Metrics for 2sin (example 3.3)

analyze45.0ms (0.3%)

Memory

16.4MiB live, 53.8MiB 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)

sample5.8s (40.9%)

Memory

-184.4MiB live, 7 408.6MiB allocated

Samples

3.2s	25 979×	0	invalid
618.0ms	5 468×	0	valid
501.0ms	2 788×	1	valid

Precisions

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

const: 659.0ms (20.7% of total)

ival-sin: 568.0ms (17.8% of total)

ival-<=: 462.0ms (14.5% of total)

ival-add: 340.0ms (10.7% of total)

ival-fabs: 253.0ms (7.9% of total)

ival-sub: 250.0ms (7.8% of total)

ival-mult: 241.0ms (7.6% of total)

ival-<: 216.0ms (6.8% of total)

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

exact: 46.0ms (1.4% of total)

adjust: 36.0ms (1.1% of total)

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

Bogosity

preprocess24.0ms (0.2%)

Memory

9.4MiB live, 9.4MiB allocated

Algorithm

2×	egg-herbie

Rules

114×	`sub-neg`
80×	`accelerator-lowering-fma.f32`
80×	`accelerator-lowering-fma.f64`
76×	`cancel-sign-sub-inv`
62×	`associate--r+`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	46
1	43	42
2	92	42
3	181	42
4	321	42
5	398	42
6	483	42
7	525	42
8	534	42
0	6	7
1	9	7
2	14	7
3	20	7
4	28	7
5	43	7
6	76	7
7	101	7
8	144	7
9	159	7
10	167	7
0	167	7

Stop Event

1×	iter limit
1×	saturated
1×	saturated

Calls

Call 1

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

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

Call 2

Inputs
(- (sin (+ x eps)) (sin x))
(- (sin (+ (neg x) eps)) (sin (neg x)))
(- (sin (+ x (neg eps))) (sin x))
(neg (- (sin (+ (neg x) eps)) (sin (neg x))))
(neg (- (sin (+ x (neg eps))) (sin x)))
(- (sin (+ eps x)) (sin eps))

Outputs
(- (sin (+ x eps)) (sin x))
(- (sin (+ (neg x) eps)) (sin (neg x)))
(+ (sin x) (sin (- eps x)))
(- (sin (+ x (neg eps))) (sin x))
(- (sin (- x eps)) (sin x))
(neg (- (sin (+ (neg x) eps)) (sin (neg x))))
(- (sin (- x eps)) (sin x))
(neg (- (sin (+ x (neg eps))) (sin x)))
(+ (sin x) (sin (- eps x)))
(- (sin (+ eps x)) (sin eps))
(- (sin (+ x eps)) (sin eps))

explain120.0ms (0.9%)

Memory

-8.3MiB live, 82.4MiB allocated

FPErrors

Click to see full error table

Ground Truth	Overpredictions	Example	Underpredictions	Example	Subexpression
224	2	(2.6350061737742762e-148 1.828268937053433e-150)	3	(-4.272956259198589e-216 8.963890421763868e-218)	`(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))`
0	0	-	0	-	`(sin.f64 (+.f64 x eps))`
0	0	-	0	-	`eps`
0	0	-	0	-	`(+.f64 x eps)`
0	0	-	0	-	`(sin.f64 x)`
0	0	-	0	-	`x`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`-.f64`	`(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))`	cancellation	223	9

Confusion

	Predicted +	Predicted -
+	221	4
-	2	29

Precision

0.9910313901345291

Recall

0.9822222222222222

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	221	4	0
-	2	5	24

Precision?

0.9698275862068966

Recall?

1.0

Freqs

test

number	freq
0	33
1	223

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

43.0ms	180×	1	valid
16.0ms	330×	0	valid
0.0ms	2×	2	valid

Compiler

Compiled 58 to 28 computations (51.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 44.0ms

ival-sin: 36.0ms (81% of total)

ival-add: 3.0ms (6.7% of total)

ival-sub: 3.0ms (6.7% of total)

adjust: 2.0ms (4.5% of total)

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

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

eval0.0ms (0%)

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

prune1.0ms (0%)

Memory

1.0MiB live, 1.0MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	61.3%	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))

Compiler

Compiled 9 to 6 computations (33.3% saved)

simplify8.0ms (0.1%)

Memory

8.0MiB live, 8.0MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

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

Rules

80×	`accelerator-lowering-fma.f32`
80×	`accelerator-lowering-fma.f64`
48×	`-lowering-.f32`
48×	`-lowering-.f64`
36×	`+-lowering-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	18
1	9	18
2	14	18
3	20	18
4	28	18
5	43	18
6	76	18
7	101	18
8	144	18
9	159	18
10	167	18
0	167	18

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

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

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

localize29.0ms (0.2%)

Memory

-9.7MiB live, 27.5MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(+.f64 x eps)
✓	accuracy	100.0%	(sin.f64 x)
✓	accuracy	100.0%	(sin.f64 (+.f64 x eps))
✓	accuracy	61.3%	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))

Samples

14.0ms	90×	1	valid
8.0ms	165×	0	valid
0.0ms	1×	2	valid

Compiler

Compiled 20 to 8 computations (60% saved)

Precisions

Click to see histograms. Total time spent on operations: 15.0ms

ival-add: 8.0ms (54.3% of total)

ival-sin: 4.0ms (27.1% of total)

adjust: 1.0ms (6.8% of total)

ival-sub: 1.0ms (6.8% of total)

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

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

series4.0ms (0%)

Memory

5.5MiB live, 5.5MiB allocated

Counts

4 → 84

Calls

Call 1

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

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

Calls

21 calls:

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

rewrite601.0ms (4.3%)

Memory

27.7MiB live, 301.2MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

4 986×	`accelerator-lowering-fma.f32`
4 986×	`accelerator-lowering-fma.f64`
4 676×	`-lowering-.f32`
4 676×	`-lowering-.f64`
2 176×	`/-lowering-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	16
1	49	16
2	376	16
3	4763	16
0	8212	16

Stop Event

1×	iter limit
1×	node limit

Counts

4 → 214

Calls

Call 1

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

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

simplify413.0ms (2.9%)

Memory

-27.7MiB live, 527.7MiB allocated

Algorithm

1×	egg-herbie

Rules

16 678×	`accelerator-lowering-fma.f32`
16 678×	`accelerator-lowering-fma.f64`
4 132×	`-lowering-.f32`
4 132×	`-lowering-.f64`
2 614×	`+-lowering-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	iter limit
1×	node limit

Counts

84 → 84

Calls

Call 1

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

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

eval36.0ms (0.3%)

Memory: 13.5MiB live, 91.1MiB allocated
Compiler: Compiled 7 797 to 843 computations (89.2% saved)

prune36.0ms (0.3%)

Memory

-13.8MiB live, 102.5MiB allocated

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	291	7	298
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	291	8	299

Accuracy

100.0%

Counts

299 → 8

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	60.6%	(-.f64 (sin.f64 (+.f64 x eps)) (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) (.f64 x (*.f64 x x)) x))
▶	60.8%	(-.f64 (sin.f64 (+.f64 x eps)) (fma.f64 (fma.f64 x (.f64 x (fma.f64 (.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64))) #s(literal -1/6 binary64)) (.f64 x (.f64 x x)) x))
✓	61.3%	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
▶	100.0%	(.f64 (.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (cos.f64 (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
	99.9%	(.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (.f64 (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x))))
	99.7%	(.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x)))
▶	99.3%	(*.f64 eps (cos.f64 x))
▶	98.4%	(sin.f64 eps)

Compiler

Compiled 219 to 140 computations (36.1% saved)

simplify314.0ms (2.2%)

Memory

48.2MiB live, 597.7MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 15 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(fma.f64 (fma.f64 x (.f64 x (fma.f64 (.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64))) #s(literal -1/6 binary64)) (.f64 x (.f64 x x)) x)
✓	cost-diff	0	(+.f64 x eps)
✓	cost-diff	0	(sin.f64 (+.f64 x eps))
✓	cost-diff	128	(-.f64 (sin.f64 (+.f64 x eps)) (fma.f64 (fma.f64 x (.f64 x (fma.f64 (.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64))) #s(literal -1/6 binary64)) (.f64 x (.f64 x x)) x))
✓	cost-diff	0	(fma.f64 (fma.f64 (.f64 x x) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) (.f64 x (*.f64 x x)) x)
✓	cost-diff	0	(+.f64 x eps)
✓	cost-diff	0	(sin.f64 (+.f64 x eps))
✓	cost-diff	128	(-.f64 (sin.f64 (+.f64 x eps)) (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) (.f64 x (*.f64 x x)) x))
✓	cost-diff	0	(cos.f64 x)
✓	cost-diff	0	(*.f64 eps (cos.f64 x))
✓	cost-diff	0	(sin.f64 eps)
✓	cost-diff	0	(.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (cos.f64 (*.f64 (+.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))) (cos.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

13 638×	`accelerator-lowering-fma.f32`
13 638×	`accelerator-lowering-fma.f64`
3 030×	`-lowering-.f32`
3 030×	`-lowering-.f64`
2 196×	`--lowering--.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	36	220
1	85	220
2	227	220
3	632	212
4	2205	212
5	4253	212
6	6021	212
7	7790	212
0	8222	192

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

Inputs
(* (* (sin (* (+ eps 0) 1/2)) (cos (* (+ x (+ x eps)) 1/2))) 2)
(* (sin (* (+ eps 0) 1/2)) (cos (* (+ x (+ x eps)) 1/2)))
(sin (* (+ eps 0) 1/2))
(* (+ eps 0) 1/2)
(+ eps 0)
eps
0
1/2
(cos (* (+ x (+ x eps)) 1/2))
(* (+ x (+ x eps)) 1/2)
(+ x (+ x eps))
x
(+ x eps)
2
(sin eps)
eps
(* eps (cos x))
eps
(cos x)
x
(- (sin (+ x eps)) (+ (* (+ (* (* x x) 1/120) -1/6) (* x (* x x))) x))
(sin (+ x eps))
(+ x eps)
x
eps
(+ (* (+ (* (* x x) 1/120) -1/6) (* x (* x x))) x)
(+ (* (* x x) 1/120) -1/6)
(* x x)
1/120
-1/6
(* x (* x x))
(- (sin (+ x eps)) (+ (* (+ (* x (* x (+ (* (* x x) -1/5040) 1/120))) -1/6) (* x (* x x))) x))
(sin (+ x eps))
(+ x eps)
x
eps
(+ (* (+ (* x (* x (+ (* (* x x) -1/5040) 1/120))) -1/6) (* x (* x x))) x)
(+ (* x (* x (+ (* (* x x) -1/5040) 1/120))) -1/6)
(* x (+ (* (* x x) -1/5040) 1/120))
(+ (* (* x x) -1/5040) 1/120)
(* x x)
-1/5040
1/120
-1/6
(* x (* x x))

Outputs
(* (* (sin (* (+ eps 0) 1/2)) (cos (* (+ x (+ x eps)) 1/2))) 2)
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (*.f64 (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) #s(literal 2 binary64)))
(* (sin (* (+ eps 0) 1/2)) (cos (* (+ x (+ x eps)) 1/2)))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))
(sin (* (+ eps 0) 1/2))
(sin.f64 (*.f64 eps #s(literal 1/2 binary64)))
(* (+ eps 0) 1/2)
(*.f64 eps #s(literal 1/2 binary64))
(+ eps 0)
eps
eps
0
#s(literal 0 binary64)
1/2
#s(literal 1/2 binary64)
(cos (* (+ x (+ x eps)) 1/2))
(cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x))
(* (+ x (+ x eps)) 1/2)
(fma.f64 eps #s(literal 1/2 binary64) x)
(+ x (+ x eps))
(+.f64 eps (+.f64 x x))
x
(+ x eps)
(+.f64 eps x)
2
#s(literal 2 binary64)
(sin eps)
(sin.f64 eps)
eps
(* eps (cos x))
(*.f64 eps (cos.f64 x))
eps
(cos x)
(cos.f64 x)
x
(- (sin (+ x eps)) (+ (* (+ (* (* x x) 1/120) -1/6) (* x (* x x))) x))
(fma.f64 x (fma.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal -1/120 binary64)) #s(literal 1/6 binary64))) #s(literal -1 binary64)) (sin.f64 (+.f64 eps x)))
(sin (+ x eps))
(sin.f64 (+.f64 eps x))
(+ x eps)
(+.f64 eps x)
x
eps
(+ (* (+ (* (* x x) 1/120) -1/6) (* x (* x x))) x)
(fma.f64 (fma.f64 x (.f64 x #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) (.f64 x (*.f64 x x)) x)
(+ (* (* x x) 1/120) -1/6)
(fma.f64 x (*.f64 x #s(literal 1/120 binary64)) #s(literal -1/6 binary64))
(* x x)
(*.f64 x x)
1/120
#s(literal 1/120 binary64)
-1/6
#s(literal -1/6 binary64)
(* x (* x x))
(.f64 x (.f64 x x))
(- (sin (+ x eps)) (+ (* (+ (* x (* x (+ (* (* x x) -1/5040) 1/120))) -1/6) (* x (* x x))) x))
(fma.f64 x (fma.f64 x (.f64 x (fma.f64 x (.f64 x (fma.f64 x (*.f64 x #s(literal 1/5040 binary64)) #s(literal -1/120 binary64))) #s(literal 1/6 binary64))) #s(literal -1 binary64)) (sin.f64 (+.f64 eps x)))
(sin (+ x eps))
(sin.f64 (+.f64 eps x))
(+ x eps)
(+.f64 eps x)
x
eps
(+ (* (+ (* x (* x (+ (* (* x x) -1/5040) 1/120))) -1/6) (* x (* x x))) x)
(fma.f64 (.f64 x (.f64 x x)) (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) x)
(+ (* x (* x (+ (* (* x x) -1/5040) 1/120))) -1/6)
(fma.f64 (.f64 x x) (fma.f64 (.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) #s(literal -1/6 binary64))
(* x (+ (* (* x x) -1/5040) 1/120))
(.f64 x (fma.f64 (.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)))
(+ (* (* x x) -1/5040) 1/120)
(fma.f64 (*.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64))
(* x x)
(*.f64 x x)
-1/5040
#s(literal -1/5040 binary64)
1/120
#s(literal 1/120 binary64)
-1/6
#s(literal -1/6 binary64)
(* x (* x x))
(.f64 x (.f64 x x))

localize148.0ms (1.1%)

Memory

-58.7MiB live, 251.7MiB allocated

Localize:

Found 15 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(sin.f64 (+.f64 x eps))
✓	accuracy	99.9%	(.f64 x (.f64 x x))
✓	accuracy	99.8%	(.f64 x (fma.f64 (.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)))
✓	accuracy	61.4%	(-.f64 (sin.f64 (+.f64 x eps)) (fma.f64 (fma.f64 x (.f64 x (fma.f64 (.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64))) #s(literal -1/6 binary64)) (.f64 x (.f64 x x)) x))
✓	accuracy	100.0%	(fma.f64 (*.f64 x x) #s(literal 1/120 binary64) #s(literal -1/6 binary64))
✓	accuracy	100.0%	(sin.f64 (+.f64 x eps))
✓	accuracy	99.9%	(.f64 x (.f64 x x))
✓	accuracy	61.4%	(-.f64 (sin.f64 (+.f64 x eps)) (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) (.f64 x (*.f64 x x)) x))
✓	accuracy	100.0%	(cos.f64 x)
✓	accuracy	100.0%	(*.f64 eps (cos.f64 x))
✓	accuracy	100.0%	(sin.f64 eps)
✓	accuracy	100.0%	(sin.f64 (*.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64)))
✓	accuracy	100.0%	(.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (cos.f64 (*.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64))))
✓	accuracy	100.0%	(cos.f64 (*.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)))
✓	accuracy	99.6%	(+.f64 x (+.f64 x eps))

Samples

49.0ms	165×	0	valid
38.0ms	89×	1	valid
1.0ms	2×	2	valid

Compiler

Compiled 229 to 38 computations (83.4% saved)

Precisions

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

ival-mult: 21.0ms (32.3% of total)

ival-add: 13.0ms (20% of total)

const: 12.0ms (18.5% of total)

ival-sin: 6.0ms (9.2% of total)

ival-cos: 6.0ms (9.2% of total)

adjust: 4.0ms (6.2% of total)

ival-sub: 3.0ms (4.6% of total)

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

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

exact: 0.0ms (0% of total)

series27.0ms (0.2%)

Memory

24.5MiB live, 63.4MiB allocated

Counts

19 → 348

Calls

Call 1

Inputs
#<alt (* (+ x (+ x eps)) 1/2)>
#<alt (+ eps 0)>
#<alt (* (* (sin (* (+ eps 0) 1/2)) (cos (* (+ x (+ x eps)) 1/2))) 2)>
#<alt (* (sin (* (+ eps 0) 1/2)) (cos (* (+ x (+ x eps)) 1/2)))>
#<alt (sin eps)>
#<alt (* eps (cos x))>
#<alt (cos x)>
#<alt (- (sin (+ x eps)) (+ (* (+ (* (* x x) 1/120) -1/6) (* x (* x x))) x))>
#<alt (sin (+ x eps))>
#<alt (+ x eps)>
#<alt (+ (* (+ (* (* x x) 1/120) -1/6) (* x (* x x))) x)>
#<alt (- (sin (+ x eps)) (+ (* (+ (* x (* x (+ (* (* x x) -1/5040) 1/120))) -1/6) (* x (* x x))) x))>
#<alt (+ (* (+ (* x (* x (+ (* (* x x) -1/5040) 1/120))) -1/6) (* x (* x x))) x)>
#<alt (+ x (+ x eps))>
#<alt (cos (* (+ x (+ x eps)) 1/2))>
#<alt (sin (* (+ eps 0) 1/2))>
#<alt (* x (* x x))>
#<alt (+ (* (* x x) 1/120) -1/6)>
#<alt (* x (+ (* (* x x) -1/5040) 1/120))>

