10))))))>
#<alt (* -2 (* eps (* (sin (+ x (* 1/2 eps))) (+ 1/2 (* -1/48 (pow eps 10))))))>
#<alt (* -2 (* eps (* (sin (+ x (* 1/2 eps))) (+ 1/2 (* -1/48 (pow eps 10))))))>
#<alt (* -2 (* eps (* (sin (+ x (* 1/2 eps))) (+ 1/2 (* -1/48 (pow eps 10))))))>
#<alt (* -2 (* eps (* (sin (- (* 1/2 eps) (* -1 x))) (+ 1/2 (* -1/48 (pow eps 10))))))>
#<alt (* -2 (* eps (* (sin (- (* 1/2 eps) (* -1 x))) (+ 1/2 (* -1/48 (pow eps 10))))))>
#<alt (* -2 (* eps (* (sin (- (* 1/2 eps) (* -1 x))) (+ 1/2 (* -1/48 (pow eps 10))))))>
#<alt (* -2 (* eps (* (sin (- (* 1/2 eps) (* -1 x))) (+ 1/2 (* -1/48 (pow eps 10))))))>
#<alt (* 1/2 (* eps (sin x)))>
#<alt (* eps (+ (* 1/4 (* eps (cos x))) (* 1/2 (sin x))))>
#<alt (* eps (+ (* 1/2 (sin x)) (* eps (+ (* -1/16 (* eps (sin x))) (* 1/4 (cos x))))))>
#<alt (* eps (+ (* 1/2 (sin x)) (* eps (+ (* 1/4 (cos x)) (* eps (+ (* -1/16 (sin x)) (* -1/96 (* eps (cos x)))))))))>
#<alt (* -1/48 (* (pow eps 10) (sin (+ x (* 1/2 eps)))))>
#<alt (* -1/48 (* (pow eps 10) (sin (+ x (* 1/2 eps)))))>
#<alt (* (pow eps 10) (+ (* -1/48 (sin (+ x (* 1/2 eps)))) (* 1/2 (/ (sin (+ x (* 1/2 eps))) (pow eps 9)))))>
#<alt (* (pow eps 10) (+ (* -1/48 (sin (+ x (* 1/2 eps)))) (* 1/2 (/ (sin (+ x (* 1/2 eps))) (pow eps 9)))))>
#<alt (* -1/48 (* (pow eps 11) (sin (- x (* -1/2 eps)))))>
#<alt (* -1/48 (* (pow eps 11) (sin (- x (* -1/2 eps)))))>
#<alt (* -1 (* (pow eps 11) (+ (* -1/2 (/ (sin (- x (* -1/2 eps))) (pow eps 10))) (* 1/48 (sin (- x (* -1/2 eps)))))))>
#<alt (* -1 (* (pow eps 11) (+ (* -1/2 (/ (sin (- x (* -1/2 eps))) (pow eps 10))) (* 1/48 (sin (- x (* -1/2 eps)))))))>
#<alt (* eps (* (sin (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 7)))))>
#<alt (+ (* eps (* x (* (cos (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 7)))))) (* eps (* (sin (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 7))))))>
#<alt (+ (* eps (* (sin (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 7))))) (* x (+ (* -1/2 (* eps (* x (* (sin (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 7))))))) (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 7))))))))>
#<alt (+ (* eps (* (sin (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 7))))) (* x (+ (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 7))))) (* x (+ (* -1/2 (* eps (* (sin (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 7)))))) (* -1/6 (* eps (* x (* (cos (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 7))))))))))))>
#<alt (* eps (* (sin (+ x (* 1/2 eps))) (+ 1/2 (* -1/48 (pow eps 9)))))>
#<alt (* eps (* (sin (+ x (* 1/2 eps))) (+ 1/2 (* -1/48 (pow eps 9)))))>
#<alt (* eps (* (sin (+ x (* 1/2 eps))) (+ 1/2 (* -1/48 (pow eps 9)))))>
#<alt (* eps (* (sin (+ x (* 1/2 eps))) (+ 1/2 (* -1/48 (pow eps 9)))))>
#<alt (* eps (* (sin (- (* 1/2 eps) (* -1 x))) (+ 1/2 (* -1/48 (pow eps 9)))))>
#<alt (* eps (* (sin (- (* 1/2 eps) (* -1 x))) (+ 1/2 (* -1/48 (pow eps 9)))))>
#<alt (* eps (* (sin (- (* 1/2 eps) (* -1 x))) (+ 1/2 (* -1/48 (pow eps 9)))))>
#<alt (* eps (* (sin (- (* 1/2 eps) (* -1 x))) (+ 1/2 (* -1/48 (pow eps 9)))))>
#<alt 1/2>
#<alt (+ 1/2 (* -1/48 (pow eps 3)))>
#<alt (+ 1/2 (* -1/48 (pow eps 3)))>
#<alt (+ 1/2 (* -1/48 (pow eps 3)))>
#<alt (* -1/48 (pow eps 4))>
#<alt (* (pow eps 4) (- (* 1/2 (/ 1 (pow eps 4))) 1/48))>
#<alt (* (pow eps 4) (- (* 1/2 (/ 1 (pow eps 4))) 1/48))>
#<alt (* (pow eps 4) (- (* 1/2 (/ 1 (pow eps 4))) 1/48))>
#<alt (* -1/48 (pow eps 4))>
#<alt (* (pow eps 4) (- (* 1/2 (/ 1 (pow eps 4))) 1/48))>
#<alt (* (pow eps 4) (- (* 1/2 (/ 1 (pow eps 4))) 1/48))>
#<alt (* (pow eps 4) (- (* 1/2 (/ 1 (pow eps 4))) 1/48))>
#<alt (* 1/6 x)>
#<alt (* 1/6 x)>
#<alt (* 1/6 x)>
#<alt (* 1/6 x)>
#<alt x>
#<alt x>
#<alt x>
#<alt x>
#<alt (* -1 x)>
#<alt (* -1 x)>
#<alt (* -1 x)>
#<alt (* -1 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 (+ x (* 1/2 eps)))>
#<alt (sin (+ x (* 1/2 eps)))>
#<alt (sin (+ x (* 1/2 eps)))>
#<alt (sin (+ x (* 1/2 eps)))>
#<alt (sin (- x (* -1/2 eps)))>
#<alt (sin (- x (* -1/2 eps)))>
#<alt (sin (- x (* -1/2 eps)))>
#<alt (sin (- x (* -1/2 eps)))>
#<alt (sin (* 1/2 eps))>
#<alt (+ (sin (* 1/2 eps)) (* x (cos (* 1/2 eps))))>
#<alt (+ (sin (* 1/2 eps)) (* x (+ (cos (* 1/2 eps)) (* -1/2 (* x (sin (* 1/2 eps)))))))>
#<alt (+ (sin (* 1/2 eps)) (* x (+ (cos (* 1/2 eps)) (* x (+ (* -1/2 (sin (* 1/2 eps))) (* -1/6 (* x (cos (* 1/2 eps)))))))))>
#<alt (sin (+ x (* 1/2 eps)))>
#<alt (sin (+ x (* 1/2 eps)))>
#<alt (sin (+ x (* 1/2 eps)))>
#<alt (sin (+ x (* 1/2 eps)))>
#<alt (sin (- (* 1/2 eps) (* -1 x)))>
#<alt (sin (- (* 1/2 eps) (* -1 x)))>
#<alt (sin (- (* 1/2 eps) (* -1 x)))>
#<alt (sin (- (* 1/2 eps) (* -1 x)))>

Calls

81 calls:

Time	Variable		Point	Expression
10.0ms	x	@	-inf	(+ (* x (+ (* eps 1/4) (* x 1/6))) -1)
5.0ms	x	@	inf	(* (* eps (+ (* eps (* eps -1/48)) 1/2)) (sin (+ (* eps 1/2) x)))
3.0ms	x	@	inf	(* (* (* eps (+ (* eps (* eps -1/48)) 1/2)) (+ (* (sin (* (+ x x) 1/2)) (cos (* eps 1/2))) (* (cos (* (+ x x) 1/2)) (sin (* eps 1/2))))) -2)
3.0ms	x	@	-inf	(* (* (* eps (+ (* eps (* eps -1/48)) 1/2)) (+ (* (sin (* (+ x x) 1/2)) (cos (* eps 1/2))) (* (cos (* (+ x x) 1/2)) (sin (* eps 1/2))))) -2)
2.0ms	eps	@	inf	(* (* (* eps (+ (* eps (* eps -1/48)) 1/2)) (sin (+ (* eps 1/2) x))) -2)

Compiler

Compiled 1 314 to 963 computations (26.7% saved)

rewrite285.0ms (1.7%)

Memory

24.9MiB live, 151.1MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

7 172×	`lower-fma.f32`
7 158×	`lower-fma.f64`
4 372×	`lower-*.f32`
4 344×	`lower-*.f64`
3 552×	`lower-/.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	37	185
0	71	185
1	249	155
2	1929	155
0	8123	153