Outputs
#<alt (* 1/2 eps)>
#<alt (+ x (* 1/2 eps))>
#<alt (+ x (* 1/2 eps))>
#<alt (+ x (* 1/2 eps))>
#<alt x>
#<alt (* x (+ 1 (* 1/2 (/ eps x))))>
#<alt (* x (+ 1 (* 1/2 (/ eps x))))>
#<alt (* x (+ 1 (* 1/2 (/ eps x))))>
#<alt x>
#<alt (* -1 (* x (- (* -1/2 (/ eps x)) 1)))>
#<alt (* -1 (* x (- (* -1/2 (/ eps x)) 1)))>
#<alt (* -1 (* x (- (* -1/2 (/ eps x)) 1)))>
#<alt x>
#<alt (+ x (* 1/2 eps))>
#<alt (+ x (* 1/2 eps))>
#<alt (+ x (* 1/2 eps))>
#<alt (* 1/2 eps)>
#<alt (* eps (+ 1/2 (/ x eps)))>
#<alt (* eps (+ 1/2 (/ x eps)))>
#<alt (* eps (+ 1/2 (/ x eps)))>
#<alt (* 1/2 eps)>
#<alt (* -1 (* eps (- (* -1 (/ x eps)) 1/2)))>
#<alt (* -1 (* eps (- (* -1 (/ x eps)) 1/2)))>
#<alt (* -1 (* eps (- (* -1 (/ x eps)) 1/2)))>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt (* eps (cos x))>
#<alt (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))>
#<alt (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* 2 (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x)))))))))>
#<alt (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* 1/24 (* eps (sin x))) (* 2 (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))))>
#<alt (* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))>
#<alt (+ (* -2 (* x (pow (sin (* 1/2 eps)) 2))) (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))))>
#<alt (+ (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* -1 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))))>
#<alt (+ (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -1 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* 1/3 (* x (pow (sin (* 1/2 eps)) 2))))))))>
#<alt (* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))>
#<alt (* 1/2 (* eps (cos x)))>
#<alt (* eps (+ (* -1/4 (* eps (sin x))) (* 1/2 (cos x))))>
#<alt (* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))>
#<alt (* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (+ (* -1/48 (cos x)) (* 1/48 (* eps (sin x))))))))))>
#<alt (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))>
#<alt (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))>
#<alt (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))>
#<alt (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))>
#<alt (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))>
#<alt (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))>
#<alt (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))>
#<alt (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))>
#<alt (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))>
#<alt (+ (* -1 (* x (pow (sin (* 1/2 eps)) 2))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))>
#<alt (+ (* x (+ (* -1 (pow (sin (* 1/2 eps)) 2)) (* -1/2 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))>
#<alt (+ (* x (+ (* -1 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -1/2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* 1/6 (* x (pow (sin (* 1/2 eps)) 2))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))>
#<alt (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))>
#<alt (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))>
#<alt (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))>
#<alt (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))>
#<alt (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))>
#<alt (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))>
#<alt (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))>
#<alt (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))>
#<alt eps>
#<alt (* eps (+ 1 (* -1/6 (pow eps 2))))>
#<alt (* eps (+ 1 (* (pow eps 2) (- (* 1/120 (pow eps 2)) 1/6))))>
#<alt (* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/120 (* -1/5040 (pow eps 2)))) 1/6))))>
#<alt (sin eps)>
#<alt (sin eps)>
#<alt (sin eps)>
#<alt (sin eps)>
#<alt (sin eps)>
#<alt (sin eps)>
#<alt (sin eps)>
#<alt (sin eps)>
#<alt (* eps (cos x))>
#<alt (* eps (cos x))>
#<alt (* eps (cos x))>
#<alt (* eps (cos x))>
#<alt (* eps (cos x))>
#<alt (* eps (cos x))>
#<alt (* eps (cos x))>
#<alt (* eps (cos x))>
#<alt (* eps (cos x))>
#<alt (* eps (cos x))>
#<alt (* eps (cos x))>
#<alt (* eps (cos x))>
#<alt eps>
#<alt (+ eps (* -1/2 (* eps (pow x 2))))>
#<alt (+ eps (* (pow x 2) (+ (* -1/2 eps) (* 1/24 (* eps (pow x 2))))))>
#<alt (+ eps (* (pow x 2) (+ (* -1/2 eps) (* (pow x 2) (+ (* -1/720 (* eps (pow x 2))) (* 1/24 eps))))))>
#<alt (* eps (cos x))>
#<alt (* eps (cos x))>
#<alt (* eps (cos x))>
#<alt (* eps (cos x))>
#<alt (* eps (cos x))>
#<alt (* eps (cos x))>
#<alt (* eps (cos x))>
#<alt (* eps (cos x))>
#<alt 1>
#<alt (+ 1 (* -1/2 (pow x 2)))>
#<alt (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))>
#<alt (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))>
#<alt (cos x)>
#<alt (cos x)>
#<alt (cos x)>
#<alt (cos x)>
#<alt (cos x)>
#<alt (cos x)>
#<alt (cos x)>
#<alt (cos x)>
#<alt (sin eps)>
#<alt (+ (sin eps) (* x (- (cos eps) 1)))>
#<alt (+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))>
#<alt (+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1)))>
#<alt (* -1/120 (pow x 5))>
#<alt (* (pow x 5) (- (* 1/6 (/ 1 (pow x 2))) 1/120))>
#<alt (* (pow x 5) (- (* 1/6 (/ 1 (pow x 2))) (+ 1/120 (/ 1 (pow x 4)))))>
#<alt (* (pow x 5) (- (+ (* 1/6 (/ 1 (pow x 2))) (/ (sin (+ eps x)) (pow x 5))) (+ 1/120 (/ 1 (pow x 4)))))>
#<alt (* -1/120 (pow x 5))>
#<alt (* -1 (* (pow x 5) (- 1/120 (* 1/6 (/ 1 (pow x 2))))))>
#<alt (* -1 (* (pow x 5) (- (+ 1/120 (/ 1 (pow x 4))) (* 1/6 (/ 1 (pow x 2))))))>
#<alt (* -1 (* (pow x 5) (- (+ 1/120 (+ (* -1 (/ (sin (- eps (* -1 x))) (pow x 5))) (/ 1 (pow x 4)))) (* 1/6 (/ 1 (pow x 2))))))>
#<alt (- (sin x) (+ x (* (pow x 3) (- (* 1/120 (pow x 2)) 1/6))))>
#<alt (- (+ (sin x) (* eps (cos x))) (+ x (* (pow x 3) (- (* 1/120 (pow x 2)) 1/6))))>
#<alt (- (+ (sin x) (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))) (+ x (* (pow x 3) (- (* 1/120 (pow x 2)) 1/6))))>
#<alt (- (+ (sin x) (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))) (+ x (* (pow x 3) (- (* 1/120 (pow x 2)) 1/6))))>
#<alt (- (sin (+ eps x)) (+ x (* (pow x 3) (- (* 1/120 (pow x 2)) 1/6))))>
#<alt (- (sin (+ eps x)) (+ x (* (pow x 3) (- (* 1/120 (pow x 2)) 1/6))))>
#<alt (- (sin (+ eps x)) (+ x (* (pow x 3) (- (* 1/120 (pow x 2)) 1/6))))>
#<alt (- (sin (+ eps x)) (+ x (* (pow x 3) (- (* 1/120 (pow x 2)) 1/6))))>
#<alt (- (sin (- x (* -1 eps))) (+ x (* (pow x 3) (- (* 1/120 (pow x 2)) 1/6))))>
#<alt (- (sin (- x (* -1 eps))) (+ x (* (pow x 3) (- (* 1/120 (pow x 2)) 1/6))))>
#<alt (- (sin (- x (* -1 eps))) (+ x (* (pow x 3) (- (* 1/120 (pow x 2)) 1/6))))>
#<alt (- (sin (- x (* -1 eps))) (+ x (* (pow x 3) (- (* 1/120 (pow x 2)) 1/6))))>
#<alt (sin eps)>
#<alt (+ (sin eps) (* x (cos eps)))>
#<alt (+ (sin eps) (* x (+ (cos eps) (* -1/2 (* x (sin eps))))))>
#<alt (+ (sin eps) (* x (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* -1/6 (* x (cos eps))))))))>
#<alt (sin (+ eps x))>
#<alt (sin (+ eps x))>
#<alt (sin (+ eps x))>
#<alt (sin (+ eps x))>
#<alt (sin (- eps (* -1 x)))>
#<alt (sin (- eps (* -1 x)))>
#<alt (sin (- eps (* -1 x)))>
#<alt (sin (- eps (* -1 x)))>
#<alt (sin x)>
#<alt (+ (sin x) (* eps (cos x)))>
#<alt (+ (sin x) (* eps (+ (cos x) (* -1/2 (* eps (sin x))))))>
#<alt (+ (sin x) (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))))>
#<alt (sin (+ eps x))>
#<alt (sin (+ eps x))>
#<alt (sin (+ eps x))>
#<alt (sin (+ eps x))>
#<alt (sin (- x (* -1 eps)))>
#<alt (sin (- x (* -1 eps)))>
#<alt (sin (- x (* -1 eps)))>
#<alt (sin (- x (* -1 eps)))>
#<alt eps>
#<alt (+ eps x)>
#<alt (+ eps x)>
#<alt (+ eps x)>
#<alt x>
#<alt (* x (+ 1 (/ eps x)))>
#<alt (* x (+ 1 (/ eps x)))>
#<alt (* x (+ 1 (/ eps x)))>
#<alt x>
#<alt (* -1 (* x (- (* -1 (/ eps x)) 1)))>
#<alt (* -1 (* x (- (* -1 (/ eps x)) 1)))>
#<alt (* -1 (* x (- (* -1 (/ eps x)) 1)))>
#<alt x>
#<alt (+ eps x)>
#<alt (+ eps x)>
#<alt (+ eps x)>
#<alt eps>
#<alt (* eps (+ 1 (/ x eps)))>
#<alt (* eps (+ 1 (/ x eps)))>
#<alt (* eps (+ 1 (/ x eps)))>
#<alt eps>
#<alt (* -1 (* eps (- (* -1 (/ x eps)) 1)))>
#<alt (* -1 (* eps (- (* -1 (/ x eps)) 1)))>
#<alt (* -1 (* eps (- (* -1 (/ x eps)) 1)))>
#<alt x>
#<alt (* x (+ 1 (* -1/6 (pow x 2))))>
#<alt (* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))))>
#<alt (* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))))>
#<alt (* 1/120 (pow x 5))>
#<alt (* (pow x 5) (- 1/120 (* 1/6 (/ 1 (pow x 2)))))>
#<alt (* (pow x 5) (- (+ 1/120 (/ 1 (pow x 4))) (* 1/6 (/ 1 (pow x 2)))))>
#<alt (* (pow x 5) (- (+ 1/120 (/ 1 (pow x 4))) (* 1/6 (/ 1 (pow x 2)))))>
#<alt (* 1/120 (pow x 5))>
#<alt (* -1 (* (pow x 5) (- (* 1/6 (/ 1 (pow x 2))) 1/120)))>
#<alt (* -1 (* (pow x 5) (- (* 1/6 (/ 1 (pow x 2))) (+ 1/120 (/ 1 (pow x 4))))))>
#<alt (* -1 (* (pow x 5) (- (* 1/6 (/ 1 (pow x 2))) (+ 1/120 (/ 1 (pow x 4))))))>
#<alt (sin eps)>
#<alt (+ (sin eps) (* x (- (cos eps) 1)))>
#<alt (+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))>
#<alt (+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1)))>
#<alt (* 1/5040 (pow x 7))>
#<alt (* (pow x 7) (- 1/5040 (* 1/120 (/ 1 (pow x 2)))))>
#<alt (* (pow x 7) (- (+ 1/5040 (/ 1/6 (pow x 4))) (* 1/120 (/ 1 (pow x 2)))))>
#<alt (* (pow x 7) (- (+ 1/5040 (/ 1/6 (pow x 4))) (+ (* 1/120 (/ 1 (pow x 2))) (/ 1 (pow x 6)))))>
#<alt (* 1/5040 (pow x 7))>
#<alt (* -1 (* (pow x 7) (- (* 1/120 (/ 1 (pow x 2))) 1/5040)))>
#<alt (* -1 (* (pow x 7) (- (* 1/120 (/ 1 (pow x 2))) (+ 1/5040 (/ 1/6 (pow x 4))))))>
#<alt (* -1 (* (pow x 7) (- (+ (* 1/120 (/ 1 (pow x 2))) (/ 1 (pow x 6))) (+ 1/5040 (/ 1/6 (pow x 4))))))>
#<alt (- (sin x) (+ x (* (pow x 3) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))>
#<alt (- (+ (sin x) (* eps (cos x))) (+ x (* (pow x 3) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))>
#<alt (- (+ (sin x) (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))) (+ x (* (pow x 3) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))>
#<alt (- (+ (sin x) (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))) (+ x (* (pow x 3) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))>
#<alt (- (sin (+ eps x)) (+ x (* (pow x 3) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))>
#<alt (- (sin (+ eps x)) (+ x (* (pow x 3) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))>
#<alt (- (sin (+ eps x)) (+ x (* (pow x 3) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))>
#<alt (- (sin (+ eps x)) (+ x (* (pow x 3) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))>
#<alt (- (sin (- x (* -1 eps))) (+ x (* (pow x 3) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))>
#<alt (- (sin (- x (* -1 eps))) (+ x (* (pow x 3) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))>
#<alt (- (sin (- x (* -1 eps))) (+ x (* (pow x 3) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))>
#<alt (- (sin (- x (* -1 eps))) (+ x (* (pow x 3) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))>
#<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 (* -1/5040 (pow x 7))>
#<alt (* (pow x 7) (- (* 1/120 (/ 1 (pow x 2))) 1/5040))>
#<alt (* (pow x 7) (- (* 1/120 (/ 1 (pow x 2))) (+ 1/5040 (/ 1/6 (pow x 4)))))>
#<alt (* (pow x 7) (- (+ (* 1/120 (/ 1 (pow x 2))) (/ 1 (pow x 6))) (+ 1/5040 (/ 1/6 (pow x 4)))))>
#<alt (* -1/5040 (pow x 7))>
#<alt (* -1 (* (pow x 7) (- 1/5040 (* 1/120 (/ 1 (pow x 2))))))>
#<alt (* -1 (* (pow x 7) (- (+ 1/5040 (/ 1/6 (pow x 4))) (* 1/120 (/ 1 (pow x 2))))))>
#<alt (* -1 (* (pow x 7) (- (+ 1/5040 (/ 1/6 (pow x 4))) (+ (* 1/120 (/ 1 (pow x 2))) (/ 1 (pow x 6))))))>
#<alt eps>
#<alt (+ eps (* 2 x))>
#<alt (+ eps (* 2 x))>
#<alt (+ eps (* 2 x))>
#<alt (* 2 x)>
#<alt (* x (+ 2 (/ eps x)))>
#<alt (* x (+ 2 (/ eps x)))>
#<alt (* x (+ 2 (/ eps x)))>
#<alt (* 2 x)>
#<alt (* -1 (* x (- (* -1 (/ eps x)) 2)))>
#<alt (* -1 (* x (- (* -1 (/ eps x)) 2)))>
#<alt (* -1 (* x (- (* -1 (/ eps x)) 2)))>
#<alt (* 2 x)>
#<alt (+ eps (* 2 x))>
#<alt (+ eps (* 2 x))>
#<alt (+ eps (* 2 x))>
#<alt eps>
#<alt (* eps (+ 1 (* 2 (/ x eps))))>
#<alt (* eps (+ 1 (* 2 (/ x eps))))>
#<alt (* eps (+ 1 (* 2 (/ x eps))))>
#<alt eps>
#<alt (* -1 (* eps (- (* -2 (/ x eps)) 1)))>
#<alt (* -1 (* eps (- (* -2 (/ x eps)) 1)))>
#<alt (* -1 (* eps (- (* -2 (/ x eps)) 1)))>
#<alt (cos (* 1/2 eps))>
#<alt (+ (cos (* 1/2 eps)) (* -1 (* x (sin (* 1/2 eps)))))>
#<alt (+ (cos (* 1/2 eps)) (* x (- (* -1/2 (* x (cos (* 1/2 eps)))) (sin (* 1/2 eps)))))>
#<alt (+ (cos (* 1/2 eps)) (* x (- (* x (+ (* -1/2 (cos (* 1/2 eps))) (* 1/6 (* x (sin (* 1/2 eps)))))) (sin (* 1/2 eps)))))>
#<alt (cos (* 1/2 (+ eps (* 2 x))))>
#<alt (cos (* 1/2 (+ eps (* 2 x))))>
#<alt (cos (* 1/2 (+ eps (* 2 x))))>
#<alt (cos (* 1/2 (+ eps (* 2 x))))>
#<alt (cos (* 1/2 (- eps (* -2 x))))>
#<alt (cos (* 1/2 (- eps (* -2 x))))>
#<alt (cos (* 1/2 (- eps (* -2 x))))>
#<alt (cos (* 1/2 (- eps (* -2 x))))>
#<alt (cos x)>
#<alt (+ (cos x) (* -1/2 (* eps (sin x))))>
#<alt (+ (cos x) (* eps (- (* -1/8 (* eps (cos x))) (* 1/2 (sin x)))))>
#<alt (+ (cos x) (* eps (- (* eps (+ (* -1/8 (cos x)) (* 1/48 (* eps (sin x))))) (* 1/2 (sin x)))))>
#<alt (cos (* 1/2 (+ eps (* 2 x))))>
#<alt (cos (* 1/2 (+ eps (* 2 x))))>
#<alt (cos (* 1/2 (+ eps (* 2 x))))>
#<alt (cos (* 1/2 (+ eps (* 2 x))))>
#<alt (cos (* 1/2 (- (* 2 x) (* -1 eps))))>
#<alt (cos (* 1/2 (- (* 2 x) (* -1 eps))))>
#<alt (cos (* 1/2 (- (* 2 x) (* -1 eps))))>
#<alt (cos (* 1/2 (- (* 2 x) (* -1 eps))))>
#<alt (* 1/2 eps)>
#<alt (* eps (+ 1/2 (* -1/48 (pow eps 2))))>
#<alt (* eps (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))>
#<alt (* eps (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))>
#<alt (sin (* 1/2 eps))>
#<alt (sin (* 1/2 eps))>
#<alt (sin (* 1/2 eps))>
#<alt (sin (* 1/2 eps))>
#<alt (sin (* 1/2 eps))>
#<alt (sin (* 1/2 eps))>
#<alt (sin (* 1/2 eps))>
#<alt (sin (* 1/2 eps))>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt -1/6>
#<alt (- (* 1/120 (pow x 2)) 1/6)>
#<alt (- (* 1/120 (pow x 2)) 1/6)>
#<alt (- (* 1/120 (pow x 2)) 1/6)>
#<alt (* 1/120 (pow x 2))>
#<alt (* (pow x 2) (- 1/120 (* 1/6 (/ 1 (pow x 2)))))>
#<alt (* (pow x 2) (- 1/120 (* 1/6 (/ 1 (pow x 2)))))>
#<alt (* (pow x 2) (- 1/120 (* 1/6 (/ 1 (pow x 2)))))>
#<alt (* 1/120 (pow x 2))>
#<alt (* (pow x 2) (- 1/120 (* 1/6 (/ 1 (pow x 2)))))>
#<alt (* (pow x 2) (- 1/120 (* 1/6 (/ 1 (pow x 2)))))>
#<alt (* (pow x 2) (- 1/120 (* 1/6 (/ 1 (pow x 2)))))>
#<alt (* 1/120 x)>
#<alt (* x (+ 1/120 (* -1/5040 (pow x 2))))>
#<alt (* x (+ 1/120 (* -1/5040 (pow x 2))))>
#<alt (* x (+ 1/120 (* -1/5040 (pow x 2))))>
#<alt (* -1/5040 (pow x 3))>
#<alt (* (pow x 3) (- (* 1/120 (/ 1 (pow x 2))) 1/5040))>
#<alt (* (pow x 3) (- (* 1/120 (/ 1 (pow x 2))) 1/5040))>
#<alt (* (pow x 3) (- (* 1/120 (/ 1 (pow x 2))) 1/5040))>
#<alt (* -1/5040 (pow x 3))>
#<alt (* -1 (* (pow x 3) (- 1/5040 (* 1/120 (/ 1 (pow x 2))))))>
#<alt (* -1 (* (pow x 3) (- 1/5040 (* 1/120 (/ 1 (pow x 2))))))>
#<alt (* -1 (* (pow x 3) (- 1/5040 (* 1/120 (/ 1 (pow x 2))))))>

Calls

87 calls:

Time	Variable		Point	Expression
3.0ms	eps	@	inf	(- (sin (+ x eps)) (+ (* (+ (* (* x x) 1/120) -1/6) (* x (* x x))) x))
2.0ms	x	@	-inf	(- (sin (+ x eps)) (+ (* (+ (* x (* x (+ (* (* x x) -1/5040) 1/120))) -1/6) (* x (* x x))) x))
1.0ms	x	@	0	(* (* (sin (* (+ eps 0) 1/2)) (cos (* (+ x (+ x eps)) 1/2))) 2)
1.0ms	x	@	inf	(* (* (sin (* (+ eps 0) 1/2)) (cos (* (+ x (+ x eps)) 1/2))) 2)
1.0ms	eps	@	inf	(- (sin (+ x eps)) (+ (* (+ (* x (* x (+ (* (* x x) -1/5040) 1/120))) -1/6) (* x (* x x))) x))

rewrite413.0ms (2.9%)

Memory

16.8MiB live, 519.3MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

5 426×	`accelerator-lowering-fma.f32`
5 426×	`accelerator-lowering-fma.f64`
5 370×	`-lowering-.f32`
5 370×	`-lowering-.f64`
4 618×	`/-lowering-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	36	161
1	207	161
2	1939	161
0	9908	144

Stop Event

1×	iter limit
1×	node limit

Counts

19 → 581

Calls

Call 1

Inputs
(* (+ x (+ x eps)) 1/2)
(+ eps 0)
(* (* (sin (* (+ eps 0) 1/2)) (cos (* (+ x (+ x eps)) 1/2))) 2)
(* (sin (* (+ eps 0) 1/2)) (cos (* (+ x (+ x eps)) 1/2)))
(sin eps)
(* eps (cos x))
(cos x)
(- (sin (+ x eps)) (+ (* (+ (* (* x x) 1/120) -1/6) (* x (* x x))) x))
(sin (+ x eps))
(+ x eps)
(+ (* (+ (* (* x x) 1/120) -1/6) (* x (* x x))) x)
(- (sin (+ x eps)) (+ (* (+ (* x (* x (+ (* (* x x) -1/5040) 1/120))) -1/6) (* x (* x x))) x))
(+ (* (+ (* x (* x (+ (* (* x x) -1/5040) 1/120))) -1/6) (* x (* x x))) x)
(+ x (+ x eps))
(cos (* (+ x (+ x eps)) 1/2))
(sin (* (+ eps 0) 1/2))
(* x (* x x))
(+ (* (* x x) 1/120) -1/6)
(* x (+ (* (* x x) -1/5040) 1/120))