Stop Event

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

Counts

17 → 508

Calls

Call 1

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

Outputs
(exp.f64 (*.f64 (log.f64 (+.f64 x x)) #s(literal 3 binary64)))
(+.f64 x x)
(+.f64 (/.f64 (.f64 x x) #s(literal 0 binary64)) (neg.f64 (/.f64 (.f64 x x) #s(literal 0 binary64))))
(+.f64 (.f64 #s(literal 1/2 binary64) x) (.f64 #s(literal 1/2 binary64) x))
(+.f64 (.f64 x #s(literal 1/2 binary64)) (.f64 x #s(literal 1/2 binary64)))
(-.f64 (/.f64 (.f64 x x) #s(literal 0 binary64)) (/.f64 (.f64 x x) #s(literal 0 binary64)))
(-.f64 (/.f64 (fma.f64 x x (.f64 x x)) (.f64 (fma.f64 x x #s(literal 0 binary64)) (+.f64 x x))) (/.f64 (.f64 x x) (.f64 (fma.f64 x x #s(literal 0 binary64)) (+.f64 x x))))
(fma.f64 x #s(literal 1/2 binary64) (*.f64 x #s(literal 1/2 binary64)))
(fma.f64 #s(literal 1/2 binary64) x (*.f64 #s(literal 1/2 binary64) x))
(fma.f64 (.f64 x x) (/.f64 #s(literal -1 binary64) #s(literal 0 binary64)) (neg.f64 (/.f64 (.f64 x x) #s(literal 0 binary64))))
(/.f64 #s(literal 1/2 binary64) (+.f64 x x))
(/.f64 #s(literal -1 binary64) (neg.f64 (+.f64 x x)))
(/.f64 #s(literal 1 binary64) (+.f64 x x))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 x x) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 x x #s(literal 0 binary64)) (.f64 #s(literal 1/2 binary64) (.f64 (fma.f64 x x #s(literal 0 binary64)) (+.f64 x x)))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 x x #s(literal 0 binary64)) (.f64 (.f64 (fma.f64 x x #s(literal 0 binary64)) (+.f64 x x)) #s(literal 1/2 binary64))))
(/.f64 (*.f64 (fma.f64 x x #s(literal 0 binary64)) (+.f64 x x)) (fma.f64 x x #s(literal 0 binary64)))
(/.f64 (fma.f64 x x #s(literal 0 binary64)) (*.f64 (fma.f64 x x #s(literal 0 binary64)) (+.f64 x x)))
(/.f64 #s(literal 0 binary64) #s(literal 0 binary64))
(/.f64 (neg.f64 (*.f64 (fma.f64 x x #s(literal 0 binary64)) (+.f64 x x))) (neg.f64 (fma.f64 x x #s(literal 0 binary64))))
(/.f64 (neg.f64 (fma.f64 x x #s(literal 0 binary64))) (neg.f64 (*.f64 (fma.f64 x x #s(literal 0 binary64)) (+.f64 x x))))
(/.f64 (.f64 #s(literal 1/2 binary64) (.f64 (fma.f64 x x #s(literal 0 binary64)) (+.f64 x x))) (fma.f64 x x #s(literal 0 binary64)))
(/.f64 (.f64 (.f64 (fma.f64 x x #s(literal 0 binary64)) (+.f64 x x)) #s(literal 1/2 binary64)) (fma.f64 x x #s(literal 0 binary64)))
(/.f64 (pow.f64 (*.f64 (fma.f64 x x #s(literal 0 binary64)) (+.f64 x x)) #s(literal 3 binary64)) (pow.f64 (fma.f64 x x #s(literal 0 binary64)) #s(literal 3 binary64)))
(/.f64 (pow.f64 (neg.f64 (*.f64 (fma.f64 x x #s(literal 0 binary64)) (+.f64 x x))) #s(literal 3 binary64)) (pow.f64 (neg.f64 (fma.f64 x x #s(literal 0 binary64))) #s(literal 3 binary64)))
(/.f64 (pow.f64 (.f64 #s(literal 1/2 binary64) (.f64 (fma.f64 x x #s(literal 0 binary64)) (+.f64 x x))) #s(literal 3 binary64)) (pow.f64 (fma.f64 x x #s(literal 0 binary64)) #s(literal 3 binary64)))
(/.f64 (pow.f64 (.f64 (.f64 (fma.f64 x x #s(literal 0 binary64)) (+.f64 x x)) #s(literal 1/2 binary64)) #s(literal 3 binary64)) (pow.f64 (fma.f64 x x #s(literal 0 binary64)) #s(literal 3 binary64)))
(/.f64 (-.f64 (.f64 (.f64 x x) #s(literal 0 binary64)) (.f64 #s(literal 0 binary64) (.f64 x x))) #s(literal 0 binary64))
(/.f64 (neg.f64 (neg.f64 (*.f64 (fma.f64 x x #s(literal 0 binary64)) (+.f64 x x)))) (neg.f64 (neg.f64 (fma.f64 x x #s(literal 0 binary64)))))
(/.f64 (neg.f64 (.f64 #s(literal 1/2 binary64) (.f64 (fma.f64 x x #s(literal 0 binary64)) (+.f64 x x)))) (neg.f64 (fma.f64 x x #s(literal 0 binary64))))
(/.f64 (neg.f64 (.f64 (.f64 (fma.f64 x x #s(literal 0 binary64)) (+.f64 x x)) #s(literal 1/2 binary64))) (neg.f64 (fma.f64 x x #s(literal 0 binary64))))
(/.f64 (+.f64 (pow.f64 (.f64 #s(literal 1/2 binary64) x) #s(literal 3 binary64)) (pow.f64 (.f64 #s(literal 1/2 binary64) x) #s(literal 3 binary64))) (fma.f64 (.f64 #s(literal 1/2 binary64) x) (.f64 #s(literal 1/2 binary64) x) (-.f64 (.f64 (.f64 #s(literal 1/2 binary64) x) (.f64 #s(literal 1/2 binary64) x)) (.f64 (.f64 #s(literal 1/2 binary64) x) (.f64 #s(literal 1/2 binary64) x)))))
(/.f64 (+.f64 (pow.f64 (.f64 x #s(literal 1/2 binary64)) #s(literal 3 binary64)) (pow.f64 (.f64 x #s(literal 1/2 binary64)) #s(literal 3 binary64))) (fma.f64 (.f64 x #s(literal 1/2 binary64)) (.f64 x #s(literal 1/2 binary64)) (-.f64 (.f64 (.f64 x #s(literal 1/2 binary64)) (.f64 x #s(literal 1/2 binary64))) (.f64 (.f64 x #s(literal 1/2 binary64)) (.f64 x #s(literal 1/2 binary64))))))
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(-.f64 (/.f64 (.f64 (.f64 (.f64 eps eps) (.f64 eps eps)) #s(literal 1/2304 binary64)) (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal -1/2 binary64))) (/.f64 #s(literal 1/4 binary64) (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal -1/2 binary64))))
(-.f64 (/.f64 #s(literal 1/4 binary64) (-.f64 #s(literal 1/2 binary64) (.f64 eps (.f64 eps #s(literal -1/48 binary64))))) (/.f64 (.f64 (.f64 (.f64 eps eps) (.f64 eps eps)) #s(literal 1/2304 binary64)) (-.f64 #s(literal 1/2 binary64) (.f64 eps (.f64 eps #s(literal -1/48 binary64))))))
(fma.f64 eps (*.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64))
(fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/2 binary64))
(fma.f64 (*.f64 eps #s(literal -1/48 binary64)) eps #s(literal 1/2 binary64))
(fma.f64 (*.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/2 binary64))
(fma.f64 (.f64 (.f64 (.f64 eps eps) (.f64 eps eps)) #s(literal 1/2304 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal -1/2 binary64))) (neg.f64 (/.f64 #s(literal 1/4 binary64) (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal -1/2 binary64)))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/2 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/2 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/2 binary64))) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1/4 binary64) (fma.f64 (.f64 (.f64 eps eps) (.f64 eps eps)) #s(literal 1/2304 binary64) (neg.f64 (.f64 (.f64 eps eps) #s(literal -1/96 binary64))))) (fma.f64 (.f64 (.f64 eps eps) (.f64 (.f64 eps eps) (.f64 eps eps))) #s(literal -1/110592 binary64) #s(literal 1/8 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (.f64 eps (.f64 eps #s(literal -1/48 binary64)))) (-.f64 #s(literal 1/4 binary64) (.f64 (.f64 (.f64 eps eps) (.f64 eps eps)) #s(literal 1/2304 binary64)))))
(/.f64 (fma.f64 (.f64 (.f64 eps eps) (.f64 (.f64 eps eps) (.f64 eps eps))) #s(literal -1/110592 binary64) #s(literal 1/8 binary64)) (-.f64 (fma.f64 (.f64 (.f64 eps eps) (.f64 eps eps)) #s(literal 1/2304 binary64) #s(literal 1/4 binary64)) (.f64 (.f64 eps eps) #s(literal -1/96 binary64))))
(/.f64 (fma.f64 (.f64 (.f64 eps eps) (.f64 (.f64 eps eps) (.f64 eps eps))) #s(literal -1/110592 binary64) #s(literal 1/8 binary64)) (+.f64 #s(literal 1/4 binary64) (fma.f64 (.f64 (.f64 eps eps) (.f64 eps eps)) #s(literal 1/2304 binary64) (neg.f64 (.f64 (.f64 eps eps) #s(literal -1/96 binary64))))))
(/.f64 (fma.f64 (.f64 (.f64 eps eps) (.f64 eps eps)) #s(literal 1/2304 binary64) #s(literal -1/4 binary64)) (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal -1/2 binary64)))
(/.f64 (neg.f64 (fma.f64 (.f64 (.f64 eps eps) (.f64 (.f64 eps eps) (.f64 eps eps))) #s(literal -1/110592 binary64) #s(literal 1/8 binary64))) (neg.f64 (-.f64 (fma.f64 (.f64 (.f64 eps eps) (.f64 eps eps)) #s(literal 1/2304 binary64) #s(literal 1/4 binary64)) (.f64 (.f64 eps eps) #s(literal -1/96 binary64)))))
(/.f64 (neg.f64 (fma.f64 (.f64 (.f64 eps eps) (.f64 (.f64 eps eps) (.f64 eps eps))) #s(literal -1/110592 binary64) #s(literal 1/8 binary64))) (neg.f64 (+.f64 #s(literal 1/4 binary64) (fma.f64 (.f64 (.f64 eps eps) (.f64 eps eps)) #s(literal 1/2304 binary64) (neg.f64 (.f64 (.f64 eps eps) #s(literal -1/96 binary64)))))))
(/.f64 (neg.f64 (fma.f64 (.f64 (.f64 eps eps) (.f64 eps eps)) #s(literal 1/2304 binary64) #s(literal -1/4 binary64))) (neg.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal -1/2 binary64))))
(/.f64 (-.f64 #s(literal 1/4 binary64) (.f64 (.f64 (.f64 eps eps) (.f64 eps eps)) #s(literal 1/2304 binary64))) (-.f64 #s(literal 1/2 binary64) (.f64 eps (.f64 eps #s(literal -1/48 binary64)))))
(/.f64 (-.f64 (.f64 (.f64 (.f64 (.f64 eps eps) (.f64 eps eps)) #s(literal 1/2304 binary64)) (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal -1/2 binary64))) (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal -1/2 binary64)) #s(literal 1/4 binary64))) (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal -1/2 binary64)) (fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal -1/2 binary64))))
(/.f64 (neg.f64 (neg.f64 (fma.f64 (.f64 (.f64 eps eps) (.f64 (.f64 eps eps) (.f64 eps eps))) #s(literal -1/110592 binary64) #s(literal 1/8 binary64)))) (neg.f64 (neg.f64 (-.f64 (fma.f64 (.f64 (.f64 eps eps) (.f64 eps eps)) #s(literal 1/2304 binary64) #s(literal 1/4 binary64)) (.f64 (.f64 eps eps) #s(literal -1/96 binary64))))))