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)))
(fma.f64 (+.f64 x x) #s(literal 1/2 binary64) (*.f64 eps #s(literal 1/2 binary64)))
(/.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 (+.f64 x eps) (.f64 (+.f64 x eps) (+.f64 x eps)) (.f64 x (.f64 x x)))) (fma.f64 (+.f64 x eps) (-.f64 (+.f64 x eps) x) (*.f64 x x)))
(/.f64 (.f64 #s(literal 1/2 binary64) (.f64 (+.f64 x (+.f64 x eps)) (-.f64 x (+.f64 x eps)))) (-.f64 x (+.f64 x eps)))
(/.f64 (.f64 (fma.f64 (+.f64 x eps) (.f64 (+.f64 x eps) (+.f64 x eps)) (.f64 x (.f64 x x))) #s(literal 1/2 binary64)) (fma.f64 (+.f64 x eps) (-.f64 (+.f64 x eps) x) (*.f64 x x)))
(/.f64 (.f64 (.f64 (+.f64 x (+.f64 x eps)) (-.f64 x (+.f64 x eps))) #s(literal 1/2 binary64)) (-.f64 x (+.f64 x eps)))
(/.f64 (neg.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 (+.f64 x eps) (.f64 (+.f64 x eps) (+.f64 x eps)) (.f64 x (.f64 x x))))) (neg.f64 (fma.f64 (+.f64 x eps) (-.f64 (+.f64 x eps) x) (*.f64 x x))))
(/.f64 (neg.f64 (.f64 #s(literal 1/2 binary64) (.f64 (+.f64 x (+.f64 x eps)) (-.f64 x (+.f64 x eps))))) (neg.f64 (-.f64 x (+.f64 x eps))))
(/.f64 (neg.f64 (.f64 (fma.f64 (+.f64 x eps) (.f64 (+.f64 x eps) (+.f64 x eps)) (.f64 x (.f64 x x))) #s(literal 1/2 binary64))) (neg.f64 (fma.f64 (+.f64 x eps) (-.f64 (+.f64 x eps) x) (*.f64 x x))))
(/.f64 (neg.f64 (.f64 (.f64 (+.f64 x (+.f64 x eps)) (-.f64 x (+.f64 x eps))) #s(literal 1/2 binary64))) (neg.f64 (-.f64 x (+.f64 x eps))))
(/.f64 (+.f64 (pow.f64 (.f64 #s(literal 1/2 binary64) x) #s(literal 3 binary64)) (pow.f64 (.f64 #s(literal 1/2 binary64) (+.f64 x eps)) #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) (+.f64 x eps)) (.f64 #s(literal 1/2 binary64) (+.f64 x eps))) (.f64 (.f64 #s(literal 1/2 binary64) x) (.f64 #s(literal 1/2 binary64) (+.f64 x eps))))))
(/.f64 (+.f64 (pow.f64 (.f64 #s(literal 1/2 binary64) (+.f64 x eps)) #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) (+.f64 x eps)) (.f64 #s(literal 1/2 binary64) (+.f64 x eps)) (-.f64 (.f64 (.f64 #s(literal 1/2 binary64) x) (.f64 #s(literal 1/2 binary64) x)) (.f64 (.f64 #s(literal 1/2 binary64) (+.f64 x eps)) (.f64 #s(literal 1/2 binary64) x)))))
(/.f64 (+.f64 (pow.f64 (.f64 #s(literal 1/2 binary64) (+.f64 x x)) #s(literal 3 binary64)) (.f64 (.f64 eps (.f64 eps eps)) #s(literal 1/8 binary64))) (fma.f64 (.f64 #s(literal 1/2 binary64) (+.f64 x x)) (.f64 #s(literal 1/2 binary64) (+.f64 x x)) (-.f64 (.f64 (.f64 eps #s(literal 1/2 binary64)) (.f64 eps #s(literal 1/2 binary64))) (.f64 (.f64 #s(literal 1/2 binary64) (+.f64 x x)) (.f64 eps #s(literal 1/2 binary64))))))
(/.f64 (+.f64 (pow.f64 (.f64 x #s(literal 1/2 binary64)) #s(literal 3 binary64)) (pow.f64 (.f64 (+.f64 x eps) #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 (+.f64 x eps) #s(literal 1/2 binary64)) (.f64 (+.f64 x 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 (pow.f64 (.f64 (+.f64 x eps) #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 (+.f64 x eps) #s(literal 1/2 binary64)) (.f64 (+.f64 x eps) #s(literal 1/2 binary64)) (-.f64 (.f64 (.f64 x #s(literal 1/2 binary64)) (.f64 x #s(literal 1/2 binary64))) (.f64 (.f64 (+.f64 x eps) #s(literal 1/2 binary64)) (.f64 x #s(literal 1/2 binary64))))))
(/.f64 (+.f64 (pow.f64 (.f64 (+.f64 x x) #s(literal 1/2 binary64)) #s(literal 3 binary64)) (.f64 (.f64 eps (.f64 eps eps)) #s(literal 1/8 binary64))) (fma.f64 (.f64 (+.f64 x x) #s(literal 1/2 binary64)) (.f64 (+.f64 x x) #s(literal 1/2 binary64)) (-.f64 (.f64 (.f64 eps #s(literal 1/2 binary64)) (.f64 eps #s(literal 1/2 binary64))) (.f64 (.f64 (+.f64 x x) #s(literal 1/2 binary64)) (.f64 eps #s(literal 1/2 binary64))))))
(*.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64))
(*.f64 #s(literal 1/2 binary64) (+.f64 x (+.f64 x eps)))
eps
(+.f64 eps #s(literal 0 binary64))
(+.f64 #s(literal 0 binary64) eps)
(-.f64 eps #s(literal 0 binary64))
(-.f64 eps (/.f64 #s(literal 0 binary64) eps))
(-.f64 eps (/.f64 #s(literal 0 binary64) (*.f64 eps eps)))
(-.f64 (/.f64 #s(literal 0 binary64) (-.f64 #s(literal 0 binary64) eps)) (/.f64 (*.f64 eps eps) (-.f64 #s(literal 0 binary64) eps)))
(fma.f64 eps (/.f64 eps eps) #s(literal 0 binary64))
(fma.f64 (.f64 eps (.f64 eps eps)) (/.f64 #s(literal 1 binary64) (*.f64 eps eps)) #s(literal 0 binary64))
(fma.f64 (*.f64 eps eps) (/.f64 #s(literal 1 binary64) eps) #s(literal 0 binary64))
(fma.f64 (/.f64 eps (*.f64 eps eps)) (/.f64 eps (/.f64 #s(literal 1 binary64) eps)) #s(literal 0 binary64))
(fma.f64 (/.f64 eps eps) eps #s(literal 0 binary64))
(fma.f64 (/.f64 (pow.f64 eps #s(literal 3/2 binary64)) eps) (/.f64 (pow.f64 eps #s(literal 3/2 binary64)) eps) #s(literal 0 binary64))
(fma.f64 (/.f64 eps (.f64 eps (.f64 eps eps))) (/.f64 eps (/.f64 #s(literal 1 binary64) (*.f64 eps eps))) #s(literal 0 binary64))
(/.f64 (.f64 eps (.f64 eps eps)) (*.f64 eps eps))
(/.f64 (*.f64 eps eps) eps)
(/.f64 #s(literal 1 binary64) (/.f64 eps (*.f64 eps eps)))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps))
(/.f64 (neg.f64 (.f64 eps (.f64 eps eps))) (neg.f64 (*.f64 eps eps)))
(/.f64 (-.f64 (.f64 eps (.f64 eps eps)) #s(literal 0 binary64)) (*.f64 eps eps))
(/.f64 (neg.f64 (*.f64 eps eps)) (neg.f64 eps))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal 1 binary64) eps)))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 eps (*.f64 eps eps))))
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(/.f64 (-.f64 (.f64 (.f64 eps (.f64 eps eps)) eps) (.f64 (.f64 eps eps) #s(literal 0 binary64))) (.f64 eps (*.f64 eps eps)))
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(fma.f64 #s(literal 1/120 binary64) x (.f64 x (.f64 x (*.f64 x #s(literal -1/5040 binary64)))))
(fma.f64 (.f64 x (.f64 x x)) #s(literal -1/5040 binary64) (*.f64 x #s(literal 1/120 binary64)))
(fma.f64 #s(literal -1/5040 binary64) (.f64 x (.f64 x x)) (*.f64 x #s(literal 1/120 binary64)))
(fma.f64 (.f64 x (.f64 x #s(literal -1/5040 binary64))) x (*.f64 x #s(literal 1/120 binary64)))
(fma.f64 (.f64 x #s(literal -1/5040 binary64)) (.f64 x x) (*.f64 x #s(literal 1/120 binary64)))
(/.f64 (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal -1/128024064000 binary64))) (.f64 (.f64 x (.f64 x x)) #s(literal 1/1728000 binary64))) (fma.f64 (.f64 x (.f64 x (.f64 x #s(literal -1/5040 binary64)))) (.f64 x (.f64 x (.f64 x #s(literal -1/5040 binary64)))) (-.f64 (.f64 (.f64 x #s(literal 1/120 binary64)) (.f64 x #s(literal 1/120 binary64))) (.f64 (.f64 x (.f64 x (.f64 x #s(literal -1/5040 binary64)))) (*.f64 x #s(literal 1/120 binary64))))))
(/.f64 (-.f64 (.f64 (.f64 x (.f64 x (.f64 x #s(literal -1/5040 binary64)))) (.f64 x (.f64 x (.f64 x #s(literal -1/5040 binary64))))) (.f64 (.f64 x #s(literal 1/120 binary64)) (.f64 x #s(literal 1/120 binary64)))) (-.f64 (.f64 x (.f64 x (.f64 x #s(literal -1/5040 binary64)))) (.f64 x #s(literal 1/120 binary64))))
(/.f64 (.f64 x (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal -1/128024064000 binary64)) #s(literal 1/1728000 binary64))) (-.f64 (fma.f64 (.f64 (.f64 x (.f64 x x)) x) #s(literal 1/25401600 binary64) #s(literal 1/14400 binary64)) (.f64 (*.f64 x x) #s(literal -1/604800 binary64))))
(/.f64 (.f64 x (fma.f64 (.f64 (.f64 x (.f64 x x)) x) #s(literal 1/25401600 binary64) #s(literal -1/14400 binary64))) (fma.f64 x (*.f64 x #s(literal -1/5040 binary64)) #s(literal -1/120 binary64)))
(/.f64 (.f64 (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal -1/128024064000 binary64)) #s(literal 1/1728000 binary64)) x) (-.f64 (fma.f64 (.f64 (.f64 x (.f64 x x)) x) #s(literal 1/25401600 binary64) #s(literal 1/14400 binary64)) (.f64 (*.f64 x x) #s(literal -1/604800 binary64))))
(/.f64 (.f64 (fma.f64 (.f64 (.f64 x (.f64 x x)) x) #s(literal 1/25401600 binary64) #s(literal -1/14400 binary64)) x) (fma.f64 x (*.f64 x #s(literal -1/5040 binary64)) #s(literal -1/120 binary64)))
(/.f64 (neg.f64 (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal -1/128024064000 binary64))) (.f64 (.f64 x (.f64 x x)) #s(literal 1/1728000 binary64)))) (neg.f64 (fma.f64 (.f64 x (.f64 x (.f64 x #s(literal -1/5040 binary64)))) (.f64 x (.f64 x (.f64 x #s(literal -1/5040 binary64)))) (-.f64 (.f64 (.f64 x #s(literal 1/120 binary64)) (.f64 x #s(literal 1/120 binary64))) (.f64 (.f64 x (.f64 x (.f64 x #s(literal -1/5040 binary64)))) (*.f64 x #s(literal 1/120 binary64)))))))
(/.f64 (neg.f64 (-.f64 (.f64 (.f64 x (.f64 x (.f64 x #s(literal -1/5040 binary64)))) (.f64 x (.f64 x (.f64 x #s(literal -1/5040 binary64))))) (.f64 (.f64 x #s(literal 1/120 binary64)) (.f64 x #s(literal 1/120 binary64))))) (neg.f64 (-.f64 (.f64 x (.f64 x (.f64 x #s(literal -1/5040 binary64)))) (.f64 x #s(literal 1/120 binary64)))))
(/.f64 (neg.f64 (.f64 x (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal -1/128024064000 binary64)) #s(literal 1/1728000 binary64)))) (neg.f64 (-.f64 (fma.f64 (.f64 (.f64 x (.f64 x x)) x) #s(literal 1/25401600 binary64) #s(literal 1/14400 binary64)) (.f64 (*.f64 x x) #s(literal -1/604800 binary64)))))
(/.f64 (neg.f64 (.f64 x (fma.f64 (.f64 (.f64 x (.f64 x x)) x) #s(literal 1/25401600 binary64) #s(literal -1/14400 binary64)))) (neg.f64 (fma.f64 x (*.f64 x #s(literal -1/5040 binary64)) #s(literal -1/120 binary64))))
(/.f64 (neg.f64 (.f64 (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal -1/128024064000 binary64)) #s(literal 1/1728000 binary64)) x)) (neg.f64 (-.f64 (fma.f64 (.f64 (.f64 x (.f64 x x)) x) #s(literal 1/25401600 binary64) #s(literal 1/14400 binary64)) (.f64 (*.f64 x x) #s(literal -1/604800 binary64)))))
(/.f64 (neg.f64 (.f64 (fma.f64 (.f64 (.f64 x (.f64 x x)) x) #s(literal 1/25401600 binary64) #s(literal -1/14400 binary64)) x)) (neg.f64 (fma.f64 x (*.f64 x #s(literal -1/5040 binary64)) #s(literal -1/120 binary64))))
(/.f64 (fma.f64 (.f64 x (.f64 x x)) #s(literal 1/1728000 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal -1/128024064000 binary64))))) (fma.f64 (.f64 x #s(literal 1/120 binary64)) (.f64 x #s(literal 1/120 binary64)) (-.f64 (.f64 (.f64 x (.f64 x (.f64 x #s(literal -1/5040 binary64)))) (.f64 x (.f64 x (.f64 x #s(literal -1/5040 binary64))))) (.f64 (.f64 x #s(literal 1/120 binary64)) (.f64 x (.f64 x (*.f64 x #s(literal -1/5040 binary64))))))))
(.f64 x (fma.f64 (.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)))
(.f64 (fma.f64 (.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) x)

simplify398.0ms (2.8%)

Memory

-5.8MiB live, 431.0MiB allocated

Algorithm

1×	egg-herbie

Rules

12 218×	`accelerator-lowering-fma.f32`
12 218×	`accelerator-lowering-fma.f64`
5 358×	`-lowering-.f32`
5 358×	`-lowering-.f64`
4 926×	`+-lowering-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	393	3354
1	1192	3234
2	3296	3198
0	8204	2943

Stop Event

1×	iter limit
1×	node limit

Counts

348 → 348

Calls

Call 1

Inputs
(* 1/2 eps)
(+ x (* 1/2 eps))
(+ x (* 1/2 eps))
(+ x (* 1/2 eps))
x
(* x (+ 1 (* 1/2 (/ eps x))))
(* x (+ 1 (* 1/2 (/ eps x))))
(* x (+ 1 (* 1/2 (/ eps x))))
x
(* -1 (* x (- (* -1/2 (/ eps x)) 1)))
(* -1 (* x (- (* -1/2 (/ eps x)) 1)))
(* -1 (* x (- (* -1/2 (/ eps x)) 1)))
x
(+ x (* 1/2 eps))
(+ x (* 1/2 eps))
(+ x (* 1/2 eps))
(* 1/2 eps)
(* eps (+ 1/2 (/ x eps)))
(* eps (+ 1/2 (/ x eps)))
(* eps (+ 1/2 (/ x eps)))
(* 1/2 eps)
(* -1 (* eps (- (* -1 (/ x eps)) 1/2)))
(* -1 (* eps (- (* -1 (/ x eps)) 1/2)))
(* -1 (* eps (- (* -1 (/ x eps)) 1/2)))
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
(* eps (cos x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* 2 (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x)))))))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* 1/24 (* eps (sin x))) (* 2 (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))
(+ (* -2 (* x (pow (sin (* 1/2 eps)) 2))) (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))))
(+ (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* -1 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))))
(+ (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -1 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* 1/3 (* x (pow (sin (* 1/2 eps)) 2))))))))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))
(* 1/2 (* eps (cos x)))
(* eps (+ (* -1/4 (* eps (sin x))) (* 1/2 (cos x))))
(* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))
(* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (+ (* -1/48 (cos x)) (* 1/48 (* eps (sin x))))))))))
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 eps)) (sin (* 1/2 eps)))
(+ (* -1 (* x (pow (sin (* 1/2 eps)) 2))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))
(+ (* x (+ (* -1 (pow (sin (* 1/2 eps)) 2)) (* -1/2 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))
(+ (* x (+ (* -1 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -1/2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* 1/6 (* x (pow (sin (* 1/2 eps)) 2))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))
eps
(* eps (+ 1 (* -1/6 (pow eps 2))))
(* eps (+ 1 (* (pow eps 2) (- (* 1/120 (pow eps 2)) 1/6))))
(* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/120 (* -1/5040 (pow eps 2)))) 1/6))))
(sin eps)
(sin eps)
(sin eps)
(sin eps)
(sin eps)
(sin eps)
(sin eps)
(sin eps)
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
eps
(+ eps (* -1/2 (* eps (pow x 2))))
(+ eps (* (pow x 2) (+ (* -1/2 eps) (* 1/24 (* eps (pow x 2))))))
(+ eps (* (pow x 2) (+ (* -1/2 eps) (* (pow x 2) (+ (* -1/720 (* eps (pow x 2))) (* 1/24 eps))))))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
1
(+ 1 (* -1/2 (pow x 2)))
(+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))
(cos x)
(cos x)
(cos x)
(cos x)
(cos x)
(cos x)
(cos x)
(cos x)
(sin eps)
(+ (sin eps) (* x (- (cos eps) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1)))
(* -1/120 (pow x 5))
(* (pow x 5) (- (* 1/6 (/ 1 (pow x 2))) 1/120))
(* (pow x 5) (- (* 1/6 (/ 1 (pow x 2))) (+ 1/120 (/ 1 (pow x 4)))))
(* (pow x 5) (- (+ (* 1/6 (/ 1 (pow x 2))) (/ (sin (+ eps x)) (pow x 5))) (+ 1/120 (/ 1 (pow x 4)))))
(* -1/120 (pow x 5))
(* -1 (* (pow x 5) (- 1/120 (* 1/6 (/ 1 (pow x 2))))))
(* -1 (* (pow x 5) (- (+ 1/120 (/ 1 (pow x 4))) (* 1/6 (/ 1 (pow x 2))))))
(* -1 (* (pow x 5) (- (+ 1/120 (+ (* -1 (/ (sin (- eps (* -1 x))) (pow x 5))) (/ 1 (pow x 4)))) (* 1/6 (/ 1 (pow x 2))))))
(- (sin x) (+ x (* (pow x 3) (- (* 1/120 (pow x 2)) 1/6))))
(- (+ (sin x) (* eps (cos x))) (+ x (* (pow x 3) (- (* 1/120 (pow x 2)) 1/6))))
(- (+ (sin x) (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))) (+ x (* (pow x 3) (- (* 1/120 (pow x 2)) 1/6))))
(- (+ (sin x) (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))) (+ x (* (pow x 3) (- (* 1/120 (pow x 2)) 1/6))))
(- (sin (+ eps x)) (+ x (* (pow x 3) (- (* 1/120 (pow x 2)) 1/6))))
(- (sin (+ eps x)) (+ x (* (pow x 3) (- (* 1/120 (pow x 2)) 1/6))))
(- (sin (+ eps x)) (+ x (* (pow x 3) (- (* 1/120 (pow x 2)) 1/6))))
(- (sin (+ eps x)) (+ x (* (pow x 3) (- (* 1/120 (pow x 2)) 1/6))))
(- (sin (- x (* -1 eps))) (+ x (* (pow x 3) (- (* 1/120 (pow x 2)) 1/6))))
(- (sin (- x (* -1 eps))) (+ x (* (pow x 3) (- (* 1/120 (pow x 2)) 1/6))))
(- (sin (- x (* -1 eps))) (+ x (* (pow x 3) (- (* 1/120 (pow x 2)) 1/6))))
(- (sin (- x (* -1 eps))) (+ x (* (pow x 3) (- (* 1/120 (pow x 2)) 1/6))))
(sin eps)
(+ (sin eps) (* x (cos eps)))
(+ (sin eps) (* x (+ (cos eps) (* -1/2 (* x (sin eps))))))
(+ (sin eps) (* x (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* -1/6 (* x (cos eps))))))))
(sin (+ eps x))
(sin (+ eps x))
(sin (+ eps x))
(sin (+ eps x))
(sin (- eps (* -1 x)))
(sin (- eps (* -1 x)))
(sin (- eps (* -1 x)))
(sin (- eps (* -1 x)))
(sin x)
(+ (sin x) (* eps (cos x)))
(+ (sin x) (* eps (+ (cos x) (* -1/2 (* eps (sin x))))))
(+ (sin x) (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))))
(sin (+ eps x))
(sin (+ eps x))
(sin (+ eps x))
(sin (+ eps x))
(sin (- x (* -1 eps)))
(sin (- x (* -1 eps)))
(sin (- x (* -1 eps)))
(sin (- x (* -1 eps)))
eps
(+ eps x)
(+ eps x)
(+ eps x)
x
(* x (+ 1 (/ eps x)))
(* x (+ 1 (/ eps x)))
(* x (+ 1 (/ eps x)))
x
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(* -1 (* x (- (* -1 (/ eps x)) 1)))
x
(+ eps x)
(+ eps x)
(+ eps x)
eps
(* eps (+ 1 (/ x eps)))
(* eps (+ 1 (/ x eps)))
(* eps (+ 1 (/ x eps)))
eps
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
x
(* x (+ 1 (* -1/6 (pow x 2))))
(* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))))
(* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))))
(* 1/120 (pow x 5))
(* (pow x 5) (- 1/120 (* 1/6 (/ 1 (pow x 2)))))
(* (pow x 5) (- (+ 1/120 (/ 1 (pow x 4))) (* 1/6 (/ 1 (pow x 2)))))
(* (pow x 5) (- (+ 1/120 (/ 1 (pow x 4))) (* 1/6 (/ 1 (pow x 2)))))
(* 1/120 (pow x 5))
(* -1 (* (pow x 5) (- (* 1/6 (/ 1 (pow x 2))) 1/120)))
(* -1 (* (pow x 5) (- (* 1/6 (/ 1 (pow x 2))) (+ 1/120 (/ 1 (pow x 4))))))
(* -1 (* (pow x 5) (- (* 1/6 (/ 1 (pow x 2))) (+ 1/120 (/ 1 (pow x 4))))))
(sin eps)
(+ (sin eps) (* x (- (cos eps) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1)))
(* 1/5040 (pow x 7))
(* (pow x 7) (- 1/5040 (* 1/120 (/ 1 (pow x 2)))))
(* (pow x 7) (- (+ 1/5040 (/ 1/6 (pow x 4))) (* 1/120 (/ 1 (pow x 2)))))
(* (pow x 7) (- (+ 1/5040 (/ 1/6 (pow x 4))) (+ (* 1/120 (/ 1 (pow x 2))) (/ 1 (pow x 6)))))
(* 1/5040 (pow x 7))
(* -1 (* (pow x 7) (- (* 1/120 (/ 1 (pow x 2))) 1/5040)))
(* -1 (* (pow x 7) (- (* 1/120 (/ 1 (pow x 2))) (+ 1/5040 (/ 1/6 (pow x 4))))))
(* -1 (* (pow x 7) (- (+ (* 1/120 (/ 1 (pow x 2))) (/ 1 (pow x 6))) (+ 1/5040 (/ 1/6 (pow x 4))))))
(- (sin x) (+ x (* (pow x 3) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))
(- (+ (sin x) (* eps (cos x))) (+ x (* (pow x 3) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))
(- (+ (sin x) (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))) (+ x (* (pow x 3) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))
(- (+ (sin x) (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))) (+ x (* (pow x 3) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))
(- (sin (+ eps x)) (+ x (* (pow x 3) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))
(- (sin (+ eps x)) (+ x (* (pow x 3) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))
(- (sin (+ eps x)) (+ x (* (pow x 3) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))
(- (sin (+ eps x)) (+ x (* (pow x 3) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))
(- (sin (- x (* -1 eps))) (+ x (* (pow x 3) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))
(- (sin (- x (* -1 eps))) (+ x (* (pow x 3) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))
(- (sin (- x (* -1 eps))) (+ x (* (pow x 3) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))
(- (sin (- x (* -1 eps))) (+ x (* (pow x 3) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))
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))))
(* -1/5040 (pow x 7))
(* (pow x 7) (- (* 1/120 (/ 1 (pow x 2))) 1/5040))
(* (pow x 7) (- (* 1/120 (/ 1 (pow x 2))) (+ 1/5040 (/ 1/6 (pow x 4)))))
(* (pow x 7) (- (+ (* 1/120 (/ 1 (pow x 2))) (/ 1 (pow x 6))) (+ 1/5040 (/ 1/6 (pow x 4)))))
(* -1/5040 (pow x 7))
(* -1 (* (pow x 7) (- 1/5040 (* 1/120 (/ 1 (pow x 2))))))
(* -1 (* (pow x 7) (- (+ 1/5040 (/ 1/6 (pow x 4))) (* 1/120 (/ 1 (pow x 2))))))
(* -1 (* (pow x 7) (- (+ 1/5040 (/ 1/6 (pow x 4))) (+ (* 1/120 (/ 1 (pow x 2))) (/ 1 (pow x 6))))))
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)))
(cos (* 1/2 eps))
(+ (cos (* 1/2 eps)) (* -1 (* x (sin (* 1/2 eps)))))
(+ (cos (* 1/2 eps)) (* x (- (* -1/2 (* x (cos (* 1/2 eps)))) (sin (* 1/2 eps)))))
(+ (cos (* 1/2 eps)) (* x (- (* x (+ (* -1/2 (cos (* 1/2 eps))) (* 1/6 (* x (sin (* 1/2 eps)))))) (sin (* 1/2 eps)))))
(cos (* 1/2 (+ eps (* 2 x))))
(cos (* 1/2 (+ eps (* 2 x))))
(cos (* 1/2 (+ eps (* 2 x))))
(cos (* 1/2 (+ eps (* 2 x))))
(cos (* 1/2 (- eps (* -2 x))))
(cos (* 1/2 (- eps (* -2 x))))
(cos (* 1/2 (- eps (* -2 x))))
(cos (* 1/2 (- eps (* -2 x))))
(cos x)
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* eps (- (* -1/8 (* eps (cos x))) (* 1/2 (sin x)))))
(+ (cos x) (* eps (- (* eps (+ (* -1/8 (cos x)) (* 1/48 (* eps (sin x))))) (* 1/2 (sin x)))))
(cos (* 1/2 (+ eps (* 2 x))))
(cos (* 1/2 (+ eps (* 2 x))))
(cos (* 1/2 (+ eps (* 2 x))))
(cos (* 1/2 (+ eps (* 2 x))))
(cos (* 1/2 (- (* 2 x) (* -1 eps))))
(cos (* 1/2 (- (* 2 x) (* -1 eps))))
(cos (* 1/2 (- (* 2 x) (* -1 eps))))
(cos (* 1/2 (- (* 2 x) (* -1 eps))))
(* 1/2 eps)
(* eps (+ 1/2 (* -1/48 (pow eps 2))))
(* eps (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))
(* eps (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
-1/6
(- (* 1/120 (pow x 2)) 1/6)
(- (* 1/120 (pow x 2)) 1/6)
(- (* 1/120 (pow x 2)) 1/6)
(* 1/120 (pow x 2))
(* (pow x 2) (- 1/120 (* 1/6 (/ 1 (pow x 2)))))
(* (pow x 2) (- 1/120 (* 1/6 (/ 1 (pow x 2)))))
(* (pow x 2) (- 1/120 (* 1/6 (/ 1 (pow x 2)))))
(* 1/120 (pow x 2))
(* (pow x 2) (- 1/120 (* 1/6 (/ 1 (pow x 2)))))
(* (pow x 2) (- 1/120 (* 1/6 (/ 1 (pow x 2)))))
(* (pow x 2) (- 1/120 (* 1/6 (/ 1 (pow x 2)))))
(* 1/120 x)
(* x (+ 1/120 (* -1/5040 (pow x 2))))
(* x (+ 1/120 (* -1/5040 (pow x 2))))
(* x (+ 1/120 (* -1/5040 (pow x 2))))
(* -1/5040 (pow x 3))
(* (pow x 3) (- (* 1/120 (/ 1 (pow x 2))) 1/5040))
(* (pow x 3) (- (* 1/120 (/ 1 (pow x 2))) 1/5040))
(* (pow x 3) (- (* 1/120 (/ 1 (pow x 2))) 1/5040))
(* -1/5040 (pow x 3))
(* -1 (* (pow x 3) (- 1/5040 (* 1/120 (/ 1 (pow x 2))))))
(* -1 (* (pow x 3) (- 1/5040 (* 1/120 (/ 1 (pow x 2))))))
(* -1 (* (pow x 3) (- 1/5040 (* 1/120 (/ 1 (pow x 2))))))