(/.f64 (neg.f64 (neg.f64 (fma.f64 (.f64 (.f64 eps eps) (.f64 eps eps)) #s(literal 1/2304 binary64) #s(literal -1/4 binary64)))) (neg.f64 (neg.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal -1/2 binary64)))))
(/.f64 (neg.f64 (-.f64 #s(literal 1/4 binary64) (.f64 (.f64 (.f64 eps eps) (.f64 eps eps)) #s(literal 1/2304 binary64)))) (neg.f64 (-.f64 #s(literal 1/2 binary64) (.f64 eps (.f64 eps #s(literal -1/48 binary64))))))
(/.f64 (-.f64 (pow.f64 (/.f64 (.f64 (.f64 (.f64 eps eps) (.f64 eps eps)) #s(literal 1/2304 binary64)) (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal -1/2 binary64))) #s(literal 3 binary64)) (pow.f64 (/.f64 #s(literal 1/4 binary64) (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal -1/2 binary64))) #s(literal 3 binary64))) (fma.f64 (/.f64 (.f64 (.f64 (.f64 eps eps) (.f64 eps eps)) #s(literal 1/2304 binary64)) (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal -1/2 binary64))) (/.f64 (.f64 (.f64 (.f64 eps eps) (.f64 eps eps)) #s(literal 1/2304 binary64)) (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal -1/2 binary64))) (fma.f64 (/.f64 #s(literal 1/4 binary64) (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal -1/2 binary64))) (/.f64 #s(literal 1/4 binary64) (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal -1/2 binary64))) (.f64 (/.f64 (.f64 (.f64 (.f64 eps eps) (.f64 eps eps)) #s(literal 1/2304 binary64)) (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal -1/2 binary64))) (/.f64 #s(literal 1/4 binary64) (fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal -1/2 binary64)))))))
(pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/2 binary64))) #s(literal -1 binary64))
(.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)))
(.f64 (fma.f64 (.f64 (.f64 eps eps) (.f64 (.f64 eps eps) (.f64 eps eps))) #s(literal -1/110592 binary64) #s(literal 1/8 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 (.f64 (.f64 eps eps) (.f64 eps eps)) #s(literal 1/2304 binary64) #s(literal 1/4 binary64)) (.f64 (*.f64 eps eps) #s(literal -1/96 binary64)))))
(.f64 (fma.f64 (.f64 (.f64 eps eps) (.f64 (.f64 eps eps) (.f64 eps eps))) #s(literal -1/110592 binary64) #s(literal 1/8 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/4 binary64) (fma.f64 (.f64 (.f64 eps eps) (.f64 eps eps)) #s(literal 1/2304 binary64) (neg.f64 (.f64 (*.f64 eps eps) #s(literal -1/96 binary64)))))))
(.f64 (fma.f64 (.f64 (.f64 eps eps) (.f64 eps eps)) #s(literal 1/2304 binary64) #s(literal -1/4 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal -1/2 binary64))))
(.f64 (neg.f64 (fma.f64 (.f64 (.f64 eps eps) (.f64 (.f64 eps eps) (.f64 eps eps))) #s(literal -1/110592 binary64) #s(literal 1/8 binary64))) (/.f64 #s(literal 1 binary64) (neg.f64 (-.f64 (fma.f64 (.f64 (.f64 eps eps) (.f64 eps eps)) #s(literal 1/2304 binary64) #s(literal 1/4 binary64)) (.f64 (*.f64 eps eps) #s(literal -1/96 binary64))))))
(.f64 (neg.f64 (fma.f64 (.f64 (.f64 eps eps) (.f64 eps eps)) #s(literal 1/2304 binary64) #s(literal -1/4 binary64))) (/.f64 #s(literal 1 binary64) (neg.f64 (fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal -1/2 binary64)))))
(.f64 (-.f64 #s(literal 1/4 binary64) (.f64 (.f64 (.f64 eps eps) (.f64 eps eps)) #s(literal 1/2304 binary64))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (.f64 eps (*.f64 eps #s(literal -1/48 binary64))))))
(*.f64 x #s(literal 1/6 binary64))
(*.f64 #s(literal 1/6 binary64) x)
(+.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x)) (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 x)))
(+.f64 (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 x)) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x)))
(-.f64 (.f64 (sin.f64 (/.f64 (.f64 (.f64 eps eps) #s(literal 1/4 binary64)) (-.f64 (.f64 #s(literal 1/2 binary64) eps) x))) (cos.f64 (/.f64 (.f64 x x) (-.f64 (.f64 #s(literal 1/2 binary64) eps) x)))) (.f64 (cos.f64 (/.f64 (.f64 (.f64 eps eps) #s(literal 1/4 binary64)) (-.f64 (.f64 #s(literal 1/2 binary64) eps) x))) (sin.f64 (/.f64 (.f64 x x) (-.f64 (.f64 #s(literal 1/2 binary64) eps) x)))))
(-.f64 (/.f64 (pow.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x)) #s(literal 2 binary64)) (sin.f64 (-.f64 (.f64 #s(literal 1/2 binary64) eps) x))) (/.f64 (pow.f64 (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 x)) #s(literal 2 binary64)) (sin.f64 (-.f64 (.f64 #s(literal 1/2 binary64) eps) x))))
(sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(fma.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 x) (.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x)))
(fma.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x) (.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 x)))
(fma.f64 (cos.f64 x) (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 x)))
(fma.f64 (sin.f64 x) (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x)))
(fma.f64 (+.f64 (sin.f64 (-.f64 (.f64 #s(literal 1/2 binary64) eps) x)) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) #s(literal 1/2 binary64) (.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 x)))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (pow.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x)) #s(literal 2 binary64)) (-.f64 (pow.f64 (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 x)) #s(literal 2 binary64)) (.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x)) (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 x))))) (+.f64 (pow.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x)) #s(literal 3 binary64)) (pow.f64 (.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 x)) #s(literal 3 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (sin.f64 (-.f64 (.f64 #s(literal 1/2 binary64) eps) x)) (-.f64 (pow.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x)) #s(literal 2 binary64)) (pow.f64 (.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 x)) #s(literal 2 binary64)))))
(/.f64 (+.f64 (pow.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x)) #s(literal 3 binary64)) (pow.f64 (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 x)) #s(literal 3 binary64))) (+.f64 (pow.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x)) #s(literal 2 binary64)) (-.f64 (pow.f64 (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 x)) #s(literal 2 binary64)) (.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x)) (.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 x))))))
(/.f64 (-.f64 (pow.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x)) #s(literal 2 binary64)) (pow.f64 (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 x)) #s(literal 2 binary64))) (sin.f64 (-.f64 (*.f64 #s(literal 1/2 binary64) eps) x)))
(/.f64 (neg.f64 (+.f64 (pow.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x)) #s(literal 3 binary64)) (pow.f64 (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 x)) #s(literal 3 binary64)))) (neg.f64 (+.f64 (pow.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x)) #s(literal 2 binary64)) (-.f64 (pow.f64 (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 x)) #s(literal 2 binary64)) (.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x)) (.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 x)))))))
(/.f64 (neg.f64 (-.f64 (pow.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x)) #s(literal 2 binary64)) (pow.f64 (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 x)) #s(literal 2 binary64)))) (neg.f64 (sin.f64 (-.f64 (*.f64 #s(literal 1/2 binary64) eps) x))))
(/.f64 (+.f64 (pow.f64 (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 x)) #s(literal 3 binary64)) (pow.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x)) #s(literal 3 binary64))) (+.f64 (pow.f64 (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 x)) #s(literal 2 binary64)) (-.f64 (pow.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x)) #s(literal 2 binary64)) (.f64 (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 x)) (.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x))))))
(.f64 (+.f64 (pow.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x)) #s(literal 3 binary64)) (pow.f64 (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 x)) #s(literal 3 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x)) #s(literal 2 binary64)) (-.f64 (pow.f64 (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 x)) #s(literal 2 binary64)) (.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x)) (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 x)))))))
(.f64 (-.f64 (pow.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x)) #s(literal 2 binary64)) (pow.f64 (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 x)) #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (sin.f64 (-.f64 (.f64 #s(literal 1/2 binary64) eps) x))))

simplify267.0ms (1.6%)

Memory

-17.7MiB live, 143.6MiB allocated

Algorithm

1×	egg-herbie

Rules

8 404×	`lower-fma.f64`
8 404×	`lower-fma.f32`
7 796×	`lower-*.f64`
7 796×	`lower-*.f32`
2 526×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	521	4435
1	1690	4318
2	5821	4194
0	8204	3857

Stop Event

1×	iter limit
1×	node limit

Counts

324 → 308

Calls

Call 1

Inputs
x
x
x
x
x
x
x
x
(* -1 x)
(* -1 x)
(* -1 x)
(* -1 x)
(* -1 (* eps (sin x)))
(* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))
(* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* 1/8 (* eps (sin x)))))))
(* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/48 (* eps (cos x))) (* 1/8 (sin x))))))))
(* 1/24 (* (pow eps 15) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))
(* 1/24 (* (pow eps 15) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))
(* 1/24 (* (pow eps 15) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))
(* (pow eps 15) (+ (* -1 (/ (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))) (pow eps 14))) (* 1/24 (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))))
(* 1/24 (* (pow eps 3) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))
(* -1 (* (pow eps 3) (+ (* -1/24 (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))) (+ (/ (* (cos x) (sin (* 1/2 eps))) (pow eps 2)) (/ (* (cos (* 1/2 eps)) (sin x)) (pow eps 2))))))
(* -1 (* (pow eps 3) (+ (* -1/24 (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))) (+ (/ (* (cos x) (sin (* 1/2 eps))) (pow eps 2)) (/ (* (cos (* 1/2 eps)) (sin x)) (pow eps 2))))))
(* -1 (* (pow eps 3) (+ (* -1/24 (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))) (+ (/ (* (cos x) (sin (* 1/2 eps))) (pow eps 2)) (/ (* (cos (* 1/2 eps)) (sin x)) (pow eps 2))))))
(* -2 (* eps (* (sin (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 5))))))
(+ (* -2 (* eps (* x (* (cos (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 5))))))) (* -2 (* eps (* (sin (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 5)))))))
(+ (* -2 (* eps (* (sin (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 5)))))) (* x (+ (* -2 (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 5)))))) (* eps (* x (* (sin (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 5)))))))))
(+ (* -2 (* eps (* (sin (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 5)))))) (* x (+ (* -2 (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 5)))))) (* x (+ (* 1/3 (* eps (* x (* (cos (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 5))))))) (* eps (* (sin (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 5))))))))))
(* -2 (* eps (* (+ 1/2 (* -1/48 (pow eps 5))) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))))
(* -2 (* eps (* (+ 1/2 (* -1/48 (pow eps 5))) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))))
(* -2 (* eps (* (+ 1/2 (* -1/48 (pow eps 5))) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))))
(* -2 (* eps (* (+ 1/2 (* -1/48 (pow eps 5))) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))))
(* -2 (* eps (* (+ 1/2 (* -1/48 (pow eps 5))) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))))
(* -2 (* eps (* (+ 1/2 (* -1/48 (pow eps 5))) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))))
(* -2 (* eps (* (+ 1/2 (* -1/48 (pow eps 5))) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))))
(* -2 (* eps (* (+ 1/2 (* -1/48 (pow eps 5))) (+ (* (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 (+ (* -1/16 (* eps (sin x))) (* 1/4 (cos x))))))
(* eps (+ (* 1/2 (sin x)) (* eps (+ (* 1/4 (cos x)) (* eps (+ (* -1/16 (sin x)) (* -1/96 (* eps (cos x)))))))))
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(* -1/48 (* (pow eps 14) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))
(* -1/48 (* (pow eps 14) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))
(* (pow eps 14) (+ (* -1/48 (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))) (* 1/2 (/ (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))) (pow eps 13)))))
(* 1/48 (* (pow eps 16) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))
(* 1/48 (* (pow eps 16) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))
(* 1/48 (* (pow eps 16) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))
(* (pow eps 16) (+ (* 1/48 (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))) (* 1/2 (/ (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))) (pow eps 15)))))
(* eps (* (sin (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 4)))))
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(+ (* eps (* (sin (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 4))))) (* x (+ (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 4))))) (* x (+ (* -1/2 (* eps (* (sin (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 4)))))) (* -1/6 (* eps (* x (* (cos (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 4))))))))))))
(* eps (* (+ 1/2 (* -1/48 (pow eps 4))) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))
(* eps (* (+ 1/2 (* -1/48 (pow eps 4))) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))
(* eps (* (+ 1/2 (* -1/48 (pow eps 4))) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))
(* eps (* (+ 1/2 (* -1/48 (pow eps 4))) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))
(* eps (* (+ 1/2 (* -1/48 (pow eps 4))) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))
(* eps (* (+ 1/2 (* -1/48 (pow eps 4))) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))
(* eps (* (+ 1/2 (* -1/48 (pow eps 4))) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))
(* eps (* (+ 1/2 (* -1/48 (pow eps 4))) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))
(* 1/2 eps)
(* eps (+ 1/2 (* -1/48 (pow eps 3))))
(* eps (+ 1/2 (* -1/48 (pow eps 3))))
(* eps (+ 1/2 (* -1/48 (pow eps 3))))
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(* (pow eps 5) (- (* 1/2 (/ 1 (pow eps 4))) 1/48))
(* (pow eps 5) (- (* 1/2 (/ 1 (pow eps 4))) 1/48))
(* 1/48 (pow eps 6))
(* (pow eps 6) (+ 1/48 (* 1/2 (/ 1 (pow eps 5)))))
(* (pow eps 6) (+ 1/48 (* 1/2 (/ 1 (pow eps 5)))))
(* (pow eps 6) (+ 1/48 (* 1/2 (/ 1 (pow eps 5)))))
(* -1/2 (pow eps 6))
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(* x (- (* -1/2 (/ (pow eps 6) x)) 1))
(* x (- (* -1/2 (/ (pow eps 6) x)) 1))
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(* -1 (* x (+ 1 (* 1/2 (/ (pow eps 3) x)))))
(* -1 (* x (+ 1 (* 1/2 (/ (pow eps 3) x)))))
(* -1 (* eps x))
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(* eps (+ (* -1 x) (* -1/2 (pow eps 5))))
(* eps (+ (* -1 x) (* -1/2 (pow eps 5))))
(* -1/2 (pow eps 7))
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(* (pow eps 7) (- (* -1 (/ x (pow eps 6))) 1/2))
(* (pow eps 7) (- (* -1 (/ x (pow eps 6))) 1/2))
(* 1/2 (pow eps 5))
(* -1 (* (pow eps 5) (- (/ x (pow eps 4)) 1/2)))
(* -1 (* (pow eps 5) (- (/ x (pow eps 4)) 1/2)))
(* -1 (* (pow eps 5) (- (/ x (pow eps 4)) 1/2)))
(* -1 eps)
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(* -1 eps)
(* -1 eps)
(* -1 eps)
(* -1 eps)
(* -1 eps)
(* -1 eps)
(* -1 eps)
(* -1 eps)
(* -1 eps)