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 x (/.f64 eps x)) x)
(* x (+ 1 (* 1/2 (/ eps x))))
(fma.f64 #s(literal 1/2 binary64) (*.f64 x (/.f64 eps x)) x)
(* x (+ 1 (* 1/2 (/ eps x))))
(fma.f64 #s(literal 1/2 binary64) (*.f64 x (/.f64 eps x)) x)
x
(* -1 (* x (- (* -1/2 (/ eps x)) 1)))
(fma.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) (neg.f64 x) x)
(* -1 (* x (- (* -1/2 (/ eps x)) 1)))
(fma.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) (neg.f64 x) x)
(* -1 (* x (- (* -1/2 (/ eps x)) 1)))
(fma.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) (neg.f64 x) x)
x
(+ x (* 1/2 eps))
(fma.f64 #s(literal 1/2 binary64) eps x)
(+ x (* 1/2 eps))
(fma.f64 #s(literal 1/2 binary64) eps x)
(+ x (* 1/2 eps))
(fma.f64 #s(literal 1/2 binary64) eps x)
(* 1/2 eps)
(*.f64 #s(literal 1/2 binary64) eps)
(* eps (+ 1/2 (/ x eps)))
(*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)))
(* eps (+ 1/2 (/ x eps)))
(*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)))
(* eps (+ 1/2 (/ x eps)))
(*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)))
(* 1/2 eps)
(*.f64 #s(literal 1/2 binary64) eps)
(* -1 (* eps (- (* -1 (/ x eps)) 1/2)))
(*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)))
(* -1 (* eps (- (* -1 (/ x eps)) 1/2)))
(*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)))
(* -1 (* eps (- (* -1 (/ x eps)) 1/2)))
(*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)))
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
(* eps (cos x))
(*.f64 eps (cos.f64 x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x)))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* 2 (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x)))))))))
(.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (.f64 (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* 1/24 (* eps (sin x))) (* 2 (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))))
(.f64 eps (fma.f64 eps (fma.f64 (sin.f64 x) (+.f64 #s(literal -1/2 binary64) (.f64 eps (.f64 eps #s(literal 1/24 binary64)))) (.f64 eps (*.f64 (cos.f64 x) #s(literal -1/6 binary64)))) (cos.f64 x)))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (*.f64 #s(literal 2 binary64) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (*.f64 #s(literal 2 binary64) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (*.f64 #s(literal 2 binary64) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (*.f64 #s(literal 2 binary64) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))))
(* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (*.f64 #s(literal 2 binary64) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))))
(* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (*.f64 #s(literal 2 binary64) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))))
(* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (*.f64 #s(literal 2 binary64) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))))
(* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (*.f64 #s(literal 2 binary64) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))))
(* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))
(.f64 #s(literal 2 binary64) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (.f64 #s(literal 1/2 binary64) eps))))
(+ (* -2 (* x (pow (sin (* 1/2 eps)) 2))) (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (fma.f64 #s(literal 2 binary64) (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (.f64 (.f64 x #s(literal -2 binary64)) (sin.f64 (.f64 #s(literal 1/2 binary64) eps)))))
(+ (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* -1 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))))
(fma.f64 x (.f64 #s(literal -2 binary64) (pow.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64))) (.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (.f64 #s(literal 1/2 binary64) eps))) (fma.f64 x (neg.f64 x) #s(literal 2 binary64))))
(+ (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -1 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* 1/3 (* x (pow (sin (* 1/2 eps)) 2))))))))
(fma.f64 x (fma.f64 x (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (neg.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)))) (.f64 (pow.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (fma.f64 x (.f64 x #s(literal 1/3 binary64)) #s(literal -2 binary64)))) (.f64 #s(literal 2 binary64) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (.f64 #s(literal 1/2 binary64) eps)))))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (*.f64 #s(literal 2 binary64) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (*.f64 #s(literal 2 binary64) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (*.f64 #s(literal 2 binary64) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (*.f64 #s(literal 2 binary64) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))))
(* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (*.f64 #s(literal 2 binary64) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))))
(* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (*.f64 #s(literal 2 binary64) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))))
(* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (*.f64 #s(literal 2 binary64) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))))
(* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (*.f64 #s(literal 2 binary64) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))))
(* 1/2 (* eps (cos x)))
(.f64 eps (.f64 #s(literal 1/2 binary64) (cos.f64 x)))
(* eps (+ (* -1/4 (* eps (sin x))) (* 1/2 (cos x))))
(.f64 eps (fma.f64 #s(literal 1/2 binary64) (cos.f64 x) (.f64 (*.f64 eps (sin.f64 x)) #s(literal -1/4 binary64))))
(* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))
(.f64 eps (fma.f64 #s(literal 1/2 binary64) (cos.f64 x) (.f64 eps (fma.f64 eps (.f64 (cos.f64 x) #s(literal -1/12 binary64)) (.f64 (sin.f64 x) #s(literal -1/4 binary64))))))
(* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (+ (* -1/48 (cos x)) (* 1/48 (* eps (sin x))))))))))
(.f64 eps (fma.f64 eps (fma.f64 eps (fma.f64 (.f64 eps (sin.f64 x)) #s(literal 1/48 binary64) (.f64 (cos.f64 x) #s(literal -1/12 binary64))) (.f64 (sin.f64 x) #s(literal -1/4 binary64))) (*.f64 #s(literal 1/2 binary64) (cos.f64 x))))
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))
(* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))
(* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))
(* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))
(* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))
(* (cos (* 1/2 eps)) (sin (* 1/2 eps)))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)))
(+ (* -1 (* x (pow (sin (* 1/2 eps)) 2))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (fma.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (neg.f64 x) (cos.f64 (.f64 #s(literal 1/2 binary64) eps))))
(+ (* x (+ (* -1 (pow (sin (* 1/2 eps)) 2)) (* -1/2 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))
(fma.f64 x (neg.f64 (pow.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64))) (.f64 (fma.f64 #s(literal -1/2 binary64) (.f64 x x) #s(literal 1 binary64)) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (.f64 #s(literal 1/2 binary64) eps)))))
(+ (* x (+ (* -1 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -1/2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* 1/6 (* x (pow (sin (* 1/2 eps)) 2))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))
(fma.f64 x (fma.f64 x (.f64 #s(literal -1/2 binary64) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (.f64 #s(literal 1/2 binary64) eps)))) (.f64 (pow.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (fma.f64 x (.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64)))) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (.f64 #s(literal 1/2 binary64) eps))))
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))
(* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))
(* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))
(* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))
(* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))
eps
(* eps (+ 1 (* -1/6 (pow eps 2))))
(fma.f64 eps (.f64 eps (.f64 eps #s(literal -1/6 binary64))) eps)
(* eps (+ 1 (* (pow eps 2) (- (* 1/120 (pow eps 2)) 1/6))))
(fma.f64 (.f64 eps eps) (.f64 (fma.f64 (*.f64 #s(literal 1/120 binary64) eps) eps #s(literal -1/6 binary64)) eps) eps)
(* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/120 (* -1/5040 (pow eps 2)))) 1/6))))
(fma.f64 (fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps #s(literal -1/5040 binary64)) #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) (.f64 eps (.f64 eps eps)) eps)
(sin eps)
(sin.f64 eps)
(sin eps)
(sin.f64 eps)
(sin eps)
(sin.f64 eps)
(sin eps)
(sin.f64 eps)
(sin eps)
(sin.f64 eps)
(sin eps)
(sin.f64 eps)
(sin eps)
(sin.f64 eps)
(sin eps)
(sin.f64 eps)
(* eps (cos x))
(*.f64 eps (cos.f64 x))
(* eps (cos x))
(*.f64 eps (cos.f64 x))
(* eps (cos x))
(*.f64 eps (cos.f64 x))
(* eps (cos x))
(*.f64 eps (cos.f64 x))
(* eps (cos x))
(*.f64 eps (cos.f64 x))
(* eps (cos x))
(*.f64 eps (cos.f64 x))
(* eps (cos x))
(*.f64 eps (cos.f64 x))
(* eps (cos x))
(*.f64 eps (cos.f64 x))
(* eps (cos x))
(*.f64 eps (cos.f64 x))
(* eps (cos x))
(*.f64 eps (cos.f64 x))
(* eps (cos x))
(*.f64 eps (cos.f64 x))
(* eps (cos x))
(*.f64 eps (cos.f64 x))
eps
(+ eps (* -1/2 (* eps (pow x 2))))
(fma.f64 eps (.f64 #s(literal -1/2 binary64) (.f64 x x)) eps)
(+ eps (* (pow x 2) (+ (* -1/2 eps) (* 1/24 (* eps (pow x 2))))))
(fma.f64 (.f64 eps (.f64 x x)) (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal -1/2 binary64)) eps)
(+ eps (* (pow x 2) (+ (* -1/2 eps) (* (pow x 2) (+ (* -1/720 (* eps (pow x 2))) (* 1/24 eps))))))
(fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (.f64 eps (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64))) (*.f64 eps #s(literal -1/2 binary64))) eps)
(* eps (cos x))
(*.f64 eps (cos.f64 x))
(* eps (cos x))
(*.f64 eps (cos.f64 x))
(* eps (cos x))
(*.f64 eps (cos.f64 x))
(* eps (cos x))
(*.f64 eps (cos.f64 x))
(* eps (cos x))
(*.f64 eps (cos.f64 x))
(* eps (cos x))
(*.f64 eps (cos.f64 x))
(* eps (cos x))
(*.f64 eps (cos.f64 x))
(* eps (cos x))
(*.f64 eps (cos.f64 x))
1
#s(literal 1 binary64)
(+ 1 (* -1/2 (pow x 2)))
(fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #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 x (.f64 x (fma.f64 (.f64 x x) (fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) #s(literal -1/2 binary64))) #s(literal 1 binary64))
(cos x)
(cos.f64 x)
(cos x)
(cos.f64 x)
(cos x)
(cos.f64 x)
(cos x)
(cos.f64 x)
(cos x)
(cos.f64 x)
(cos x)
(cos.f64 x)
(cos x)
(cos.f64 x)
(cos x)
(cos.f64 x)
(sin eps)
(sin.f64 eps)
(+ (sin eps) (* x (- (cos eps) 1)))
(fma.f64 x (+.f64 #s(literal -1 binary64) (cos.f64 eps)) (sin.f64 eps))
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))
(+.f64 (fma.f64 x (cos.f64 eps) (.f64 (fma.f64 #s(literal -1/2 binary64) (.f64 x x) #s(literal 1 binary64)) (sin.f64 eps))) (neg.f64 x))
(+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1)))
(fma.f64 x (+.f64 #s(literal -1 binary64) (fma.f64 x (.f64 #s(literal -1/2 binary64) (sin.f64 eps)) (fma.f64 x (.f64 x #s(literal 1/6 binary64)) (.f64 (fma.f64 x (.f64 x #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 eps))))) (sin.f64 eps))
(* -1/120 (pow x 5))
(*.f64 #s(literal -1/120 binary64) (pow.f64 x #s(literal 5 binary64)))
(* (pow x 5) (- (* 1/6 (/ 1 (pow x 2))) 1/120))
(.f64 (pow.f64 x #s(literal 5 binary64)) (+.f64 #s(literal -1/120 binary64) (/.f64 #s(literal 1/6 binary64) (.f64 x x))))
(* (pow x 5) (- (* 1/6 (/ 1 (pow x 2))) (+ 1/120 (/ 1 (pow x 4)))))
(.f64 (pow.f64 x #s(literal 5 binary64)) (+.f64 (+.f64 #s(literal -1/120 binary64) (/.f64 #s(literal 1/6 binary64) (.f64 x x))) (/.f64 #s(literal -1 binary64) (.f64 (.f64 x x) (*.f64 x x)))))
(* (pow x 5) (- (+ (* 1/6 (/ 1 (pow x 2))) (/ (sin (+ eps x)) (pow x 5))) (+ 1/120 (/ 1 (pow x 4)))))
(.f64 (pow.f64 x #s(literal 5 binary64)) (+.f64 (+.f64 (+.f64 #s(literal -1/120 binary64) (/.f64 #s(literal 1/6 binary64) (.f64 x x))) (/.f64 #s(literal -1 binary64) (.f64 (.f64 x x) (*.f64 x x)))) (/.f64 (sin.f64 (+.f64 eps x)) (pow.f64 x #s(literal 5 binary64)))))
(* -1/120 (pow x 5))
(*.f64 #s(literal -1/120 binary64) (pow.f64 x #s(literal 5 binary64)))
(* -1 (* (pow x 5) (- 1/120 (* 1/6 (/ 1 (pow x 2))))))
(.f64 (pow.f64 x #s(literal 5 binary64)) (+.f64 #s(literal -1/120 binary64) (/.f64 #s(literal 1/6 binary64) (.f64 x x))))
(* -1 (* (pow x 5) (- (+ 1/120 (/ 1 (pow x 4))) (* 1/6 (/ 1 (pow x 2))))))
(.f64 (pow.f64 x #s(literal 5 binary64)) (+.f64 (+.f64 #s(literal -1/120 binary64) (/.f64 #s(literal 1/6 binary64) (.f64 x x))) (/.f64 #s(literal -1 binary64) (.f64 (.f64 x x) (*.f64 x x)))))
(* -1 (* (pow x 5) (- (+ 1/120 (+ (* -1 (/ (sin (- eps (* -1 x))) (pow x 5))) (/ 1 (pow x 4)))) (* 1/6 (/ 1 (pow x 2))))))
(.f64 (pow.f64 x #s(literal 5 binary64)) (neg.f64 (+.f64 #s(literal 1/120 binary64) (+.f64 (-.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (.f64 x x))) (/.f64 (sin.f64 (+.f64 eps x)) (pow.f64 x #s(literal 5 binary64)))) (/.f64 #s(literal -1/6 binary64) (*.f64 x x))))))
(- (sin x) (+ x (* (pow x 3) (- (* 1/120 (pow x 2)) 1/6))))
(-.f64 (sin.f64 x) (fma.f64 (.f64 x x) (.f64 (fma.f64 #s(literal 1/120 binary64) (*.f64 x x) #s(literal -1/6 binary64)) x) x))
(- (+ (sin x) (* eps (cos x))) (+ x (* (pow x 3) (- (* 1/120 (pow x 2)) 1/6))))
(fma.f64 eps (cos.f64 x) (-.f64 (sin.f64 x) (fma.f64 (.f64 x x) (.f64 (fma.f64 #s(literal 1/120 binary64) (*.f64 x x) #s(literal -1/6 binary64)) x) x)))
(- (+ (sin x) (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))) (+ x (* (pow x 3) (- (* 1/120 (pow x 2)) 1/6))))
(-.f64 (fma.f64 eps (cos.f64 x) (.f64 (fma.f64 eps (.f64 eps #s(literal -1/2 binary64)) #s(literal 1 binary64)) (sin.f64 x))) (fma.f64 (.f64 x x) (.f64 (fma.f64 #s(literal 1/120 binary64) (*.f64 x x) #s(literal -1/6 binary64)) x) x))
(- (+ (sin x) (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))) (+ x (* (pow x 3) (- (* 1/120 (pow x 2)) 1/6))))
(-.f64 (fma.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (.f64 (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x))) (sin.f64 x)) (fma.f64 (.f64 x x) (.f64 (fma.f64 #s(literal 1/120 binary64) (.f64 x x) #s(literal -1/6 binary64)) x) x))
(- (sin (+ eps x)) (+ x (* (pow x 3) (- (* 1/120 (pow x 2)) 1/6))))
(-.f64 (sin.f64 (+.f64 eps x)) (fma.f64 (.f64 x x) (.f64 (fma.f64 #s(literal 1/120 binary64) (*.f64 x x) #s(literal -1/6 binary64)) x) x))
(- (sin (+ eps x)) (+ x (* (pow x 3) (- (* 1/120 (pow x 2)) 1/6))))
(-.f64 (sin.f64 (+.f64 eps x)) (fma.f64 (.f64 x x) (.f64 (fma.f64 #s(literal 1/120 binary64) (*.f64 x x) #s(literal -1/6 binary64)) x) x))
(- (sin (+ eps x)) (+ x (* (pow x 3) (- (* 1/120 (pow x 2)) 1/6))))
(-.f64 (sin.f64 (+.f64 eps x)) (fma.f64 (.f64 x x) (.f64 (fma.f64 #s(literal 1/120 binary64) (*.f64 x x) #s(literal -1/6 binary64)) x) x))
(- (sin (+ eps x)) (+ x (* (pow x 3) (- (* 1/120 (pow x 2)) 1/6))))
(-.f64 (sin.f64 (+.f64 eps x)) (fma.f64 (.f64 x x) (.f64 (fma.f64 #s(literal 1/120 binary64) (*.f64 x x) #s(literal -1/6 binary64)) x) x))
(- (sin (- x (* -1 eps))) (+ x (* (pow x 3) (- (* 1/120 (pow x 2)) 1/6))))
(-.f64 (sin.f64 (+.f64 eps x)) (fma.f64 (.f64 x x) (.f64 (fma.f64 #s(literal 1/120 binary64) (*.f64 x x) #s(literal -1/6 binary64)) x) x))
(- (sin (- x (* -1 eps))) (+ x (* (pow x 3) (- (* 1/120 (pow x 2)) 1/6))))
(-.f64 (sin.f64 (+.f64 eps x)) (fma.f64 (.f64 x x) (.f64 (fma.f64 #s(literal 1/120 binary64) (*.f64 x x) #s(literal -1/6 binary64)) x) x))
(- (sin (- x (* -1 eps))) (+ x (* (pow x 3) (- (* 1/120 (pow x 2)) 1/6))))
(-.f64 (sin.f64 (+.f64 eps x)) (fma.f64 (.f64 x x) (.f64 (fma.f64 #s(literal 1/120 binary64) (*.f64 x x) #s(literal -1/6 binary64)) x) x))
(- (sin (- x (* -1 eps))) (+ x (* (pow x 3) (- (* 1/120 (pow x 2)) 1/6))))
(-.f64 (sin.f64 (+.f64 eps x)) (fma.f64 (.f64 x x) (.f64 (fma.f64 #s(literal 1/120 binary64) (*.f64 x x) #s(literal -1/6 binary64)) x) x))
(sin eps)
(sin.f64 eps)
(+ (sin eps) (* x (cos eps)))
(fma.f64 x (cos.f64 eps) (sin.f64 eps))
(+ (sin eps) (* x (+ (cos eps) (* -1/2 (* x (sin eps))))))
(fma.f64 x (cos.f64 eps) (.f64 (fma.f64 #s(literal -1/2 binary64) (.f64 x x) #s(literal 1 binary64)) (sin.f64 eps)))
(+ (sin eps) (* x (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* -1/6 (* x (cos eps))))))))
(fma.f64 x (fma.f64 x (.f64 #s(literal -1/2 binary64) (sin.f64 eps)) (.f64 (fma.f64 x (*.f64 x #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 eps))) (sin.f64 eps))
(sin (+ eps x))
(sin.f64 (+.f64 eps x))
(sin (+ eps x))
(sin.f64 (+.f64 eps x))
(sin (+ eps x))
(sin.f64 (+.f64 eps x))
(sin (+ eps x))
(sin.f64 (+.f64 eps x))
(sin (- eps (* -1 x)))
(sin.f64 (+.f64 eps x))
(sin (- eps (* -1 x)))
(sin.f64 (+.f64 eps x))
(sin (- eps (* -1 x)))
(sin.f64 (+.f64 eps x))
(sin (- eps (* -1 x)))
(sin.f64 (+.f64 eps x))
(sin x)
(sin.f64 x)
(+ (sin x) (* eps (cos x)))
(fma.f64 eps (cos.f64 x) (sin.f64 x))
(+ (sin x) (* eps (+ (cos x) (* -1/2 (* eps (sin x))))))
(fma.f64 eps (cos.f64 x) (.f64 (fma.f64 eps (.f64 eps #s(literal -1/2 binary64)) #s(literal 1 binary64)) (sin.f64 x)))
(+ (sin x) (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))))
(fma.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (.f64 (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x))) (sin.f64 x))
(sin (+ eps x))
(sin.f64 (+.f64 eps x))
(sin (+ eps x))
(sin.f64 (+.f64 eps x))
(sin (+ eps x))
(sin.f64 (+.f64 eps x))
(sin (+ eps x))
(sin.f64 (+.f64 eps x))
(sin (- x (* -1 eps)))
(sin.f64 (+.f64 eps x))
(sin (- x (* -1 eps)))
(sin.f64 (+.f64 eps x))
(sin (- x (* -1 eps)))
(sin.f64 (+.f64 eps x))
(sin (- x (* -1 eps)))
(sin.f64 (+.f64 eps x))
eps
(+ eps x)
(+.f64 eps x)
(+ eps x)
(+.f64 eps x)
(+ eps x)
(+.f64 eps x)
x
(* x (+ 1 (/ eps x)))
(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)
x
(* x (+ 1 (* -1/6 (pow x 2))))
(fma.f64 x (.f64 #s(literal -1/6 binary64) (.f64 x x)) x)
(* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))))
(fma.f64 (.f64 x x) (.f64 (fma.f64 #s(literal 1/120 binary64) (*.f64 x x) #s(literal -1/6 binary64)) x) x)
(* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))))
(fma.f64 (.f64 x x) (.f64 (fma.f64 #s(literal 1/120 binary64) (*.f64 x x) #s(literal -1/6 binary64)) x) x)
(* 1/120 (pow x 5))
(*.f64 #s(literal 1/120 binary64) (pow.f64 x #s(literal 5 binary64)))
(* (pow x 5) (- 1/120 (* 1/6 (/ 1 (pow x 2)))))
(.f64 (pow.f64 x #s(literal 5 binary64)) (+.f64 #s(literal 1/120 binary64) (/.f64 #s(literal -1/6 binary64) (.f64 x x))))
(* (pow x 5) (- (+ 1/120 (/ 1 (pow x 4))) (* 1/6 (/ 1 (pow x 2)))))
(.f64 (pow.f64 x #s(literal 5 binary64)) (+.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (.f64 x x))) (+.f64 #s(literal 1/120 binary64) (/.f64 #s(literal -1/6 binary64) (*.f64 x x)))))
(* (pow x 5) (- (+ 1/120 (/ 1 (pow x 4))) (* 1/6 (/ 1 (pow x 2)))))
(.f64 (pow.f64 x #s(literal 5 binary64)) (+.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (.f64 x x))) (+.f64 #s(literal 1/120 binary64) (/.f64 #s(literal -1/6 binary64) (*.f64 x x)))))
(* 1/120 (pow x 5))
(*.f64 #s(literal 1/120 binary64) (pow.f64 x #s(literal 5 binary64)))
(* -1 (* (pow x 5) (- (* 1/6 (/ 1 (pow x 2))) 1/120)))
(.f64 (pow.f64 x #s(literal 5 binary64)) (+.f64 #s(literal 1/120 binary64) (/.f64 #s(literal -1/6 binary64) (.f64 x x))))
(* -1 (* (pow x 5) (- (* 1/6 (/ 1 (pow x 2))) (+ 1/120 (/ 1 (pow x 4))))))
(.f64 (pow.f64 x #s(literal 5 binary64)) (+.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (.f64 x x))) (+.f64 #s(literal 1/120 binary64) (/.f64 #s(literal -1/6 binary64) (*.f64 x x)))))
(* -1 (* (pow x 5) (- (* 1/6 (/ 1 (pow x 2))) (+ 1/120 (/ 1 (pow x 4))))))
(.f64 (pow.f64 x #s(literal 5 binary64)) (+.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (.f64 x x))) (+.f64 #s(literal 1/120 binary64) (/.f64 #s(literal -1/6 binary64) (*.f64 x x)))))
(sin eps)
(sin.f64 eps)
(+ (sin eps) (* x (- (cos eps) 1)))
(fma.f64 x (+.f64 #s(literal -1 binary64) (cos.f64 eps)) (sin.f64 eps))
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))
(+.f64 (fma.f64 x (cos.f64 eps) (.f64 (fma.f64 #s(literal -1/2 binary64) (.f64 x x) #s(literal 1 binary64)) (sin.f64 eps))) (neg.f64 x))
(+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1)))
(fma.f64 x (+.f64 #s(literal -1 binary64) (fma.f64 x (.f64 #s(literal -1/2 binary64) (sin.f64 eps)) (fma.f64 x (.f64 x #s(literal 1/6 binary64)) (.f64 (fma.f64 x (.f64 x #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 eps))))) (sin.f64 eps))
(* 1/5040 (pow x 7))
(*.f64 #s(literal 1/5040 binary64) (pow.f64 x #s(literal 7 binary64)))
(* (pow x 7) (- 1/5040 (* 1/120 (/ 1 (pow x 2)))))
(.f64 (pow.f64 x #s(literal 7 binary64)) (+.f64 #s(literal 1/5040 binary64) (/.f64 #s(literal -1/120 binary64) (.f64 x x))))
(* (pow x 7) (- (+ 1/5040 (/ 1/6 (pow x 4))) (* 1/120 (/ 1 (pow x 2)))))
(.f64 (pow.f64 x #s(literal 7 binary64)) (+.f64 (+.f64 #s(literal 1/5040 binary64) (/.f64 #s(literal -1/120 binary64) (.f64 x x))) (/.f64 #s(literal 1/6 binary64) (.f64 (.f64 x x) (*.f64 x x)))))
(* (pow x 7) (- (+ 1/5040 (/ 1/6 (pow x 4))) (+ (* 1/120 (/ 1 (pow x 2))) (/ 1 (pow x 6)))))
(.f64 (pow.f64 x #s(literal 7 binary64)) (+.f64 (/.f64 #s(literal 1/6 binary64) (.f64 (.f64 x x) (.f64 x x))) (+.f64 (+.f64 #s(literal 1/5040 binary64) (/.f64 #s(literal -1/120 binary64) (*.f64 x x))) (/.f64 #s(literal -1 binary64) (pow.f64 x #s(literal 6 binary64))))))
(* 1/5040 (pow x 7))
(*.f64 #s(literal 1/5040 binary64) (pow.f64 x #s(literal 7 binary64)))
(* -1 (* (pow x 7) (- (* 1/120 (/ 1 (pow x 2))) 1/5040)))
(.f64 (pow.f64 x #s(literal 7 binary64)) (+.f64 #s(literal 1/5040 binary64) (/.f64 #s(literal -1/120 binary64) (.f64 x x))))
(* -1 (* (pow x 7) (- (* 1/120 (/ 1 (pow x 2))) (+ 1/5040 (/ 1/6 (pow x 4))))))
(.f64 (pow.f64 x #s(literal 7 binary64)) (+.f64 (+.f64 #s(literal 1/5040 binary64) (/.f64 #s(literal -1/120 binary64) (.f64 x x))) (/.f64 #s(literal 1/6 binary64) (.f64 (.f64 x x) (*.f64 x x)))))
(* -1 (* (pow x 7) (- (+ (* 1/120 (/ 1 (pow x 2))) (/ 1 (pow x 6))) (+ 1/5040 (/ 1/6 (pow x 4))))))
(.f64 (pow.f64 x #s(literal 7 binary64)) (+.f64 (/.f64 #s(literal 1/6 binary64) (.f64 (.f64 x x) (.f64 x x))) (+.f64 (+.f64 #s(literal 1/5040 binary64) (/.f64 #s(literal -1/120 binary64) (*.f64 x x))) (/.f64 #s(literal -1 binary64) (pow.f64 x #s(literal 6 binary64))))))
(- (sin x) (+ x (* (pow x 3) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))
(-.f64 (sin.f64 x) (fma.f64 (.f64 x x) (.f64 x (fma.f64 (.f64 x x) (fma.f64 #s(literal -1/5040 binary64) (.f64 x x) #s(literal 1/120 binary64)) #s(literal -1/6 binary64))) x))
(- (+ (sin x) (* eps (cos x))) (+ x (* (pow x 3) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))
(-.f64 (fma.f64 eps (cos.f64 x) (sin.f64 x)) (fma.f64 (.f64 x x) (.f64 x (fma.f64 (.f64 x x) (fma.f64 #s(literal -1/5040 binary64) (.f64 x x) #s(literal 1/120 binary64)) #s(literal -1/6 binary64))) x))
(- (+ (sin x) (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))) (+ x (* (pow x 3) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))
(fma.f64 eps (cos.f64 x) (fma.f64 (fma.f64 eps (.f64 eps #s(literal -1/2 binary64)) #s(literal 1 binary64)) (sin.f64 x) (neg.f64 (fma.f64 (.f64 x x) (.f64 x (fma.f64 (.f64 x x) (fma.f64 #s(literal -1/5040 binary64) (*.f64 x x) #s(literal 1/120 binary64)) #s(literal -1/6 binary64))) x))))
(- (+ (sin x) (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))) (+ x (* (pow x 3) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))
(-.f64 (fma.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (.f64 (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x))) (sin.f64 x)) (fma.f64 (.f64 x x) (.f64 x (fma.f64 (.f64 x x) (fma.f64 #s(literal -1/5040 binary64) (*.f64 x x) #s(literal 1/120 binary64)) #s(literal -1/6 binary64))) x))
(- (sin (+ eps x)) (+ x (* (pow x 3) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))
(-.f64 (sin.f64 (+.f64 eps x)) (fma.f64 (.f64 x x) (.f64 x (fma.f64 (.f64 x x) (fma.f64 #s(literal -1/5040 binary64) (.f64 x x) #s(literal 1/120 binary64)) #s(literal -1/6 binary64))) x))
(- (sin (+ eps x)) (+ x (* (pow x 3) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))
(-.f64 (sin.f64 (+.f64 eps x)) (fma.f64 (.f64 x x) (.f64 x (fma.f64 (.f64 x x) (fma.f64 #s(literal -1/5040 binary64) (.f64 x x) #s(literal 1/120 binary64)) #s(literal -1/6 binary64))) x))
(- (sin (+ eps x)) (+ x (* (pow x 3) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))
(-.f64 (sin.f64 (+.f64 eps x)) (fma.f64 (.f64 x x) (.f64 x (fma.f64 (.f64 x x) (fma.f64 #s(literal -1/5040 binary64) (.f64 x x) #s(literal 1/120 binary64)) #s(literal -1/6 binary64))) x))
(- (sin (+ eps x)) (+ x (* (pow x 3) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))
(-.f64 (sin.f64 (+.f64 eps x)) (fma.f64 (.f64 x x) (.f64 x (fma.f64 (.f64 x x) (fma.f64 #s(literal -1/5040 binary64) (.f64 x x) #s(literal 1/120 binary64)) #s(literal -1/6 binary64))) x))
(- (sin (- x (* -1 eps))) (+ x (* (pow x 3) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))
(-.f64 (sin.f64 (+.f64 eps x)) (fma.f64 (.f64 x x) (.f64 x (fma.f64 (.f64 x x) (fma.f64 #s(literal -1/5040 binary64) (.f64 x x) #s(literal 1/120 binary64)) #s(literal -1/6 binary64))) x))
(- (sin (- x (* -1 eps))) (+ x (* (pow x 3) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))
(-.f64 (sin.f64 (+.f64 eps x)) (fma.f64 (.f64 x x) (.f64 x (fma.f64 (.f64 x x) (fma.f64 #s(literal -1/5040 binary64) (.f64 x x) #s(literal 1/120 binary64)) #s(literal -1/6 binary64))) x))
(- (sin (- x (* -1 eps))) (+ x (* (pow x 3) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))
(-.f64 (sin.f64 (+.f64 eps x)) (fma.f64 (.f64 x x) (.f64 x (fma.f64 (.f64 x x) (fma.f64 #s(literal -1/5040 binary64) (.f64 x x) #s(literal 1/120 binary64)) #s(literal -1/6 binary64))) x))
(- (sin (- x (* -1 eps))) (+ x (* (pow x 3) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))
(-.f64 (sin.f64 (+.f64 eps x)) (fma.f64 (.f64 x x) (.f64 x (fma.f64 (.f64 x x) (fma.f64 #s(literal -1/5040 binary64) (.f64 x x) #s(literal 1/120 binary64)) #s(literal -1/6 binary64))) x))
x
(* x (+ 1 (* -1/6 (pow x 2))))
(fma.f64 x (.f64 #s(literal -1/6 binary64) (.f64 x x)) x)
(* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))))
(fma.f64 (.f64 x x) (.f64 (fma.f64 #s(literal 1/120 binary64) (*.f64 x x) #s(literal -1/6 binary64)) x) x)
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))
(fma.f64 (.f64 x x) (.f64 x (fma.f64 (.f64 x x) (fma.f64 #s(literal -1/5040 binary64) (.f64 x x) #s(literal 1/120 binary64)) #s(literal -1/6 binary64))) x)
(* -1/5040 (pow x 7))
(*.f64 #s(literal -1/5040 binary64) (pow.f64 x #s(literal 7 binary64)))
(* (pow x 7) (- (* 1/120 (/ 1 (pow x 2))) 1/5040))
(.f64 (pow.f64 x #s(literal 7 binary64)) (+.f64 #s(literal -1/5040 binary64) (/.f64 #s(literal 1/120 binary64) (.f64 x x))))
(* (pow x 7) (- (* 1/120 (/ 1 (pow x 2))) (+ 1/5040 (/ 1/6 (pow x 4)))))
(.f64 (pow.f64 x #s(literal 7 binary64)) (+.f64 (+.f64 #s(literal -1/5040 binary64) (/.f64 #s(literal 1/120 binary64) (.f64 x x))) (/.f64 #s(literal -1/6 binary64) (.f64 (.f64 x x) (*.f64 x x)))))
(* (pow x 7) (- (+ (* 1/120 (/ 1 (pow x 2))) (/ 1 (pow x 6))) (+ 1/5040 (/ 1/6 (pow x 4)))))
(.f64 (pow.f64 x #s(literal 7 binary64)) (+.f64 (/.f64 #s(literal 1/120 binary64) (.f64 x x)) (+.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 6 binary64))) (+.f64 #s(literal -1/5040 binary64) (/.f64 #s(literal -1/6 binary64) (.f64 (.f64 x x) (*.f64 x x)))))))
(* -1/5040 (pow x 7))
(*.f64 #s(literal -1/5040 binary64) (pow.f64 x #s(literal 7 binary64)))
(* -1 (* (pow x 7) (- 1/5040 (* 1/120 (/ 1 (pow x 2))))))
(.f64 (pow.f64 x #s(literal 7 binary64)) (+.f64 #s(literal -1/5040 binary64) (/.f64 #s(literal 1/120 binary64) (.f64 x x))))
(* -1 (* (pow x 7) (- (+ 1/5040 (/ 1/6 (pow x 4))) (* 1/120 (/ 1 (pow x 2))))))
(.f64 (pow.f64 x #s(literal 7 binary64)) (+.f64 (+.f64 #s(literal -1/5040 binary64) (/.f64 #s(literal 1/120 binary64) (.f64 x x))) (/.f64 #s(literal -1/6 binary64) (.f64 (.f64 x x) (*.f64 x x)))))
(* -1 (* (pow x 7) (- (+ 1/5040 (/ 1/6 (pow x 4))) (+ (* 1/120 (/ 1 (pow x 2))) (/ 1 (pow x 6))))))
(.f64 (pow.f64 x #s(literal 7 binary64)) (+.f64 (/.f64 #s(literal 1/120 binary64) (.f64 x x)) (+.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 6 binary64))) (+.f64 #s(literal -1/5040 binary64) (/.f64 #s(literal -1/6 binary64) (.f64 (.f64 x x) (*.f64 x x)))))))
eps
(+ eps (* 2 x))
(fma.f64 x #s(literal 2 binary64) eps)
(+ eps (* 2 x))
(fma.f64 x #s(literal 2 binary64) eps)
(+ eps (* 2 x))
(fma.f64 x #s(literal 2 binary64) eps)
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* x (+ 2 (/ eps x)))
(*.f64 x (+.f64 (/.f64 eps x) #s(literal 2 binary64)))
(* x (+ 2 (/ eps x)))
(*.f64 x (+.f64 (/.f64 eps x) #s(literal 2 binary64)))
(* x (+ 2 (/ eps x)))
(*.f64 x (+.f64 (/.f64 eps x) #s(literal 2 binary64)))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* -1 (* x (- (* -1 (/ eps x)) 2)))
(*.f64 x (+.f64 (/.f64 eps x) #s(literal 2 binary64)))
(* -1 (* x (- (* -1 (/ eps x)) 2)))
(*.f64 x (+.f64 (/.f64 eps x) #s(literal 2 binary64)))
(* -1 (* x (- (* -1 (/ eps x)) 2)))
(*.f64 x (+.f64 (/.f64 eps x) #s(literal 2 binary64)))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(+ eps (* 2 x))
(fma.f64 x #s(literal 2 binary64) eps)
(+ eps (* 2 x))
(fma.f64 x #s(literal 2 binary64) eps)
(+ eps (* 2 x))
(fma.f64 x #s(literal 2 binary64) eps)
eps
(* eps (+ 1 (* 2 (/ x eps))))
(fma.f64 eps (/.f64 (*.f64 x #s(literal 2 binary64)) eps) eps)
(* eps (+ 1 (* 2 (/ x eps))))
(fma.f64 eps (/.f64 (*.f64 x #s(literal 2 binary64)) eps) eps)
(* eps (+ 1 (* 2 (/ x eps))))
(fma.f64 eps (/.f64 (*.f64 x #s(literal 2 binary64)) eps) eps)
eps
(* -1 (* eps (- (* -2 (/ x eps)) 1)))
(fma.f64 eps (/.f64 (*.f64 x #s(literal 2 binary64)) eps) eps)
(* -1 (* eps (- (* -2 (/ x eps)) 1)))
(fma.f64 eps (/.f64 (*.f64 x #s(literal 2 binary64)) eps) eps)
(* -1 (* eps (- (* -2 (/ x eps)) 1)))
(fma.f64 eps (/.f64 (*.f64 x #s(literal 2 binary64)) eps) eps)
(cos (* 1/2 eps))
(cos.f64 (*.f64 #s(literal 1/2 binary64) eps))
(+ (cos (* 1/2 eps)) (* -1 (* x (sin (* 1/2 eps)))))
(fma.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (neg.f64 x) (cos.f64 (.f64 #s(literal 1/2 binary64) eps)))
(+ (cos (* 1/2 eps)) (* x (- (* -1/2 (* x (cos (* 1/2 eps)))) (sin (* 1/2 eps)))))
(fma.f64 x (-.f64 (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (.f64 x #s(literal -1/2 binary64))) (sin.f64 (.f64 #s(literal 1/2 binary64) eps))) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)))
(+ (cos (* 1/2 eps)) (* x (- (* x (+ (* -1/2 (cos (* 1/2 eps))) (* 1/6 (* x (sin (* 1/2 eps)))))) (sin (* 1/2 eps)))))
(fma.f64 x (fma.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (.f64 x #s(literal -1/2 binary64)) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (fma.f64 x (.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64)))) (cos.f64 (.f64 #s(literal 1/2 binary64) eps)))
(cos (* 1/2 (+ eps (* 2 x))))
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(cos (* 1/2 (+ eps (* 2 x))))
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(cos (* 1/2 (+ eps (* 2 x))))
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(cos (* 1/2 (+ eps (* 2 x))))
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(cos (* 1/2 (- eps (* -2 x))))
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(cos (* 1/2 (- eps (* -2 x))))
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(cos (* 1/2 (- eps (* -2 x))))
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(cos (* 1/2 (- eps (* -2 x))))
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(cos x)
(cos.f64 x)
(+ (cos x) (* -1/2 (* eps (sin x))))
(fma.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x))
(+ (cos x) (* eps (- (* -1/8 (* eps (cos x))) (* 1/2 (sin x)))))
(fma.f64 eps (fma.f64 eps (.f64 (cos.f64 x) #s(literal -1/8 binary64)) (.f64 #s(literal -1/2 binary64) (sin.f64 x))) (cos.f64 x))
(+ (cos x) (* eps (- (* eps (+ (* -1/8 (cos x)) (* 1/48 (* eps (sin x))))) (* 1/2 (sin x)))))
(fma.f64 eps (fma.f64 eps (.f64 (cos.f64 x) #s(literal -1/8 binary64)) (.f64 (sin.f64 x) (fma.f64 eps (*.f64 eps #s(literal 1/48 binary64)) #s(literal -1/2 binary64)))) (cos.f64 x))
(cos (* 1/2 (+ eps (* 2 x))))
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(cos (* 1/2 (+ eps (* 2 x))))
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(cos (* 1/2 (+ eps (* 2 x))))
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(cos (* 1/2 (+ eps (* 2 x))))
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(cos (* 1/2 (- (* 2 x) (* -1 eps))))
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(cos (* 1/2 (- (* 2 x) (* -1 eps))))
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(cos (* 1/2 (- (* 2 x) (* -1 eps))))
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(cos (* 1/2 (- (* 2 x) (* -1 eps))))
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(* 1/2 eps)
(*.f64 #s(literal 1/2 binary64) eps)
(* eps (+ 1/2 (* -1/48 (pow eps 2))))
(.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))
(* eps (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))
(.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 eps (*.f64 eps #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))
(* eps (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))
(.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))
(sin (* 1/2 eps))
(sin.f64 (*.f64 #s(literal 1/2 binary64) eps))
(sin (* 1/2 eps))
(sin.f64 (*.f64 #s(literal 1/2 binary64) eps))
(sin (* 1/2 eps))
(sin.f64 (*.f64 #s(literal 1/2 binary64) eps))
(sin (* 1/2 eps))
(sin.f64 (*.f64 #s(literal 1/2 binary64) eps))
(sin (* 1/2 eps))
(sin.f64 (*.f64 #s(literal 1/2 binary64) eps))
(sin (* 1/2 eps))
(sin.f64 (*.f64 #s(literal 1/2 binary64) eps))
(sin (* 1/2 eps))
(sin.f64 (*.f64 #s(literal 1/2 binary64) eps))
(sin (* 1/2 eps))
(sin.f64 (*.f64 #s(literal 1/2 binary64) eps))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
-1/6
#s(literal -1/6 binary64)
(- (* 1/120 (pow x 2)) 1/6)
(fma.f64 #s(literal 1/120 binary64) (*.f64 x x) #s(literal -1/6 binary64))
(- (* 1/120 (pow x 2)) 1/6)
(fma.f64 #s(literal 1/120 binary64) (*.f64 x x) #s(literal -1/6 binary64))
(- (* 1/120 (pow x 2)) 1/6)
(fma.f64 #s(literal 1/120 binary64) (*.f64 x x) #s(literal -1/6 binary64))
(* 1/120 (pow x 2))
(.f64 #s(literal 1/120 binary64) (.f64 x x))
(* (pow x 2) (- 1/120 (* 1/6 (/ 1 (pow x 2)))))
(.f64 x (.f64 x (+.f64 #s(literal 1/120 binary64) (/.f64 #s(literal -1/6 binary64) (*.f64 x x)))))
(* (pow x 2) (- 1/120 (* 1/6 (/ 1 (pow x 2)))))
(.f64 x (.f64 x (+.f64 #s(literal 1/120 binary64) (/.f64 #s(literal -1/6 binary64) (*.f64 x x)))))
(* (pow x 2) (- 1/120 (* 1/6 (/ 1 (pow x 2)))))
(.f64 x (.f64 x (+.f64 #s(literal 1/120 binary64) (/.f64 #s(literal -1/6 binary64) (*.f64 x x)))))
(* 1/120 (pow x 2))
(.f64 #s(literal 1/120 binary64) (.f64 x x))
(* (pow x 2) (- 1/120 (* 1/6 (/ 1 (pow x 2)))))
(.f64 x (.f64 x (+.f64 #s(literal 1/120 binary64) (/.f64 #s(literal -1/6 binary64) (*.f64 x x)))))
(* (pow x 2) (- 1/120 (* 1/6 (/ 1 (pow x 2)))))
(.f64 x (.f64 x (+.f64 #s(literal 1/120 binary64) (/.f64 #s(literal -1/6 binary64) (*.f64 x x)))))
(* (pow x 2) (- 1/120 (* 1/6 (/ 1 (pow x 2)))))
(.f64 x (.f64 x (+.f64 #s(literal 1/120 binary64) (/.f64 #s(literal -1/6 binary64) (*.f64 x x)))))
(* 1/120 x)
(*.f64 x #s(literal 1/120 binary64))
(* x (+ 1/120 (* -1/5040 (pow x 2))))
(.f64 x (fma.f64 #s(literal -1/5040 binary64) (.f64 x x) #s(literal 1/120 binary64)))
(* x (+ 1/120 (* -1/5040 (pow x 2))))
(.f64 x (fma.f64 #s(literal -1/5040 binary64) (.f64 x x) #s(literal 1/120 binary64)))
(* x (+ 1/120 (* -1/5040 (pow x 2))))
(.f64 x (fma.f64 #s(literal -1/5040 binary64) (.f64 x x) #s(literal 1/120 binary64)))
(* -1/5040 (pow x 3))
(.f64 #s(literal -1/5040 binary64) (.f64 x (*.f64 x x)))
(* (pow x 3) (- (* 1/120 (/ 1 (pow x 2))) 1/5040))
(.f64 (.f64 x x) (.f64 x (+.f64 #s(literal -1/5040 binary64) (/.f64 #s(literal 1/120 binary64) (.f64 x x)))))
(* (pow x 3) (- (* 1/120 (/ 1 (pow x 2))) 1/5040))
(.f64 (.f64 x x) (.f64 x (+.f64 #s(literal -1/5040 binary64) (/.f64 #s(literal 1/120 binary64) (.f64 x x)))))
(* (pow x 3) (- (* 1/120 (/ 1 (pow x 2))) 1/5040))
(.f64 (.f64 x x) (.f64 x (+.f64 #s(literal -1/5040 binary64) (/.f64 #s(literal 1/120 binary64) (.f64 x x)))))
(* -1/5040 (pow x 3))
(.f64 #s(literal -1/5040 binary64) (.f64 x (*.f64 x x)))
(* -1 (* (pow x 3) (- 1/5040 (* 1/120 (/ 1 (pow x 2))))))
(.f64 (.f64 x x) (.f64 x (+.f64 #s(literal -1/5040 binary64) (/.f64 #s(literal 1/120 binary64) (.f64 x x)))))
(* -1 (* (pow x 3) (- 1/5040 (* 1/120 (/ 1 (pow x 2))))))
(.f64 (.f64 x x) (.f64 x (+.f64 #s(literal -1/5040 binary64) (/.f64 #s(literal 1/120 binary64) (.f64 x x)))))
(* -1 (* (pow x 3) (- 1/5040 (* 1/120 (/ 1 (pow x 2))))))
(.f64 (.f64 x x) (.f64 x (+.f64 #s(literal -1/5040 binary64) (/.f64 #s(literal 1/120 binary64) (.f64 x x)))))