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(* -1/2 (pow eps 2))
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(* -1/2 (pow eps 2))
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eps
eps
eps
eps
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(pow eps 2)
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(* 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))
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(* (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 11)))
(* (pow x 11) (+ (* 1/6 eps) (* 1/4 (/ (pow eps 2) (pow x 6)))))
(* (pow x 11) (+ (* -1 (/ eps (pow x 10))) (+ (* 1/6 eps) (* 1/4 (/ (pow eps 2) (pow x 6))))))
(* (pow x 11) (+ (* -1 (/ eps (pow x 10))) (+ (* -1/2 (/ (pow eps 2) (pow x 11))) (+ (* 1/6 eps) (* 1/4 (/ (pow eps 2) (pow x 6)))))))
(* 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 11))
(* (pow x 11) (+ 1/6 (* 1/4 (/ 1 (pow x 6)))))
(* (pow x 11) (- (+ 1/6 (* 1/4 (/ 1 (pow x 6)))) (/ 1 (pow x 10))))
(* (pow x 11) (- (+ 1/6 (+ (* -1/2 (/ eps (pow x 11))) (* 1/4 (/ 1 (pow x 6))))) (/ 1 (pow x 10))))
(* 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))
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(+ (* 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 6))
(* (pow x 6) (+ 1/6 (* 1/4 (/ 1 (pow x 5)))))
(* (pow x 6) (- (+ 1/6 (* 1/4 (/ 1 (pow x 5)))) (/ 1 (pow x 6))))
(* (pow x 6) (- (+ 1/6 (* 1/4 (/ 1 (pow x 5)))) (/ 1 (pow x 6))))
(* 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))
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(* -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))))
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(+ (* 1/6 x) (* 1/4 eps))
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(* x (+ 1/6 (* 1/4 (/ eps x))))
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(* -1 (* eps (sin x)))
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(* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* 1/8 (* eps (sin x)))))))
(* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/48 (* eps (cos x))) (* 1/8 (sin x))))))))
(* 1/24 (* (pow eps 11) (sin (+ x (* 1/2 eps)))))
(* 1/24 (* (pow eps 11) (sin (+ x (* 1/2 eps)))))
(* (pow eps 11) (+ (* -1 (/ (sin (+ x (* 1/2 eps))) (pow eps 10))) (* 1/24 (sin (+ x (* 1/2 eps))))))
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(* 1/24 (* (pow eps 3) (sin (- x (* -1/2 eps)))))
(* -1 (* (pow eps 3) (+ (* -1/24 (sin (- x (* -1/2 eps)))) (/ (sin (- x (* -1/2 eps))) (pow eps 2)))))
(* -1 (* (pow eps 3) (+ (* -1/24 (sin (- x (* -1/2 eps)))) (/ (sin (- x (* -1/2 eps))) (pow eps 2)))))
(* -1 (* (pow eps 3) (+ (* -1/24 (sin (- x (* -1/2 eps)))) (/ (sin (- x (* -1/2 eps))) (pow eps 2)))))
(* -2 (* eps (* (sin (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 8))))))
(+ (* -2 (* eps (* x (* (cos (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 8))))))) (* -2 (* eps (* (sin (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 8)))))))
(+ (* -2 (* eps (* (sin (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 8)))))) (* x (+ (* -2 (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 8)))))) (* eps (* x (* (sin (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 8)))))))))
(+ (* -2 (* eps (* (sin (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 8)))))) (* x (+ (* -2 (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 8)))))) (* x (+ (* 1/3 (* eps (* x (* (cos (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 8))))))) (* eps (* (sin (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 8))))))))))
(* -2 (* eps (* (sin (+ x (* 1/2 eps))) (+ 1/2 (* -1/48 (pow eps 10))))))
(* -2 (* eps (* (sin (+ x (* 1/2 eps))) (+ 1/2 (* -1/48 (pow eps 10))))))
(* -2 (* eps (* (sin (+ x (* 1/2 eps))) (+ 1/2 (* -1/48 (pow eps 10))))))
(* -2 (* eps (* (sin (+ x (* 1/2 eps))) (+ 1/2 (* -1/48 (pow eps 10))))))
(* -2 (* eps (* (sin (- (* 1/2 eps) (* -1 x))) (+ 1/2 (* -1/48 (pow eps 10))))))
(* -2 (* eps (* (sin (- (* 1/2 eps) (* -1 x))) (+ 1/2 (* -1/48 (pow eps 10))))))
(* -2 (* eps (* (sin (- (* 1/2 eps) (* -1 x))) (+ 1/2 (* -1/48 (pow eps 10))))))
(* -2 (* eps (* (sin (- (* 1/2 eps) (* -1 x))) (+ 1/2 (* -1/48 (pow eps 10))))))
(* 1/2 (* eps (sin x)))
(* eps (+ (* 1/4 (* eps (cos x))) (* 1/2 (sin x))))
(* eps (+ (* 1/2 (sin x)) (* eps (+ (* -1/16 (* eps (sin x))) (* 1/4 (cos x))))))
(* eps (+ (* 1/2 (sin x)) (* eps (+ (* 1/4 (cos x)) (* eps (+ (* -1/16 (sin x)) (* -1/96 (* eps (cos x)))))))))
(* -1/48 (* (pow eps 10) (sin (+ x (* 1/2 eps)))))
(* -1/48 (* (pow eps 10) (sin (+ x (* 1/2 eps)))))
(* (pow eps 10) (+ (* -1/48 (sin (+ x (* 1/2 eps)))) (* 1/2 (/ (sin (+ x (* 1/2 eps))) (pow eps 9)))))
(* (pow eps 10) (+ (* -1/48 (sin (+ x (* 1/2 eps)))) (* 1/2 (/ (sin (+ x (* 1/2 eps))) (pow eps 9)))))
(* -1/48 (* (pow eps 11) (sin (- x (* -1/2 eps)))))
(* -1/48 (* (pow eps 11) (sin (- x (* -1/2 eps)))))
(* -1 (* (pow eps 11) (+ (* -1/2 (/ (sin (- x (* -1/2 eps))) (pow eps 10))) (* 1/48 (sin (- x (* -1/2 eps)))))))
(* -1 (* (pow eps 11) (+ (* -1/2 (/ (sin (- x (* -1/2 eps))) (pow eps 10))) (* 1/48 (sin (- x (* -1/2 eps)))))))
(* eps (* (sin (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 7)))))
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(* eps (* (sin (+ x (* 1/2 eps))) (+ 1/2 (* -1/48 (pow eps 9)))))
(* eps (* (sin (+ x (* 1/2 eps))) (+ 1/2 (* -1/48 (pow eps 9)))))
(* eps (* (sin (+ x (* 1/2 eps))) (+ 1/2 (* -1/48 (pow eps 9)))))
(* eps (* (sin (+ x (* 1/2 eps))) (+ 1/2 (* -1/48 (pow eps 9)))))
(* eps (* (sin (- (* 1/2 eps) (* -1 x))) (+ 1/2 (* -1/48 (pow eps 9)))))
(* eps (* (sin (- (* 1/2 eps) (* -1 x))) (+ 1/2 (* -1/48 (pow eps 9)))))
(* eps (* (sin (- (* 1/2 eps) (* -1 x))) (+ 1/2 (* -1/48 (pow eps 9)))))
(* eps (* (sin (- (* 1/2 eps) (* -1 x))) (+ 1/2 (* -1/48 (pow eps 9)))))
1/2
(+ 1/2 (* -1/48 (pow eps 3)))
(+ 1/2 (* -1/48 (pow eps 3)))
(+ 1/2 (* -1/48 (pow eps 3)))
(* -1/48 (pow eps 4))
(* (pow eps 4) (- (* 1/2 (/ 1 (pow eps 4))) 1/48))
(* (pow eps 4) (- (* 1/2 (/ 1 (pow eps 4))) 1/48))
(* (pow eps 4) (- (* 1/2 (/ 1 (pow eps 4))) 1/48))
(* -1/48 (pow eps 4))
(* (pow eps 4) (- (* 1/2 (/ 1 (pow eps 4))) 1/48))
(* (pow eps 4) (- (* 1/2 (/ 1 (pow eps 4))) 1/48))
(* (pow eps 4) (- (* 1/2 (/ 1 (pow eps 4))) 1/48))
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
x
x
x
x
(* -1 x)
(* -1 x)
(* -1 x)
(* -1 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 (+ x (* 1/2 eps)))
(sin (+ x (* 1/2 eps)))
(sin (+ x (* 1/2 eps)))
(sin (+ x (* 1/2 eps)))
(sin (- x (* -1/2 eps)))
(sin (- x (* -1/2 eps)))
(sin (- x (* -1/2 eps)))
(sin (- x (* -1/2 eps)))
(sin (* 1/2 eps))
(+ (sin (* 1/2 eps)) (* x (cos (* 1/2 eps))))
(+ (sin (* 1/2 eps)) (* x (+ (cos (* 1/2 eps)) (* -1/2 (* x (sin (* 1/2 eps)))))))
(+ (sin (* 1/2 eps)) (* x (+ (cos (* 1/2 eps)) (* x (+ (* -1/2 (sin (* 1/2 eps))) (* -1/6 (* x (cos (* 1/2 eps)))))))))
(sin (+ x (* 1/2 eps)))
(sin (+ x (* 1/2 eps)))
(sin (+ x (* 1/2 eps)))
(sin (+ x (* 1/2 eps)))
(sin (- (* 1/2 eps) (* -1 x)))
(sin (- (* 1/2 eps) (* -1 x)))
(sin (- (* 1/2 eps) (* -1 x)))
(sin (- (* 1/2 eps) (* -1 x)))

Outputs
x
x
x
x
x
x
x
x
(* -1 x)
(neg.f64 x)
(* -1 x)
(neg.f64 x)
(* -1 x)
(neg.f64 x)
(* -1 x)
(neg.f64 x)
(* -1 (* eps (sin x)))
(neg.f64 (*.f64 eps (sin.f64 x)))
(* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))
(.f64 eps (-.f64 (.f64 #s(literal -1/2 binary64) (*.f64 eps (cos.f64 x))) (sin.f64 x)))
(* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* 1/8 (* eps (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 1/8 binary64)) #s(literal -1 binary64)))))
(* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/48 (* eps (cos x))) (* 1/8 (sin x))))))))
(.f64 eps (fma.f64 eps (fma.f64 (cos.f64 x) (+.f64 #s(literal -1/2 binary64) (.f64 eps (.f64 eps #s(literal 1/48 binary64)))) (.f64 (*.f64 eps (sin.f64 x)) #s(literal 1/8 binary64))) (neg.f64 (sin.f64 x))))
(* 1/24 (* (pow eps 15) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))
(.f64 (pow.f64 eps #s(literal 15 binary64)) (.f64 #s(literal 1/24 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)))))))
(* 1/24 (* (pow eps 15) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))
(.f64 (pow.f64 eps #s(literal 15 binary64)) (.f64 #s(literal 1/24 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)))))))
(* 1/24 (* (pow eps 15) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))
(.f64 (pow.f64 eps #s(literal 15 binary64)) (.f64 #s(literal 1/24 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 eps 15) (+ (* -1 (/ (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))) (pow eps 14))) (* 1/24 (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))))
(.f64 (pow.f64 eps #s(literal 15 binary64)) (fma.f64 #s(literal 1/24 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))))) (/.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))))) (neg.f64 (pow.f64 eps #s(literal 14 binary64))))))
(* 1/24 (* (pow eps 3) (+ (* (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 #s(literal 1/24 binary64) (.f64 eps (*.f64 eps eps))))
(* -1 (* (pow eps 3) (+ (* -1/24 (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))) (+ (/ (* (cos x) (sin (* 1/2 eps))) (pow eps 2)) (/ (* (cos (* 1/2 eps)) (sin x)) (pow eps 2))))))
(.f64 (fma.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))))) #s(literal -1/24 binary64) (fma.f64 (cos.f64 x) (/.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 eps eps)) (/.f64 (.f64 (sin.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64)))) (.f64 eps eps)))) (neg.f64 (.f64 eps (*.f64 eps eps))))
(* -1 (* (pow eps 3) (+ (* -1/24 (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))) (+ (/ (* (cos x) (sin (* 1/2 eps))) (pow eps 2)) (/ (* (cos (* 1/2 eps)) (sin x)) (pow eps 2))))))
(.f64 (fma.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))))) #s(literal -1/24 binary64) (fma.f64 (cos.f64 x) (/.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 eps eps)) (/.f64 (.f64 (sin.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64)))) (.f64 eps eps)))) (neg.f64 (.f64 eps (*.f64 eps eps))))
(* -1 (* (pow eps 3) (+ (* -1/24 (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))) (+ (/ (* (cos x) (sin (* 1/2 eps))) (pow eps 2)) (/ (* (cos (* 1/2 eps)) (sin x)) (pow eps 2))))))
(.f64 (fma.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))))) #s(literal -1/24 binary64) (fma.f64 (cos.f64 x) (/.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 eps eps)) (/.f64 (.f64 (sin.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64)))) (.f64 eps eps)))) (neg.f64 (.f64 eps (*.f64 eps eps))))
(* -2 (* eps (* (sin (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 5))))))
(.f64 #s(literal -2 binary64) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 eps (fma.f64 #s(literal -1/48 binary64) (pow.f64 eps #s(literal 5 binary64)) #s(literal 1/2 binary64)))))
(+ (* -2 (* eps (* x (* (cos (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 5))))))) (* -2 (* eps (* (sin (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 5)))))))
(.f64 #s(literal -2 binary64) (.f64 (.f64 eps (fma.f64 #s(literal -1/48 binary64) (pow.f64 eps #s(literal 5 binary64)) #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 (* eps (* (sin (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 5)))))) (* x (+ (* -2 (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 5)))))) (* eps (* x (* (sin (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 5)))))))))
(fma.f64 x (.f64 (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (fma.f64 #s(literal -1/48 binary64) (pow.f64 eps #s(literal 5 binary64)) #s(literal 1/2 binary64))) (.f64 eps #s(literal -2 binary64))) (.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (fma.f64 #s(literal -1/48 binary64) (pow.f64 eps #s(literal 5 binary64)) #s(literal 1/2 binary64))) (fma.f64 x (.f64 x eps) (*.f64 eps #s(literal -2 binary64)))))
(+ (* -2 (* eps (* (sin (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 5)))))) (* x (+ (* -2 (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 5)))))) (* x (+ (* 1/3 (* eps (* x (* (cos (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 5))))))) (* eps (* (sin (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 5))))))))))
(fma.f64 #s(literal -2 binary64) (.f64 (.f64 eps (fma.f64 #s(literal -1/48 binary64) (pow.f64 eps #s(literal 5 binary64)) #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 (.f64 (fma.f64 #s(literal -1/48 binary64) (pow.f64 eps #s(literal 5 binary64)) #s(literal 1/2 binary64)) (fma.f64 (.f64 eps #s(literal 1/3 binary64)) (.f64 x (cos.f64 (.f64 eps #s(literal 1/2 binary64)))) (.f64 eps (sin.f64 (.f64 eps #s(literal 1/2 binary64)))))) (.f64 x x)))
(* -2 (* eps (* (+ 1/2 (* -1/48 (pow eps 5))) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))))
(.f64 (.f64 (.f64 eps #s(literal -2 binary64)) (fma.f64 #s(literal -1/48 binary64) (pow.f64 eps #s(literal 5 binary64)) #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))))))
(* -2 (* eps (* (+ 1/2 (* -1/48 (pow eps 5))) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))))
(.f64 (.f64 (.f64 eps #s(literal -2 binary64)) (fma.f64 #s(literal -1/48 binary64) (pow.f64 eps #s(literal 5 binary64)) #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))))))
(* -2 (* eps (* (+ 1/2 (* -1/48 (pow eps 5))) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))))
(.f64 (.f64 (.f64 eps #s(literal -2 binary64)) (fma.f64 #s(literal -1/48 binary64) (pow.f64 eps #s(literal 5 binary64)) #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))))))
(* -2 (* eps (* (+ 1/2 (* -1/48 (pow eps 5))) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))))
(.f64 (.f64 (.f64 eps #s(literal -2 binary64)) (fma.f64 #s(literal -1/48 binary64) (pow.f64 eps #s(literal 5 binary64)) #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))))))
(* -2 (* eps (* (+ 1/2 (* -1/48 (pow eps 5))) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))))
(.f64 (.f64 (.f64 eps #s(literal -2 binary64)) (fma.f64 #s(literal -1/48 binary64) (pow.f64 eps #s(literal 5 binary64)) #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))))))
(* -2 (* eps (* (+ 1/2 (* -1/48 (pow eps 5))) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))))
(.f64 (.f64 (.f64 eps #s(literal -2 binary64)) (fma.f64 #s(literal -1/48 binary64) (pow.f64 eps #s(literal 5 binary64)) #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))))))
(* -2 (* eps (* (+ 1/2 (* -1/48 (pow eps 5))) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))))
(.f64 (.f64 (.f64 eps #s(literal -2 binary64)) (fma.f64 #s(literal -1/48 binary64) (pow.f64 eps #s(literal 5 binary64)) #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))))))
(* -2 (* eps (* (+ 1/2 (* -1/48 (pow eps 5))) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))))
(.f64 (.f64 (.f64 eps #s(literal -2 binary64)) (fma.f64 #s(literal -1/48 binary64) (pow.f64 eps #s(literal 5 binary64)) #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))))))
(* 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 (+ (* -1/16 (* eps (sin x))) (* 1/4 (cos x))))))
(.f64 eps (fma.f64 (sin.f64 x) (+.f64 #s(literal 1/2 binary64) (.f64 eps (.f64 eps #s(literal -1/16 binary64)))) (.f64 eps (*.f64 (cos.f64 x) #s(literal 1/4 binary64)))))
(* eps (+ (* 1/2 (sin x)) (* eps (+ (* 1/4 (cos x)) (* eps (+ (* -1/16 (sin x)) (* -1/96 (* eps (cos x)))))))))
(.f64 eps (fma.f64 eps (fma.f64 eps (.f64 (sin.f64 x) #s(literal -1/16 binary64)) (.f64 (cos.f64 x) (fma.f64 eps (.f64 eps #s(literal -1/96 binary64)) #s(literal 1/4 binary64)))) (*.f64 (sin.f64 x) #s(literal 1/2 binary64))))
(* -1/48 (* (pow eps 14) (+ (* (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 (pow.f64 eps #s(literal 14 binary64)) #s(literal -1/48 binary64)))
(* -1/48 (* (pow eps 14) (+ (* (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 (pow.f64 eps #s(literal 14 binary64)) #s(literal -1/48 binary64)))
(* -1/48 (* (pow eps 14) (+ (* (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 (pow.f64 eps #s(literal 14 binary64)) #s(literal -1/48 binary64)))
(* (pow eps 14) (+ (* -1/48 (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))) (* 1/2 (/ (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))) (pow eps 13)))))
(.f64 (pow.f64 eps #s(literal 14 binary64)) (fma.f64 #s(literal 1/2 binary64) (/.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))))) (pow.f64 eps #s(literal 13 binary64))) (.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))))) #s(literal -1/48 binary64))))
(* 1/48 (* (pow eps 16) (+ (* (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 #s(literal 1/48 binary64) (pow.f64 eps #s(literal 16 binary64))))
(* 1/48 (* (pow eps 16) (+ (* (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 #s(literal 1/48 binary64) (pow.f64 eps #s(literal 16 binary64))))
(* 1/48 (* (pow eps 16) (+ (* (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 #s(literal 1/48 binary64) (pow.f64 eps #s(literal 16 binary64))))
(* (pow eps 16) (+ (* 1/48 (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))) (* 1/2 (/ (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))) (pow eps 15)))))
(.f64 (pow.f64 eps #s(literal 16 binary64)) (fma.f64 #s(literal 1/48 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))))) (/.f64 (.f64 #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.f64 eps #s(literal 15 binary64)))))
(* eps (* (sin (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 4)))))
(.f64 eps (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (fma.f64 eps (.f64 eps (.f64 (.f64 eps eps) #s(literal -1/48 binary64))) #s(literal 1/2 binary64))))
(+ (* eps (* x (* (cos (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 4)))))) (* eps (* (sin (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 4))))))
(.f64 (.f64 eps (fma.f64 eps (.f64 eps (.f64 (.f64 eps eps) #s(literal -1/48 binary64))) #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)))))
(+ (* eps (* (sin (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 4))))) (* x (+ (* -1/2 (* eps (* x (* (sin (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 4))))))) (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 4))))))))
(fma.f64 x (.f64 (.f64 #s(literal -1/2 binary64) (.f64 x eps)) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (fma.f64 eps (.f64 eps (.f64 (.f64 eps eps) #s(literal -1/48 binary64))) #s(literal 1/2 binary64)))) (.f64 (.f64 eps (fma.f64 eps (.f64 eps (.f64 (.f64 eps eps) #s(literal -1/48 binary64))) #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))))))