eval145.0ms (1%)

Memory: 23.1MiB live, 246.9MiB allocated
Compiler: Compiled 43 412 to 3 190 computations (92.7% saved)

prune119.0ms (0.8%)

Memory

-22.8MiB live, 221.9MiB allocated

Pruning

14 alts after pruning (12 fresh and 2 done)

	Pruned	Kept	Total
New	1 126	11	1 137
Fresh	1	1	2
Picked	3	2	5
Done	1	0	1
Total	1 131	14	1 145

Accuracy

100.0%

Counts

1 145 → 14

Alt Table

Click to see full alt table

Status	Accuracy	Program
	99.1%	(fma.f64 (.f64 eps (.f64 x x)) (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal -1/2 binary64)) eps)
▶	98.4%	(fma.f64 eps (.f64 eps (.f64 eps #s(literal -1/6 binary64))) eps)
	53.3%	(/.f64 (.f64 (.f64 eps eps) (cos.f64 x)) eps)
	60.6%	(-.f64 (-.f64 (sin.f64 (+.f64 x eps)) x) (.f64 (.f64 x x) (.f64 x (fma.f64 (.f64 x x) #s(literal 1/120 binary64) #s(literal -1/6 binary64)))))
✓	60.6%	(-.f64 (sin.f64 (+.f64 x eps)) (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) (.f64 x (*.f64 x x)) x))
▶	100.0%	(.f64 (.f64 (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64))) (cos.f64 (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
	99.9%	(.f64 (.f64 (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64))) (cos.f64 (*.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
▶	99.7%	(.f64 (.f64 (.f64 #s(literal 1/2 binary64) eps) (cos.f64 (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
	99.9%	(.f64 (.f64 eps (fma.f64 #s(literal 1/2 binary64) (cos.f64 x) (.f64 eps (fma.f64 eps (.f64 (cos.f64 x) #s(literal -1/12 binary64)) (*.f64 (sin.f64 x) #s(literal -1/4 binary64)))))) #s(literal 2 binary64))
▶	99.1%	(.f64 eps (fma.f64 x (.f64 x (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) #s(literal -1/2 binary64))) #s(literal 1 binary64)))
	99.9%	(.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (.f64 (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x))))
	98.9%	(.f64 eps (fma.f64 #s(literal -1/2 binary64) (.f64 x x) #s(literal 1 binary64)))
✓	99.3%	(*.f64 eps (cos.f64 x))
▶	98.4%	eps

Compiler

Compiled 412 to 261 computations (36.7% saved)

simplify739.0ms (5.2%)

Memory

35.7MiB live, 865.4MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 15 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) (cos.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	640	(.f64 (.f64 (.f64 #s(literal 1/2 binary64) eps) (cos.f64 (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
✓	cost-diff	0	(fma.f64 (.f64 x x) (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) #s(literal -1/2 binary64))
✓	cost-diff	0	(.f64 x (fma.f64 (.f64 x x) (fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) #s(literal -1/2 binary64)))
✓	cost-diff	0	(fma.f64 x (.f64 x (fma.f64 (.f64 x x) (fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) #s(literal -1/2 binary64))) #s(literal 1 binary64))
✓	cost-diff	0	(.f64 eps (fma.f64 x (.f64 x (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) #s(literal -1/2 binary64))) #s(literal 1 binary64)))
✓	cost-diff	0	(*.f64 eps #s(literal -1/6 binary64))
✓	cost-diff	0	(.f64 eps (.f64 eps #s(literal -1/6 binary64)))
✓	cost-diff	0	(fma.f64 eps (.f64 eps (.f64 eps #s(literal -1/6 binary64))) eps)
✓	cost-diff	0	(.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 eps (*.f64 eps #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))
✓	cost-diff	0	(.f64 (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64))) (cos.f64 (*.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64))))
✓	cost-diff	128	(.f64 (.f64 (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64))) (cos.f64 (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
✓	cost-diff	320	(*.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64))

Rules

30 950×	`accelerator-lowering-fma.f32`
30 950×	`accelerator-lowering-fma.f64`
8 186×	`-lowering-.f32`
8 186×	`-lowering-.f64`
6 232×	`+-lowering-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	40	280
1	116	278
2	348	272
3	995	256
4	2239	256
5	2906	256
6	3226	256
7	3590	256
8	4155	256
9	4252	256
10	6933	256
11	7239	256
12	7319	256
13	7391	256
14	7399	256
15	7399	256
16	7399	256
17	7399	256
18	7399	254
0	10205	223

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

Inputs
(* (* (* eps (+ (* (* eps eps) (+ (* eps (* eps 1/3840)) -1/48)) 1/2)) (cos (* (+ x (+ x eps)) 1/2))) 2)
(* (* eps (+ (* (* eps eps) (+ (* eps (* eps 1/3840)) -1/48)) 1/2)) (cos (* (+ x (+ x eps)) 1/2)))
(* eps (+ (* (* eps eps) (+ (* eps (* eps 1/3840)) -1/48)) 1/2))
eps
(+ (* (* eps eps) (+ (* eps (* eps 1/3840)) -1/48)) 1/2)
(* eps eps)
(+ (* eps (* eps 1/3840)) -1/48)
(* eps 1/3840)
1/3840
-1/48
1/2
(cos (* (+ x (+ x eps)) 1/2))
(* (+ x (+ x eps)) 1/2)
(+ x (+ x eps))
x
(+ x eps)
2
eps
(+ (* eps (* eps (* eps -1/6))) eps)
eps
(* eps (* eps -1/6))
(* eps -1/6)
-1/6
(* eps (+ (* x (* x (+ (* (* x x) (+ (* (* x x) -1/720) 1/24)) -1/2))) 1))
eps
(+ (* x (* x (+ (* (* x x) (+ (* (* x x) -1/720) 1/24)) -1/2))) 1)
x
(* x (+ (* (* x x) (+ (* (* x x) -1/720) 1/24)) -1/2))
(+ (* (* x x) (+ (* (* x x) -1/720) 1/24)) -1/2)
(* x x)
(+ (* (* x x) -1/720) 1/24)
-1/720
1/24
-1/2
1
(* (* (* 1/2 eps) (cos (* (+ x (+ x eps)) 1/2))) 2)
(* (* 1/2 eps) (cos (* (+ x (+ x eps)) 1/2)))
(* 1/2 eps)
1/2
eps
(cos (* (+ x (+ x eps)) 1/2))
(* (+ x (+ x eps)) 1/2)
(+ x (+ x eps))
x
(+ x eps)
2

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

localize199.0ms (1.4%)

Memory

-31.4MiB live, 228.5MiB allocated

Localize:

Found 15 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(*.f64 #s(literal 1/2 binary64) eps)
✓	accuracy	100.0%	(.f64 (.f64 #s(literal 1/2 binary64) eps) (cos.f64 (*.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64))))
✓	accuracy	100.0%	(cos.f64 (*.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)))
✓	accuracy	99.6%	(+.f64 x (+.f64 x eps))
✓	accuracy	100.0%	(*.f64 x x)
✓	accuracy	100.0%	(.f64 x (fma.f64 (.f64 x x) (fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) #s(literal -1/2 binary64)))
✓	accuracy	100.0%	(.f64 eps (fma.f64 x (.f64 x (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) #s(literal -1/2 binary64))) #s(literal 1 binary64)))
✓	accuracy	100.0%	(fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64))
✓	accuracy	100.0%	(fma.f64 eps (.f64 eps (.f64 eps #s(literal -1/6 binary64))) eps)
✓	accuracy	99.8%	(.f64 eps (.f64 eps #s(literal -1/6 binary64)))
✓	accuracy	99.4%	(*.f64 eps #s(literal -1/6 binary64))
✓	accuracy	100.0%	(.f64 (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64))) (cos.f64 (*.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64))))
✓	accuracy	100.0%	(cos.f64 (*.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)))
✓	accuracy	99.8%	(*.f64 eps #s(literal 1/3840 binary64))
✓	accuracy	99.6%	(+.f64 x (+.f64 x eps))

Samples

91.0ms

256×

valid

Compiler

Compiled 261 to 42 computations (83.9% saved)

Precisions

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

ival-mult: 45.0ms (63.6% of total)

const: 14.0ms (19.8% of total)

ival-add: 9.0ms (12.7% of total)

ival-cos: 2.0ms (2.8% of total)

exact: 1.0ms (1.4% of total)

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

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

series33.0ms (0.2%)

Memory

-15.4MiB live, 61.3MiB allocated

Counts

19 → 324

Calls

Call 1

Inputs
#<alt (* (+ x (+ x eps)) 1/2)>
#<alt (* (* (* eps (+ (* (* eps eps) (+ (* eps (* eps 1/3840)) -1/48)) 1/2)) (cos (* (+ x (+ x eps)) 1/2))) 2)>
#<alt (* (* eps (+ (* (* eps eps) (+ (* eps (* eps 1/3840)) -1/48)) 1/2)) (cos (* (+ x (+ x eps)) 1/2)))>
#<alt (* eps (+ (* (* eps eps) (+ (* eps (* eps 1/3840)) -1/48)) 1/2))>
#<alt (+ (* eps (* eps (* eps -1/6))) eps)>
#<alt (* eps (* eps -1/6))>
#<alt (* eps -1/6)>
#<alt (* eps (+ (* x (* x (+ (* (* x x) (+ (* (* x x) -1/720) 1/24)) -1/2))) 1))>
#<alt (+ (* x (* x (+ (* (* x x) (+ (* (* x x) -1/720) 1/24)) -1/2))) 1)>
#<alt (* x (+ (* (* x x) (+ (* (* x x) -1/720) 1/24)) -1/2))>
#<alt (+ (* (* x x) (+ (* (* x x) -1/720) 1/24)) -1/2)>
#<alt (* (* (* 1/2 eps) (cos (* (+ x (+ x eps)) 1/2))) 2)>
#<alt (* (* 1/2 eps) (cos (* (+ x (+ x eps)) 1/2)))>
#<alt (* 1/2 eps)>
#<alt (+ x (+ x eps))>
#<alt (* eps 1/3840)>
#<alt (cos (* (+ x (+ x eps)) 1/2))>
#<alt (+ (* (* x x) -1/720) 1/24)>
#<alt (* x x)>

Outputs
#<alt (* 1/2 eps)>
#<alt (+ x (* 1/2 eps))>
#<alt (+ x (* 1/2 eps))>
#<alt (+ x (* 1/2 eps))>
#<alt x>
#<alt (* x (+ 1 (* 1/2 (/ eps x))))>
#<alt (* x (+ 1 (* 1/2 (/ eps x))))>
#<alt (* x (+ 1 (* 1/2 (/ eps x))))>
#<alt x>
#<alt (* -1 (* x (- (* -1/2 (/ eps x)) 1)))>
#<alt (* -1 (* x (- (* -1/2 (/ eps x)) 1)))>
#<alt (* -1 (* x (- (* -1/2 (/ eps x)) 1)))>
#<alt x>
#<alt (+ x (* 1/2 eps))>
#<alt (+ x (* 1/2 eps))>
#<alt (+ x (* 1/2 eps))>
#<alt (* 1/2 eps)>
#<alt (* eps (+ 1/2 (/ x eps)))>
#<alt (* eps (+ 1/2 (/ x eps)))>
#<alt (* eps (+ 1/2 (/ x eps)))>
#<alt (* 1/2 eps)>
#<alt (* -1 (* eps (- (* -1 (/ x eps)) 1/2)))>
#<alt (* -1 (* eps (- (* -1 (/ x eps)) 1/2)))>
#<alt (* -1 (* eps (- (* -1 (/ x eps)) 1/2)))>
#<alt (* eps (cos x))>
#<alt (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))>
#<alt (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* 2 (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x)))))))))>
#<alt (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* 1/24 (* eps (sin x))) (* 2 (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))))>
#<alt (* 1/1920 (* (pow eps 5) (cos (* 1/2 (+ eps (* 2 x))))))>
#<alt (* (pow eps 5) (+ (* -1/24 (/ (cos (* 1/2 (+ eps (* 2 x)))) (pow eps 2))) (* 1/1920 (cos (* 1/2 (+ eps (* 2 x)))))))>
#<alt (* (pow eps 5) (+ (* -1/24 (/ (cos (* 1/2 (+ eps (* 2 x)))) (pow eps 2))) (+ (* 1/1920 (cos (* 1/2 (+ eps (* 2 x))))) (/ (cos (* 1/2 (+ eps (* 2 x)))) (pow eps 4)))))>
#<alt (* (pow eps 5) (+ (* -1/24 (/ (cos (* 1/2 (+ eps (* 2 x)))) (pow eps 2))) (+ (* 1/1920 (cos (* 1/2 (+ eps (* 2 x))))) (/ (cos (* 1/2 (+ eps (* 2 x)))) (pow eps 4)))))>
#<alt (* 1/1920 (* (pow eps 5) (cos (* 1/2 (- (* 2 x) (* -1 eps))))))>
#<alt (* -1 (* (pow eps 5) (+ (* -1/1920 (cos (* 1/2 (- (* 2 x) (* -1 eps))))) (* 1/24 (/ (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (pow eps 2))))))>
#<alt (* -1 (* (pow eps 5) (+ (* -1 (/ (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (pow eps 4))) (+ (* -1/1920 (cos (* 1/2 (- (* 2 x) (* -1 eps))))) (* 1/24 (/ (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (pow eps 2)))))))>
#<alt (* -1 (* (pow eps 5) (+ (* -1 (/ (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (pow eps 4))) (+ (* -1/1920 (cos (* 1/2 (- (* 2 x) (* -1 eps))))) (* 1/24 (/ (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (pow eps 2)))))))>
#<alt (* 2 (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))>
#<alt (+ (* -2 (* eps (* x (* (sin (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))) (* 2 (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))))>
#<alt (+ (* 2 (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))) (* x (+ (* -2 (* eps (* (sin (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))) (* -1 (* eps (* x (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))))))>
#<alt (+ (* 2 (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))) (* x (+ (* -2 (* eps (* (sin (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))) (* x (+ (* -1 (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))) (* 1/3 (* eps (* x (* (sin (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))))))))>
#<alt (* 2 (* eps (* (cos (* 1/2 (+ eps (* 2 x)))) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))>
#<alt (* 2 (* eps (* (cos (* 1/2 (+ eps (* 2 x)))) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))>
#<alt (* 2 (* eps (* (cos (* 1/2 (+ eps (* 2 x)))) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))>
#<alt (* 2 (* eps (* (cos (* 1/2 (+ eps (* 2 x)))) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))>
#<alt (* 2 (* eps (* (cos (* 1/2 (- eps (* -2 x)))) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))>
#<alt (* 2 (* eps (* (cos (* 1/2 (- eps (* -2 x)))) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))>
#<alt (* 2 (* eps (* (cos (* 1/2 (- eps (* -2 x)))) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))>
#<alt (* 2 (* eps (* (cos (* 1/2 (- eps (* -2 x)))) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))>
#<alt (* 1/2 (* eps (cos x)))>
#<alt (* eps (+ (* -1/4 (* eps (sin x))) (* 1/2 (cos x))))>
#<alt (* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))>
#<alt (* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (+ (* -1/48 (cos x)) (* 1/48 (* eps (sin x))))))))))>
#<alt (* 1/3840 (* (pow eps 5) (cos (* 1/2 (+ eps (* 2 x))))))>
#<alt (* (pow eps 5) (+ (* -1/48 (/ (cos (* 1/2 (+ eps (* 2 x)))) (pow eps 2))) (* 1/3840 (cos (* 1/2 (+ eps (* 2 x)))))))>
#<alt (* (pow eps 5) (+ (* -1/48 (/ (cos (* 1/2 (+ eps (* 2 x)))) (pow eps 2))) (+ (* 1/3840 (cos (* 1/2 (+ eps (* 2 x))))) (* 1/2 (/ (cos (* 1/2 (+ eps (* 2 x)))) (pow eps 4))))))>
#<alt (* (pow eps 5) (+ (* -1/48 (/ (cos (* 1/2 (+ eps (* 2 x)))) (pow eps 2))) (+ (* 1/3840 (cos (* 1/2 (+ eps (* 2 x))))) (* 1/2 (/ (cos (* 1/2 (+ eps (* 2 x)))) (pow eps 4))))))>
#<alt (* 1/3840 (* (pow eps 5) (cos (* 1/2 (- (* 2 x) (* -1 eps))))))>
#<alt (* -1 (* (pow eps 5) (+ (* -1/3840 (cos (* 1/2 (- (* 2 x) (* -1 eps))))) (* 1/48 (/ (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (pow eps 2))))))>
#<alt (* -1 (* (pow eps 5) (+ (* -1/2 (/ (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (pow eps 4))) (+ (* -1/3840 (cos (* 1/2 (- (* 2 x) (* -1 eps))))) (* 1/48 (/ (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (pow eps 2)))))))>
#<alt (* -1 (* (pow eps 5) (+ (* -1/2 (/ (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (pow eps 4))) (+ (* -1/3840 (cos (* 1/2 (- (* 2 x) (* -1 eps))))) (* 1/48 (/ (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (pow eps 2)))))))>
#<alt (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))>
#<alt (+ (* -1 (* eps (* x (* (sin (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))) (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))>
#<alt (+ (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))) (* x (+ (* -1 (* eps (* (sin (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))) (* -1/2 (* eps (* x (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))))))>
#<alt (+ (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))) (* x (+ (* -1 (* eps (* (sin (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))) (* x (+ (* -1/2 (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))) (* 1/6 (* eps (* x (* (sin (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))))))))>
#<alt (* eps (* (cos (* 1/2 (+ eps (* 2 x)))) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))>
#<alt (* eps (* (cos (* 1/2 (+ eps (* 2 x)))) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))>
#<alt (* eps (* (cos (* 1/2 (+ eps (* 2 x)))) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))>
#<alt (* eps (* (cos (* 1/2 (+ eps (* 2 x)))) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))>
#<alt (* eps (* (cos (* 1/2 (- eps (* -2 x)))) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))>
#<alt (* eps (* (cos (* 1/2 (- eps (* -2 x)))) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))>
#<alt (* eps (* (cos (* 1/2 (- eps (* -2 x)))) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))>
#<alt (* eps (* (cos (* 1/2 (- eps (* -2 x)))) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))>
#<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) (- (* 1/3840 (pow eps 2)) 1/48))))>
#<alt (* 1/3840 (pow eps 5))>
#<alt (* (pow eps 5) (- 1/3840 (* 1/48 (/ 1 (pow eps 2)))))>
#<alt (* (pow eps 5) (- (+ 1/3840 (/ 1/2 (pow eps 4))) (* 1/48 (/ 1 (pow eps 2)))))>
#<alt (* (pow eps 5) (- (+ 1/3840 (/ 1/2 (pow eps 4))) (* 1/48 (/ 1 (pow eps 2)))))>
#<alt (* 1/3840 (pow eps 5))>
#<alt (* -1 (* (pow eps 5) (- (* 1/48 (/ 1 (pow eps 2))) 1/3840)))>
#<alt (* -1 (* (pow eps 5) (- (* 1/48 (/ 1 (pow eps 2))) (+ 1/3840 (/ 1/2 (pow eps 4))))))>
#<alt (* -1 (* (pow eps 5) (- (* 1/48 (/ 1 (pow eps 2))) (+ 1/3840 (/ 1/2 (pow eps 4))))))>
#<alt eps>
#<alt (* eps (+ 1 (* -1/6 (pow eps 2))))>
#<alt (* eps (+ 1 (* -1/6 (pow eps 2))))>
#<alt (* eps (+ 1 (* -1/6 (pow eps 2))))>
#<alt (* -1/6 (pow eps 3))>
#<alt (* (pow eps 3) (- (/ 1 (pow eps 2)) 1/6))>
#<alt (* (pow eps 3) (- (/ 1 (pow eps 2)) 1/6))>
#<alt (* (pow eps 3) (- (/ 1 (pow eps 2)) 1/6))>
#<alt (* -1/6 (pow eps 3))>
#<alt (* -1 (* (pow eps 3) (- 1/6 (/ 1 (pow eps 2)))))>
#<alt (* -1 (* (pow eps 3) (- 1/6 (/ 1 (pow eps 2)))))>
#<alt (* -1 (* (pow eps 3) (- 1/6 (/ 1 (pow eps 2)))))>
#<alt (* -1/6 (pow eps 2))>
#<alt (* -1/6 (pow eps 2))>
#<alt (* -1/6 (pow eps 2))>
#<alt (* -1/6 (pow eps 2))>
#<alt (* -1/6 (pow eps 2))>
#<alt (* -1/6 (pow eps 2))>
#<alt (* -1/6 (pow eps 2))>
#<alt (* -1/6 (pow eps 2))>
#<alt (* -1/6 (pow eps 2))>
#<alt (* -1/6 (pow eps 2))>
#<alt (* -1/6 (pow eps 2))>
#<alt (* -1/6 (pow eps 2))>
#<alt (* -1/6 eps)>
#<alt (* -1/6 eps)>
#<alt (* -1/6 eps)>
#<alt (* -1/6 eps)>
#<alt (* -1/6 eps)>
#<alt (* -1/6 eps)>
#<alt (* -1/6 eps)>
#<alt (* -1/6 eps)>
#<alt (* -1/6 eps)>
#<alt (* -1/6 eps)>
#<alt (* -1/6 eps)>
#<alt (* -1/6 eps)>
#<alt (* eps (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))))>
#<alt (* eps (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))))>
#<alt (* eps (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))))>
#<alt (* eps (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))))>
#<alt (* eps (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))))>
#<alt (* eps (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))))>
#<alt (* eps (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))))>
#<alt (* eps (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))))>
#<alt (* eps (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))))>
#<alt (* eps (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))))>
#<alt (* eps (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))))>
#<alt (* eps (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))))>
#<alt eps>
#<alt (+ eps (* -1/2 (* eps (pow x 2))))>
#<alt (+ eps (* (pow x 2) (+ (* -1/2 eps) (* 1/24 (* eps (pow x 2))))))>
#<alt (+ eps (* (pow x 2) (+ (* -1/2 eps) (* (pow x 2) (+ (* -1/720 (* eps (pow x 2))) (* 1/24 eps))))))>
#<alt (* -1/720 (* eps (pow x 6)))>
#<alt (* (pow x 6) (+ (* -1/720 eps) (* 1/24 (/ eps (pow x 2)))))>
#<alt (* (pow x 6) (+ (* -1/2 (/ eps (pow x 4))) (+ (* -1/720 eps) (* 1/24 (/ eps (pow x 2))))))>
#<alt (* (pow x 6) (+ (* -1/2 (/ eps (pow x 4))) (+ (* -1/720 eps) (+ (* 1/24 (/ eps (pow x 2))) (/ eps (pow x 6))))))>
#<alt (* -1/720 (* eps (pow x 6)))>
#<alt (* (pow x 6) (+ (* -1/720 eps) (* 1/24 (/ eps (pow x 2)))))>
#<alt (* (pow x 6) (+ (* -1/2 (/ eps (pow x 4))) (+ (* -1/720 eps) (* 1/24 (/ eps (pow x 2))))))>
#<alt (* (pow x 6) (+ (* -1/2 (/ eps (pow x 4))) (+ (* -1/720 eps) (+ (* 1/24 (/ eps (pow x 2))) (/ eps (pow x 6))))))>
#<alt 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 (* -1/720 (pow x 6))>
#<alt (* (pow x 6) (- (* 1/24 (/ 1 (pow x 2))) 1/720))>
#<alt (* (pow x 6) (- (* 1/24 (/ 1 (pow x 2))) (+ 1/720 (/ 1/2 (pow x 4)))))>
#<alt (* (pow x 6) (- (+ (* 1/24 (/ 1 (pow x 2))) (/ 1 (pow x 6))) (+ 1/720 (/ 1/2 (pow x 4)))))>
#<alt (* -1/720 (pow x 6))>
#<alt (* (pow x 6) (- (* 1/24 (/ 1 (pow x 2))) 1/720))>
#<alt (* (pow x 6) (- (* 1/24 (/ 1 (pow x 2))) (+ 1/720 (/ 1/2 (pow x 4)))))>
#<alt (* (pow x 6) (- (+ (* 1/24 (/ 1 (pow x 2))) (/ 1 (pow x 6))) (+ 1/720 (/ 1/2 (pow x 4)))))>
#<alt (* -1/2 x)>
#<alt (* x (- (* 1/24 (pow x 2)) 1/2))>
#<alt (* x (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))>
#<alt (* x (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))>
#<alt (* -1/720 (pow x 5))>
#<alt (* (pow x 5) (- (* 1/24 (/ 1 (pow x 2))) 1/720))>
#<alt (* (pow x 5) (- (* 1/24 (/ 1 (pow x 2))) (+ 1/720 (/ 1/2 (pow x 4)))))>
#<alt (* (pow x 5) (- (* 1/24 (/ 1 (pow x 2))) (+ 1/720 (/ 1/2 (pow x 4)))))>
#<alt (* -1/720 (pow x 5))>
#<alt (* -1 (* (pow x 5) (- 1/720 (* 1/24 (/ 1 (pow x 2))))))>
#<alt (* -1 (* (pow x 5) (- (+ 1/720 (/ 1/2 (pow x 4))) (* 1/24 (/ 1 (pow x 2))))))>
#<alt (* -1 (* (pow x 5) (- (+ 1/720 (/ 1/2 (pow x 4))) (* 1/24 (/ 1 (pow x 2))))))>
#<alt -1/2>
#<alt (- (* 1/24 (pow x 2)) 1/2)>
#<alt (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)>
#<alt (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)>
#<alt (* -1/720 (pow x 4))>
#<alt (* (pow x 4) (- (* 1/24 (/ 1 (pow x 2))) 1/720))>
#<alt (* (pow x 4) (- (* 1/24 (/ 1 (pow x 2))) (+ 1/720 (/ 1/2 (pow x 4)))))>
#<alt (* (pow x 4) (- (* 1/24 (/ 1 (pow x 2))) (+ 1/720 (/ 1/2 (pow x 4)))))>
#<alt (* -1/720 (pow x 4))>
#<alt (* (pow x 4) (- (* 1/24 (/ 1 (pow x 2))) 1/720))>
#<alt (* (pow x 4) (- (* 1/24 (/ 1 (pow x 2))) (+ 1/720 (/ 1/2 (pow x 4)))))>
#<alt (* (pow x 4) (- (* 1/24 (/ 1 (pow x 2))) (+ 1/720 (/ 1/2 (pow x 4)))))>
#<alt (* eps (cos x))>
#<alt (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))>
#<alt (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/8 (* eps (cos x)))))))>
#<alt (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/8 (cos x)) (* 1/48 (* eps (sin x)))))))))>
#<alt (* eps (cos (* 1/2 (+ eps (* 2 x)))))>
#<alt (* eps (cos (* 1/2 (+ eps (* 2 x)))))>
#<alt (* eps (cos (* 1/2 (+ eps (* 2 x)))))>
#<alt (* eps (cos (* 1/2 (+ eps (* 2 x)))))>
#<alt (* eps (cos (* 1/2 (- (* 2 x) (* -1 eps)))))>
#<alt (* eps (cos (* 1/2 (- (* 2 x) (* -1 eps)))))>
#<alt (* eps (cos (* 1/2 (- (* 2 x) (* -1 eps)))))>
#<alt (* eps (cos (* 1/2 (- (* 2 x) (* -1 eps)))))>
#<alt (* eps (cos (* 1/2 eps)))>
#<alt (+ (* -1 (* eps (* x (sin (* 1/2 eps))))) (* eps (cos (* 1/2 eps))))>
#<alt (+ (* eps (cos (* 1/2 eps))) (* x (+ (* -1 (* eps (sin (* 1/2 eps)))) (* -1/2 (* eps (* x (cos (* 1/2 eps))))))))>
#<alt (+ (* eps (cos (* 1/2 eps))) (* x (+ (* -1 (* eps (sin (* 1/2 eps)))) (* x (+ (* -1/2 (* eps (cos (* 1/2 eps)))) (* 1/6 (* eps (* x (sin (* 1/2 eps))))))))))>
#<alt (* eps (cos (* 1/2 (+ eps (* 2 x)))))>
#<alt (* eps (cos (* 1/2 (+ eps (* 2 x)))))>
#<alt (* eps (cos (* 1/2 (+ eps (* 2 x)))))>
#<alt (* eps (cos (* 1/2 (+ eps (* 2 x)))))>
#<alt (* eps (cos (* 1/2 (- eps (* -2 x)))))>
#<alt (* eps (cos (* 1/2 (- eps (* -2 x)))))>
#<alt (* eps (cos (* 1/2 (- eps (* -2 x)))))>
#<alt (* eps (cos (* 1/2 (- eps (* -2 x)))))>
#<alt (* 1/2 (* eps (cos x)))>
#<alt (* eps (+ (* -1/4 (* eps (sin x))) (* 1/2 (cos x))))>
#<alt (* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* -1/16 (* eps (cos x)))))))>
#<alt (* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (* 1/96 (* eps (sin x)))))))))>
#<alt (* 1/2 (* eps (cos (* 1/2 (+ eps (* 2 x))))))>
#<alt (* 1/2 (* eps (cos (* 1/2 (+ eps (* 2 x))))))>
#<alt (* 1/2 (* eps (cos (* 1/2 (+ eps (* 2 x))))))>
#<alt (* 1/2 (* eps (cos (* 1/2 (+ eps (* 2 x))))))>
#<alt (* 1/2 (* eps (cos (* 1/2 (- (* 2 x) (* -1 eps))))))>
#<alt (* 1/2 (* eps (cos (* 1/2 (- (* 2 x) (* -1 eps))))))>
#<alt (* 1/2 (* eps (cos (* 1/2 (- (* 2 x) (* -1 eps))))))>
#<alt (* 1/2 (* eps (cos (* 1/2 (- (* 2 x) (* -1 eps))))))>
#<alt (* 1/2 (* eps (cos (* 1/2 eps))))>
#<alt (+ (* -1/2 (* eps (* x (sin (* 1/2 eps))))) (* 1/2 (* eps (cos (* 1/2 eps)))))>
#<alt (+ (* 1/2 (* eps (cos (* 1/2 eps)))) (* x (+ (* -1/2 (* eps (sin (* 1/2 eps)))) (* -1/4 (* eps (* x (cos (* 1/2 eps))))))))>
#<alt (+ (* 1/2 (* eps (cos (* 1/2 eps)))) (* x (+ (* -1/2 (* eps (sin (* 1/2 eps)))) (* x (+ (* -1/4 (* eps (cos (* 1/2 eps)))) (* 1/12 (* eps (* x (sin (* 1/2 eps))))))))))>
#<alt (* 1/2 (* eps (cos (* 1/2 (+ eps (* 2 x))))))>
#<alt (* 1/2 (* eps (cos (* 1/2 (+ eps (* 2 x))))))>
#<alt (* 1/2 (* eps (cos (* 1/2 (+ eps (* 2 x))))))>
#<alt (* 1/2 (* eps (cos (* 1/2 (+ eps (* 2 x))))))>
#<alt (* 1/2 (* eps (cos (* 1/2 (- eps (* -2 x))))))>
#<alt (* 1/2 (* eps (cos (* 1/2 (- eps (* -2 x))))))>
#<alt (* 1/2 (* eps (cos (* 1/2 (- eps (* -2 x))))))>
#<alt (* 1/2 (* eps (cos (* 1/2 (- eps (* -2 x))))))>
#<alt (* 1/2 eps)>
#<alt (* 1/2 eps)>
#<alt (* 1/2 eps)>
#<alt (* 1/2 eps)>
#<alt (* 1/2 eps)>
#<alt (* 1/2 eps)>
#<alt (* 1/2 eps)>
#<alt (* 1/2 eps)>
#<alt (* 1/2 eps)>
#<alt (* 1/2 eps)>
#<alt (* 1/2 eps)>
#<alt (* 1/2 eps)>
#<alt eps>
#<alt (+ eps (* 2 x))>
#<alt (+ eps (* 2 x))>
#<alt (+ eps (* 2 x))>
#<alt (* 2 x)>
#<alt (* x (+ 2 (/ eps x)))>
#<alt (* x (+ 2 (/ eps x)))>
#<alt (* x (+ 2 (/ eps x)))>
#<alt (* 2 x)>
#<alt (* -1 (* x (- (* -1 (/ eps x)) 2)))>
#<alt (* -1 (* x (- (* -1 (/ eps x)) 2)))>
#<alt (* -1 (* x (- (* -1 (/ eps x)) 2)))>
#<alt (* 2 x)>
#<alt (+ eps (* 2 x))>
#<alt (+ eps (* 2 x))>
#<alt (+ eps (* 2 x))>
#<alt eps>
#<alt (* eps (+ 1 (* 2 (/ x eps))))>
#<alt (* eps (+ 1 (* 2 (/ x eps))))>
#<alt (* eps (+ 1 (* 2 (/ x eps))))>
#<alt eps>
#<alt (* -1 (* eps (- (* -2 (/ x eps)) 1)))>
#<alt (* -1 (* eps (- (* -2 (/ x eps)) 1)))>
#<alt (* -1 (* eps (- (* -2 (/ x eps)) 1)))>
#<alt (* 1/3840 eps)>
#<alt (* 1/3840 eps)>
#<alt (* 1/3840 eps)>
#<alt (* 1/3840 eps)>
#<alt (* 1/3840 eps)>
#<alt (* 1/3840 eps)>
#<alt (* 1/3840 eps)>
#<alt (* 1/3840 eps)>
#<alt (* 1/3840 eps)>
#<alt (* 1/3840 eps)>
#<alt (* 1/3840 eps)>
#<alt (* 1/3840 eps)>
#<alt (cos (* 1/2 eps))>
#<alt (+ (cos (* 1/2 eps)) (* -1 (* x (sin (* 1/2 eps)))))>
#<alt (+ (cos (* 1/2 eps)) (* x (- (* -1/2 (* x (cos (* 1/2 eps)))) (sin (* 1/2 eps)))))>
#<alt (+ (cos (* 1/2 eps)) (* x (- (* x (+ (* -1/2 (cos (* 1/2 eps))) (* 1/6 (* x (sin (* 1/2 eps)))))) (sin (* 1/2 eps)))))>
#<alt (cos (* 1/2 (+ eps (* 2 x))))>
#<alt (cos (* 1/2 (+ eps (* 2 x))))>
#<alt (cos (* 1/2 (+ eps (* 2 x))))>
#<alt (cos (* 1/2 (+ eps (* 2 x))))>
#<alt (cos (* 1/2 (- eps (* -2 x))))>
#<alt (cos (* 1/2 (- eps (* -2 x))))>
#<alt (cos (* 1/2 (- eps (* -2 x))))>
#<alt (cos (* 1/2 (- eps (* -2 x))))>
#<alt (cos x)>
#<alt (+ (cos x) (* -1/2 (* eps (sin x))))>
#<alt (+ (cos x) (* eps (- (* -1/8 (* eps (cos x))) (* 1/2 (sin x)))))>
#<alt (+ (cos x) (* eps (- (* eps (+ (* -1/8 (cos x)) (* 1/48 (* eps (sin x))))) (* 1/2 (sin x)))))>
#<alt (cos (* 1/2 (+ eps (* 2 x))))>
#<alt (cos (* 1/2 (+ eps (* 2 x))))>
#<alt (cos (* 1/2 (+ eps (* 2 x))))>
#<alt (cos (* 1/2 (+ eps (* 2 x))))>
#<alt (cos (* 1/2 (- (* 2 x) (* -1 eps))))>
#<alt (cos (* 1/2 (- (* 2 x) (* -1 eps))))>
#<alt (cos (* 1/2 (- (* 2 x) (* -1 eps))))>
#<alt (cos (* 1/2 (- (* 2 x) (* -1 eps))))>
#<alt 1/24>
#<alt (+ 1/24 (* -1/720 (pow x 2)))>
#<alt (+ 1/24 (* -1/720 (pow x 2)))>
#<alt (+ 1/24 (* -1/720 (pow x 2)))>
#<alt (* -1/720 (pow x 2))>
#<alt (* (pow x 2) (- (* 1/24 (/ 1 (pow x 2))) 1/720))>
#<alt (* (pow x 2) (- (* 1/24 (/ 1 (pow x 2))) 1/720))>
#<alt (* (pow x 2) (- (* 1/24 (/ 1 (pow x 2))) 1/720))>
#<alt (* -1/720 (pow x 2))>
#<alt (* (pow x 2) (- (* 1/24 (/ 1 (pow x 2))) 1/720))>
#<alt (* (pow x 2) (- (* 1/24 (/ 1 (pow x 2))) 1/720))>
#<alt (* (pow x 2) (- (* 1/24 (/ 1 (pow x 2))) 1/720))>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>