(+ (* eps (* (sin (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 4))))) (* x (+ (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 4))))) (* x (+ (* -1/2 (* eps (* (sin (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 4)))))) (* -1/6 (* eps (* x (* (cos (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 4))))))))))))
(fma.f64 eps (.f64 (fma.f64 eps (.f64 eps (.f64 (.f64 eps eps) #s(literal -1/48 binary64))) #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 (.f64 (fma.f64 eps (.f64 eps (.f64 (.f64 eps eps) #s(literal -1/48 binary64))) #s(literal 1/2 binary64)) (fma.f64 (.f64 eps #s(literal -1/6 binary64)) (.f64 x (cos.f64 (.f64 eps #s(literal 1/2 binary64)))) (.f64 (.f64 eps #s(literal -1/2 binary64)) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))))) (.f64 x x)))
(* eps (* (+ 1/2 (* -1/48 (pow eps 4))) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))
(.f64 eps (.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))))) (fma.f64 eps (.f64 eps (.f64 (.f64 eps eps) #s(literal -1/48 binary64))) #s(literal 1/2 binary64))))
(* eps (* (+ 1/2 (* -1/48 (pow eps 4))) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))
(.f64 eps (.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))))) (fma.f64 eps (.f64 eps (.f64 (.f64 eps eps) #s(literal -1/48 binary64))) #s(literal 1/2 binary64))))
(* eps (* (+ 1/2 (* -1/48 (pow eps 4))) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))
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(* (pow eps 10) (+ (* -1/48 (sin (+ x (* 1/2 eps)))) (* 1/2 (/ (sin (+ x (* 1/2 eps))) (pow eps 9)))))
(.f64 (pow.f64 eps #s(literal 10 binary64)) (fma.f64 #s(literal 1/2 binary64) (/.f64 (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (pow.f64 eps #s(literal 9 binary64))) (.f64 #s(literal -1/48 binary64) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))))
(* -1/48 (* (pow eps 11) (sin (- x (* -1/2 eps)))))
(.f64 (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (.f64 #s(literal -1/48 binary64) (pow.f64 eps #s(literal 11 binary64))))
(* -1/48 (* (pow eps 11) (sin (- x (* -1/2 eps)))))
(.f64 (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (.f64 #s(literal -1/48 binary64) (pow.f64 eps #s(literal 11 binary64))))
(* -1 (* (pow eps 11) (+ (* -1/2 (/ (sin (- x (* -1/2 eps))) (pow eps 10))) (* 1/48 (sin (- x (* -1/2 eps)))))))
(.f64 (fma.f64 #s(literal 1/48 binary64) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (.f64 #s(literal -1/2 binary64) (/.f64 (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (pow.f64 eps #s(literal 10 binary64))))) (neg.f64 (pow.f64 eps #s(literal 11 binary64))))
(* -1 (* (pow eps 11) (+ (* -1/2 (/ (sin (- x (* -1/2 eps))) (pow eps 10))) (* 1/48 (sin (- x (* -1/2 eps)))))))
(.f64 (fma.f64 #s(literal 1/48 binary64) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (.f64 #s(literal -1/2 binary64) (/.f64 (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (pow.f64 eps #s(literal 10 binary64))))) (neg.f64 (pow.f64 eps #s(literal 11 binary64))))
(* eps (* (sin (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 7)))))
(.f64 (.f64 eps (fma.f64 #s(literal -1/48 binary64) (pow.f64 eps #s(literal 7 binary64)) #s(literal 1/2 binary64))) (sin.f64 (*.f64 eps #s(literal 1/2 binary64))))
(+ (* eps (* x (* (cos (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 7)))))) (* eps (* (sin (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 7))))))
(.f64 (.f64 (fma.f64 #s(literal -1/48 binary64) (pow.f64 eps #s(literal 7 binary64)) #s(literal 1/2 binary64)) eps) (fma.f64 x (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))))
(+ (* eps (* (sin (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 7))))) (* x (+ (* -1/2 (* eps (* x (* (sin (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 7))))))) (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 7))))))))
(fma.f64 x (.f64 (.f64 (.f64 eps (fma.f64 #s(literal -1/48 binary64) (pow.f64 eps #s(literal 7 binary64)) #s(literal 1/2 binary64))) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))) (.f64 x #s(literal -1/2 binary64))) (.f64 (.f64 (fma.f64 #s(literal -1/48 binary64) (pow.f64 eps #s(literal 7 binary64)) #s(literal 1/2 binary64)) eps) (fma.f64 x (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 (*.f64 eps #s(literal 1/2 binary64))))))
(+ (* eps (* (sin (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 7))))) (* x (+ (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 7))))) (* x (+ (* -1/2 (* eps (* (sin (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 7)))))) (* -1/6 (* eps (* x (* (cos (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 7))))))))))))
(fma.f64 eps (.f64 (fma.f64 #s(literal -1/48 binary64) (pow.f64 eps #s(literal 7 binary64)) #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 (.f64 x x) (.f64 (fma.f64 #s(literal -1/48 binary64) (pow.f64 eps #s(literal 7 binary64)) #s(literal 1/2 binary64)) (fma.f64 (.f64 eps #s(literal -1/6 binary64)) (.f64 x (cos.f64 (.f64 eps #s(literal 1/2 binary64)))) (.f64 (.f64 eps #s(literal -1/2 binary64)) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))))))
(* eps (* (sin (+ x (* 1/2 eps))) (+ 1/2 (* -1/48 (pow eps 9)))))
(.f64 (fma.f64 #s(literal -1/48 binary64) (pow.f64 eps #s(literal 9 binary64)) #s(literal 1/2 binary64)) (.f64 eps (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x))))
(* eps (* (sin (+ x (* 1/2 eps))) (+ 1/2 (* -1/48 (pow eps 9)))))
(.f64 (fma.f64 #s(literal -1/48 binary64) (pow.f64 eps #s(literal 9 binary64)) #s(literal 1/2 binary64)) (.f64 eps (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x))))
(* eps (* (sin (+ x (* 1/2 eps))) (+ 1/2 (* -1/48 (pow eps 9)))))
(.f64 (fma.f64 #s(literal -1/48 binary64) (pow.f64 eps #s(literal 9 binary64)) #s(literal 1/2 binary64)) (.f64 eps (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x))))
(* eps (* (sin (+ x (* 1/2 eps))) (+ 1/2 (* -1/48 (pow eps 9)))))
(.f64 (fma.f64 #s(literal -1/48 binary64) (pow.f64 eps #s(literal 9 binary64)) #s(literal 1/2 binary64)) (.f64 eps (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x))))
(* eps (* (sin (- (* 1/2 eps) (* -1 x))) (+ 1/2 (* -1/48 (pow eps 9)))))
(.f64 (fma.f64 #s(literal -1/48 binary64) (pow.f64 eps #s(literal 9 binary64)) #s(literal 1/2 binary64)) (.f64 eps (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x))))
(* eps (* (sin (- (* 1/2 eps) (* -1 x))) (+ 1/2 (* -1/48 (pow eps 9)))))
(.f64 (fma.f64 #s(literal -1/48 binary64) (pow.f64 eps #s(literal 9 binary64)) #s(literal 1/2 binary64)) (.f64 eps (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x))))
(* eps (* (sin (- (* 1/2 eps) (* -1 x))) (+ 1/2 (* -1/48 (pow eps 9)))))
(.f64 (fma.f64 #s(literal -1/48 binary64) (pow.f64 eps #s(literal 9 binary64)) #s(literal 1/2 binary64)) (.f64 eps (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x))))
(* eps (* (sin (- (* 1/2 eps) (* -1 x))) (+ 1/2 (* -1/48 (pow eps 9)))))
(.f64 (fma.f64 #s(literal -1/48 binary64) (pow.f64 eps #s(literal 9 binary64)) #s(literal 1/2 binary64)) (.f64 eps (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x))))
1/2
#s(literal 1/2 binary64)
(+ 1/2 (* -1/48 (pow eps 3)))
(fma.f64 eps (.f64 (.f64 eps eps) #s(literal -1/48 binary64)) #s(literal 1/2 binary64))
(+ 1/2 (* -1/48 (pow eps 3)))
(fma.f64 eps (.f64 (.f64 eps eps) #s(literal -1/48 binary64)) #s(literal 1/2 binary64))
(+ 1/2 (* -1/48 (pow eps 3)))
(fma.f64 eps (.f64 (.f64 eps eps) #s(literal -1/48 binary64)) #s(literal 1/2 binary64))
(* -1/48 (pow eps 4))
(.f64 eps (.f64 eps (.f64 (.f64 eps eps) #s(literal -1/48 binary64))))
(* (pow eps 4) (- (* 1/2 (/ 1 (pow eps 4))) 1/48))
(.f64 (.f64 (.f64 eps (.f64 eps eps)) eps) (+.f64 #s(literal -1/48 binary64) (/.f64 #s(literal 1/2 binary64) (.f64 (.f64 eps (*.f64 eps eps)) eps))))
(* (pow eps 4) (- (* 1/2 (/ 1 (pow eps 4))) 1/48))
(.f64 (.f64 (.f64 eps (.f64 eps eps)) eps) (+.f64 #s(literal -1/48 binary64) (/.f64 #s(literal 1/2 binary64) (.f64 (.f64 eps (*.f64 eps eps)) eps))))
(* (pow eps 4) (- (* 1/2 (/ 1 (pow eps 4))) 1/48))
(.f64 (.f64 (.f64 eps (.f64 eps eps)) eps) (+.f64 #s(literal -1/48 binary64) (/.f64 #s(literal 1/2 binary64) (.f64 (.f64 eps (*.f64 eps eps)) eps))))
(* -1/48 (pow eps 4))
(.f64 eps (.f64 eps (.f64 (.f64 eps eps) #s(literal -1/48 binary64))))
(* (pow eps 4) (- (* 1/2 (/ 1 (pow eps 4))) 1/48))
(.f64 (.f64 (.f64 eps (.f64 eps eps)) eps) (+.f64 #s(literal -1/48 binary64) (/.f64 #s(literal 1/2 binary64) (.f64 (.f64 eps (*.f64 eps eps)) eps))))
(* (pow eps 4) (- (* 1/2 (/ 1 (pow eps 4))) 1/48))
(.f64 (.f64 (.f64 eps (.f64 eps eps)) eps) (+.f64 #s(literal -1/48 binary64) (/.f64 #s(literal 1/2 binary64) (.f64 (.f64 eps (*.f64 eps eps)) eps))))
(* (pow eps 4) (- (* 1/2 (/ 1 (pow eps 4))) 1/48))
(.f64 (.f64 (.f64 eps (.f64 eps eps)) eps) (+.f64 #s(literal -1/48 binary64) (/.f64 #s(literal 1/2 binary64) (.f64 (.f64 eps (*.f64 eps eps)) eps))))
(* 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
x
x
(* -1 x)
(neg.f64 x)
(* -1 x)
(neg.f64 x)
(* -1 x)
(neg.f64 x)
(* -1 x)
(neg.f64 x)
(sin x)
(sin.f64 x)
(+ (sin x) (* 1/2 (* eps (cos x))))
(fma.f64 (*.f64 eps (cos.f64 x)) #s(literal 1/2 binary64) (sin.f64 x))
(+ (sin x) (* eps (+ (* -1/8 (* eps (sin x))) (* 1/2 (cos x)))))
(fma.f64 eps (fma.f64 eps (.f64 (sin.f64 x) #s(literal -1/8 binary64)) (.f64 (cos.f64 x) #s(literal 1/2 binary64))) (sin.f64 x))
(+ (sin x) (* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/8 (sin x)) (* -1/48 (* eps (cos x))))))))
(fma.f64 eps (fma.f64 eps (.f64 (sin.f64 x) #s(literal -1/8 binary64)) (.f64 (cos.f64 x) (fma.f64 eps (*.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (sin.f64 x))
(sin (+ x (* 1/2 eps)))
(sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x))
(sin (+ x (* 1/2 eps)))
(sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x))
(sin (+ x (* 1/2 eps)))
(sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x))
(sin (+ x (* 1/2 eps)))
(sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x))
(sin (- x (* -1/2 eps)))
(sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x))
(sin (- x (* -1/2 eps)))
(sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x))
(sin (- x (* -1/2 eps)))
(sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x))
(sin (- x (* -1/2 eps)))
(sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x))
(sin (* 1/2 eps))
(sin.f64 (*.f64 eps #s(literal 1/2 binary64)))
(+ (sin (* 1/2 eps)) (* x (cos (* 1/2 eps))))
(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)) (* x (+ (cos (* 1/2 eps)) (* -1/2 (* x (sin (* 1/2 eps)))))))
(fma.f64 x (fma.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 x #s(literal -1/2 binary64)) (cos.f64 (.f64 eps #s(literal 1/2 binary64)))) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))
(+ (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 x (fma.f64 #s(literal -1/2 binary64) (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 x #s(literal -1/6 binary64)))) (cos.f64 (.f64 eps #s(literal 1/2 binary64)))) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))
(sin (+ x (* 1/2 eps)))
(sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x))
(sin (+ x (* 1/2 eps)))
(sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x))
(sin (+ x (* 1/2 eps)))
(sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x))
(sin (+ x (* 1/2 eps)))
(sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x))
(sin (- (* 1/2 eps) (* -1 x)))
(sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x))
(sin (- (* 1/2 eps) (* -1 x)))
(sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x))
(sin (- (* 1/2 eps) (* -1 x)))
(sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x))
(sin (- (* 1/2 eps) (* -1 x)))
(sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x))

eval109.0ms (0.6%)

Memory: 10.9MiB live, 89.8MiB allocated
Compiler: Compiled 33 310 to 2 976 computations (91.1% saved)

prune106.0ms (0.6%)

Memory

-4.6MiB live, 111.4MiB allocated

Pruning

30 alts after pruning (22 fresh and 8 done)

	Pruned	Kept	Total
New	966	10	976
Fresh	2	12	14
Picked	1	4	5
Done	0	4	4
Total	969	30	999

Accuracy

100.0%

Counts

999 → 30

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))))
	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))))
	53.2%	(fma.f64 (cos.f64 x) (cos.f64 eps) (neg.f64 (fma.f64 (sin.f64 x) (sin.f64 eps) (cos.f64 x))))
	76.6%	(fma.f64 x (neg.f64 eps) (*.f64 eps eps))
✓	98.1%	(fma.f64 x (neg.f64 eps) (.f64 #s(literal -1/2 binary64) (.f64 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))
	78.1%	(.f64 (fma.f64 (fma.f64 (.f64 x x) (fma.f64 x (.f64 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))
	99.5%	(.f64 (fma.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x)) (.f64 eps (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64))) (.f64 (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 x)) (.f64 eps (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64))))) #s(literal -2 binary64))
	99.4%	(.f64 (.f64 (/.f64 eps (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/48 binary64) (.f64 eps 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)))))) #s(literal -2 binary64))
	99.4%	(.f64 (.f64 (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64))) (fma.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x) (.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 x)))) #s(literal -2 binary64))
	99.4%	(.f64 (.f64 (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64))) (fma.f64 eps (fma.f64 eps (.f64 (sin.f64 x) #s(literal -1/8 binary64)) (.f64 (cos.f64 x) (fma.f64 eps (*.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (sin.f64 x))) #s(literal -2 binary64))
✓	99.4%	(.f64 (.f64 (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64))) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x))) #s(literal -2 binary64))
	78.0%	(.f64 (.f64 x (fma.f64 x (*.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64))) eps)
	99.1%	(*.f64 (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (neg.f64 eps))
✓	78.4%	(*.f64 (sin.f64 x) (neg.f64 eps))
	78.0%	(.f64 x (fma.f64 (.f64 x (*.f64 x #s(literal 1/6 binary64))) eps (neg.f64 eps)))
	78.1%	(.f64 x (fma.f64 x (.f64 x (.f64 eps (fma.f64 (.f64 x x) #s(literal -1/120 binary64) #s(literal 1/6 binary64)))) (neg.f64 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 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/4 binary64)) (.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))))))
	97.9%	(.f64 eps (-.f64 (.f64 eps #s(literal -1/2 binary64)) x))
	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)))
	6.5%	(neg.f64 x)
✓	51.6%	#s(literal 0 binary64)

Compiler

Compiled 1 238 to 513 computations (58.6% saved)

regimes33.0ms (0.2%)

Memory

17.2MiB live, 17.2MiB allocated

Counts

48 → 1

Calls

Call 1

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

Calls

3 calls:

11.0ms	x
11.0ms	eps
9.0ms	(-.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)

regimes27.0ms (0.2%)

Memory

-32.5MiB live, 14.1MiB allocated

Counts

37 → 1

Calls

Call 1

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

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

Calls

3 calls:

9.0ms	eps
9.0ms	x
8.0ms	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))

Results

Accuracy	Segments	Branch
99.4%	1	`x`
99.4%	1	`eps`
99.4%	1	`(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))`

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes22.0ms (0.1%)

Memory

12.5MiB live, 12.5MiB allocated

Counts

31 → 1

Calls

Call 1

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

Calls

3 calls:

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

Results

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

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes19.0ms (0.1%)

Memory

11.4MiB live, 11.4MiB allocated

Counts

26 → 1

Calls

Call 1

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

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

Calls

3 calls:

7.0ms	x
6.0ms	eps
5.0ms	(-.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)

regimes19.0ms (0.1%)

Memory

-28.6MiB live, 10.8MiB allocated

Counts

25 → 1

Calls

Call 1

Inputs
#s(literal 0 binary64)
(neg.f64 x)
(+.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 eps))
(fma.f64 x (neg.f64 eps) (.f64 #s(literal -1/2 binary64) (.f64 eps eps)))
(.f64 eps (.f64 eps (fma.f64 x (*.f64 x #s(literal 1/4 binary64)) #s(literal -1/2 binary64))))
(.f64 x (.f64 eps (fma.f64 x (*.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64))))
(.f64 (.f64 x (fma.f64 x (*.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64))) eps)
(.f64 x (fma.f64 (.f64 x (*.f64 x #s(literal 1/6 binary64))) eps (neg.f64 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))))
(fma.f64 x (-.f64 (.f64 x (.f64 eps (neg.f64 eps))) eps) (.f64 #s(literal -1/2 binary64) (.f64 eps eps)))
(.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 x (.f64 x (.f64 eps (fma.f64 (.f64 x x) #s(literal -1/120 binary64) #s(literal 1/6 binary64)))) (neg.f64 eps)))
(fma.f64 x (-.f64 (.f64 x (.f64 eps (.f64 eps #s(literal 1/4 binary64)))) eps) (.f64 #s(literal -1/2 binary64) (*.f64 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))))
(.f64 (fma.f64 (fma.f64 (.f64 x x) (fma.f64 x (.f64 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 (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 (.f64 eps eps) #s(literal 1/4 binary64)) (.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
(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
5.0ms	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))

Results

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

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes15.0ms (0.1%)

Memory

9.2MiB live, 9.2MiB allocated

Counts

19 → 1

Calls

Call 1

Inputs
#s(literal 0 binary64)
(neg.f64 x)
(+.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 eps))
(fma.f64 x (neg.f64 eps) (.f64 #s(literal -1/2 binary64) (.f64 eps eps)))
(.f64 eps (.f64 eps (fma.f64 x (*.f64 x #s(literal 1/4 binary64)) #s(literal -1/2 binary64))))
(.f64 x (.f64 eps (fma.f64 x (*.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64))))
(.f64 (.f64 x (fma.f64 x (*.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64))) eps)
(.f64 x (fma.f64 (.f64 x (*.f64 x #s(literal 1/6 binary64))) eps (neg.f64 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))))
(fma.f64 x (-.f64 (.f64 x (.f64 eps (neg.f64 eps))) eps) (.f64 #s(literal -1/2 binary64) (.f64 eps eps)))
(.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 x (.f64 x (.f64 eps (fma.f64 (.f64 x x) #s(literal -1/120 binary64) #s(literal 1/6 binary64)))) (neg.f64 eps)))
(fma.f64 x (-.f64 (.f64 x (.f64 eps (.f64 eps #s(literal 1/4 binary64)))) eps) (.f64 #s(literal -1/2 binary64) (*.f64 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	x
5.0ms	eps
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)

regimes13.0ms (0.1%)

Memory

8.3MiB live, 8.3MiB allocated

Counts

16 → 1

Calls

Call 1

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

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

7.8MiB live, 7.8MiB allocated

Counts

14 → 1

Calls

Call 1

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

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
98.1%	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)

regimes8.0ms (0%)

Memory

6.1MiB live, 6.1MiB allocated

Counts

8 → 1

Calls

Call 1

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

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

Calls

3 calls:

3.0ms	eps
3.0ms	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)

regimes7.0ms (0%)

Memory

-34.2MiB live, 5.5MiB allocated

Counts

6 → 1

Calls

Call 1

Inputs
#s(literal 0 binary64)
(neg.f64 x)
(+.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:

3.0ms	eps
2.0ms	x
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)

regimes5.0ms (0%)

Memory

4.6MiB live, 4.6MiB allocated

Accuracy

Total -29.5b remaining (-95.2%)

Threshold costs -29.5b (-95.2%)

Counts

3 → 1

Calls

Call 1

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

Outputs
#s(literal 0 binary64)

Calls

3 calls:

2.0ms	eps
2.0ms	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)

simplify8.0ms (0%)

Memory

4.9MiB live, 4.9MiB allocated

Algorithm

1×	egg-herbie

Rules

58×	`*-commutative_binary64`
22×	`+-commutative_binary64`
18×	`sub-neg_binary64`
14×	`neg-sub0_binary64`
14×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	53	115
1	88	115
2	110	115
3	126	115
4	134	115
5	135	115

Stop Event

1×

saturated

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

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

soundness1.2s (7%)

Memory

-10.5MiB live, 29.1MiB allocated

Rules

14 158×	`lower-fma.f64`
14 158×	`lower-fma.f32`
12 600×	`lower-fma.f64`
12 600×	`lower-fma.f32`
11 698×	`lower-fma.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	37	185
0	71	185
1	249	155
2	1929	155
0	8123	153
0	6	16
0	10	16
1	54	16
2	380	16
3	4694	16
0	8209	16
0	420	4200
1	1309	3899
2	4088	3827
0	8083	3542
0	34	170
0	62	170
1	186	168
2	1212	167
0	8629	160
0	521	4435
1	1690	4318
2	5821	4194
0	8204	3857
0	105	498
1	277	495
2	609	495
3	2398	494
4	7880	494
0	8026	474
0	413	3236
1	1213	3123
2	3294	3058
0	8059	2872

Stop Event

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

Compiler

Compiled 412 to 257 computations (37.6% saved)

preprocess73.0ms (0.4%)

Memory: 28.8MiB live, 71.4MiB allocated
Compiler: Compiled 320 to 166 computations (48.1% 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

analyze41.0ms (0.2%)

sample8.1s (47.4%)

preprocess29.0ms (0.2%)

explain406.0ms (2.4%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify11.0ms (0.1%)

localize89.0ms (0.5%)

series6.0ms (0%)

rewrite273.0ms (1.6%)

simplify471.0ms (2.7%)

eval35.0ms (0.2%)

prune40.0ms (0.2%)

simplify377.0ms (2.2%)

localize227.0ms (1.3%)

series42.0ms (0.2%)

rewrite357.0ms (2.1%)

simplify836.0ms (4.9%)

eval207.0ms (1.2%)

prune190.0ms (1.1%)

simplify745.0ms (4.3%)

localize522.0ms (3%)

series92.0ms (0.5%)

rewrite595.0ms (3.5%)

simplify350.0ms (2%)

eval135.0ms (0.8%)

prune124.0ms (0.7%)

simplify419.0ms (2.4%)

localize127.0ms (0.7%)

series65.0ms (0.4%)

rewrite285.0ms (1.7%)

simplify267.0ms (1.6%)

eval109.0ms (0.6%)

prune106.0ms (0.6%)

regimes33.0ms (0.2%)

regimes27.0ms (0.2%)

regimes22.0ms (0.1%)

regimes19.0ms (0.1%)

regimes19.0ms (0.1%)

regimes15.0ms (0.1%)

regimes13.0ms (0.1%)

regimes12.0ms (0.1%)

regimes8.0ms (0%)

regimes7.0ms (0%)

regimes5.0ms (0%)

simplify8.0ms (0%)

soundness1.2s (7%)

preprocess73.0ms (0.4%)

end0.0ms (0%)

Profiling

Iter	Nodes	Cost
0	18	41
1	38	37
2	81	35
3	152	35
4	278	35
5	370	35
6	448	35
7	485	35
8	531	35
9	546	35
10	554	35
0	6	7
0	10	7
1	13	7
2	18	7
3	24	7
4	32	7
5	47	7
6	80	7
7	107	7
8	151	7
9	166	7
10	174	7
0	174	7

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