Calls

81 calls:

Time	Variable		Point	Expression
5.0ms	eps	@	-inf	(* (* (* 1/2 eps) (cos (* (+ x (+ x eps)) 1/2))) 2)
3.0ms	eps	@	inf	(* eps (+ (* (* eps eps) (+ (* eps (* eps 1/3840)) -1/48)) 1/2))
2.0ms	x	@	inf	(* (* (* eps (+ (* (* eps eps) (+ (* eps (* eps 1/3840)) -1/48)) 1/2)) (cos (* (+ x (+ x eps)) 1/2))) 2)
1.0ms	eps	@	0	(* eps (+ (* x (* x (+ (* (* x x) (+ (* (* x x) -1/720) 1/24)) -1/2))) 1))
1.0ms	eps	@	inf	(* (* (* eps (+ (* (* eps eps) (+ (* eps (* eps 1/3840)) -1/48)) 1/2)) (cos (* (+ x (+ x eps)) 1/2))) 2)

rewrite479.0ms (3.4%)

Memory

19.5MiB live, 584.6MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

5 160×	`accelerator-lowering-fma.f32`
5 160×	`accelerator-lowering-fma.f64`
4 060×	`/-lowering-/.f32`
4 060×	`/-lowering-/.f64`
3 786×	`-lowering-.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	40	212
1	216	208
2	1690	206
0	8241	181

Stop Event

1×	iter limit
1×	node limit

Counts

19 → 466

Calls

Call 1

Inputs
(* (+ x (+ x eps)) 1/2)
(* (* (* eps (+ (* (* eps eps) (+ (* eps (* eps 1/3840)) -1/48)) 1/2)) (cos (* (+ x (+ x eps)) 1/2))) 2)
(* (* eps (+ (* (* eps eps) (+ (* eps (* eps 1/3840)) -1/48)) 1/2)) (cos (* (+ x (+ x eps)) 1/2)))
(* eps (+ (* (* eps eps) (+ (* eps (* eps 1/3840)) -1/48)) 1/2))
(+ (* eps (* eps (* eps -1/6))) eps)
(* eps (* eps -1/6))
(* eps -1/6)
(* eps (+ (* x (* x (+ (* (* x x) (+ (* (* x x) -1/720) 1/24)) -1/2))) 1))
(+ (* x (* x (+ (* (* x x) (+ (* (* x x) -1/720) 1/24)) -1/2))) 1)
(* x (+ (* (* x x) (+ (* (* x x) -1/720) 1/24)) -1/2))
(+ (* (* x x) (+ (* (* x x) -1/720) 1/24)) -1/2)
(* (* (* 1/2 eps) (cos (* (+ x (+ x eps)) 1/2))) 2)
(* (* 1/2 eps) (cos (* (+ x (+ x eps)) 1/2)))
(* 1/2 eps)
(+ x (+ x eps))
(* eps 1/3840)
(cos (* (+ x (+ x eps)) 1/2))
(+ (* (* x x) -1/720) 1/24)
(* x 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)))
(fma.f64 (+.f64 x x) #s(literal 1/2 binary64) (*.f64 eps #s(literal 1/2 binary64)))
(/.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (+.f64 x (+.f64 x eps))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (+.f64 x eps) (-.f64 (+.f64 x eps) x) (.f64 x x)) (.f64 #s(literal 1/2 binary64) (fma.f64 (+.f64 x eps) (.f64 (+.f64 x eps) (+.f64 x eps)) (.f64 x (*.f64 x x))))))
(/.f64 #s(literal 1 binary64) (/.f64 (neg.f64 eps) (.f64 #s(literal 1/2 binary64) (.f64 (+.f64 x (+.f64 x eps)) (neg.f64 eps)))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (+.f64 x eps) (-.f64 (+.f64 x eps) x) (.f64 x x)) (.f64 (fma.f64 (+.f64 x eps) (.f64 (+.f64 x eps) (+.f64 x eps)) (.f64 x (*.f64 x x))) #s(literal 1/2 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (neg.f64 eps) (.f64 (.f64 (+.f64 x (+.f64 x eps)) (neg.f64 eps)) #s(literal 1/2 binary64))))
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(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1/576 binary64) (-.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/518400 binary64)) (.f64 (.f64 x x) #s(literal -1/17280 binary64)))) (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (*.f64 x x)) #s(literal -1/373248000 binary64)) #s(literal 1/13824 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1/24 binary64) (.f64 (.f64 x x) #s(literal -1/720 binary64))) (-.f64 #s(literal 1/576 binary64) (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/518400 binary64)))))
(/.f64 (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal -1/373248000 binary64)) #s(literal 1/13824 binary64)) (-.f64 (fma.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/518400 binary64) #s(literal 1/576 binary64)) (.f64 (.f64 x x) #s(literal -1/17280 binary64))))
(/.f64 (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal -1/373248000 binary64)) #s(literal 1/13824 binary64)) (+.f64 #s(literal 1/576 binary64) (-.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/518400 binary64)) (.f64 (*.f64 x x) #s(literal -1/17280 binary64)))))
(/.f64 (fma.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/518400 binary64) #s(literal -1/576 binary64)) (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal -1/24 binary64)))
(/.f64 (neg.f64 (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal -1/373248000 binary64)) #s(literal 1/13824 binary64))) (neg.f64 (-.f64 (fma.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/518400 binary64) #s(literal 1/576 binary64)) (.f64 (.f64 x x) #s(literal -1/17280 binary64)))))
(/.f64 (neg.f64 (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal -1/373248000 binary64)) #s(literal 1/13824 binary64))) (neg.f64 (+.f64 #s(literal 1/576 binary64) (-.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/518400 binary64)) (.f64 (*.f64 x x) #s(literal -1/17280 binary64))))))
(/.f64 (neg.f64 (fma.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/518400 binary64) #s(literal -1/576 binary64))) (neg.f64 (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal -1/24 binary64))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)))))
(/.f64 (-.f64 #s(literal 1/576 binary64) (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/518400 binary64))) (-.f64 #s(literal 1/24 binary64) (.f64 (.f64 x x) #s(literal -1/720 binary64))))
(/.f64 (-.f64 (.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/518400 binary64)) (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal -1/24 binary64))) (.f64 (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal -1/24 binary64)) #s(literal 1/576 binary64))) (.f64 (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal -1/24 binary64)) (fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal -1/24 binary64))))
(/.f64 (neg.f64 (neg.f64 (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal -1/373248000 binary64)) #s(literal 1/13824 binary64)))) (neg.f64 (neg.f64 (-.f64 (fma.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/518400 binary64) #s(literal 1/576 binary64)) (.f64 (.f64 x x) #s(literal -1/17280 binary64))))))
(/.f64 (neg.f64 (neg.f64 (fma.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/518400 binary64) #s(literal -1/576 binary64)))) (neg.f64 (neg.f64 (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal -1/24 binary64)))))
(/.f64 (neg.f64 (-.f64 #s(literal 1/576 binary64) (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/518400 binary64)))) (neg.f64 (-.f64 #s(literal 1/24 binary64) (.f64 (.f64 x x) #s(literal -1/720 binary64)))))
(/.f64 (-.f64 (pow.f64 (/.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/518400 binary64)) (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal -1/24 binary64))) #s(literal 3 binary64)) (pow.f64 (/.f64 #s(literal 1/576 binary64) (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal -1/24 binary64))) #s(literal 3 binary64))) (fma.f64 (/.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/518400 binary64)) (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal -1/24 binary64))) (/.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/518400 binary64)) (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal -1/24 binary64))) (fma.f64 (/.f64 #s(literal 1/576 binary64) (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal -1/24 binary64))) (/.f64 #s(literal 1/576 binary64) (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal -1/24 binary64))) (.f64 (/.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/518400 binary64)) (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal -1/24 binary64))) (/.f64 #s(literal 1/576 binary64) (fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal -1/24 binary64)))))))
(/.f64 (-.f64 (.f64 (/.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/518400 binary64)) (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal -1/24 binary64))) (/.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/518400 binary64)) (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal -1/24 binary64)))) (.f64 (/.f64 #s(literal 1/576 binary64) (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal -1/24 binary64))) (/.f64 #s(literal 1/576 binary64) (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal -1/24 binary64))))) (+.f64 (/.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/518400 binary64)) (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal -1/24 binary64))) (/.f64 #s(literal 1/576 binary64) (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal -1/24 binary64)))))
(pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64))) #s(literal -1 binary64))
(.f64 #s(literal 1 binary64) (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)))
(.f64 (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal -1/373248000 binary64)) #s(literal 1/13824 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/518400 binary64) #s(literal 1/576 binary64)) (.f64 (*.f64 x x) #s(literal -1/17280 binary64)))))
(.f64 (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal -1/373248000 binary64)) #s(literal 1/13824 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/576 binary64) (-.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/518400 binary64)) (.f64 (.f64 x x) #s(literal -1/17280 binary64))))))
(.f64 (fma.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/518400 binary64) #s(literal -1/576 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal -1/24 binary64))))
(.f64 (neg.f64 (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal -1/373248000 binary64)) #s(literal 1/13824 binary64))) (/.f64 #s(literal 1 binary64) (neg.f64 (-.f64 (fma.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/518400 binary64) #s(literal 1/576 binary64)) (.f64 (*.f64 x x) #s(literal -1/17280 binary64))))))
(.f64 (neg.f64 (fma.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/518400 binary64) #s(literal -1/576 binary64))) (/.f64 #s(literal 1 binary64) (neg.f64 (fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal -1/24 binary64)))))
(.f64 (-.f64 #s(literal 1/576 binary64) (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/518400 binary64))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/24 binary64) (.f64 (*.f64 x x) #s(literal -1/720 binary64)))))
(exp.f64 (*.f64 (log.f64 x) #s(literal 2 binary64)))
(pow.f64 x #s(literal 2 binary64))
(pow.f64 (*.f64 x x) #s(literal 1 binary64))
(pow.f64 (exp.f64 (log.f64 x)) #s(literal 2 binary64))
(*.f64 x x)
(*.f64 (exp.f64 (log.f64 x)) (exp.f64 (log.f64 x)))

simplify395.0ms (2.8%)

Memory

16.9MiB live, 524.8MiB allocated

Algorithm

1×	egg-herbie

Rules

12 524×	`accelerator-lowering-fma.f32`
12 524×	`accelerator-lowering-fma.f64`
5 690×	`-lowering-.f32`
5 690×	`-lowering-.f64`
3 578×	`+-lowering-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	403	4127
1	1269	3902
2	4009	3752
3	7933	3752
0	8032	3428

Stop Event

1×	iter limit
1×	node limit

Counts

324 → 324

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 (cos x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* 2 (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x)))))))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* 1/24 (* eps (sin x))) (* 2 (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))))
(* 1/1920 (* (pow eps 5) (cos (* 1/2 (+ eps (* 2 x))))))
(* (pow eps 5) (+ (* -1/24 (/ (cos (* 1/2 (+ eps (* 2 x)))) (pow eps 2))) (* 1/1920 (cos (* 1/2 (+ eps (* 2 x)))))))
(* (pow eps 5) (+ (* -1/24 (/ (cos (* 1/2 (+ eps (* 2 x)))) (pow eps 2))) (+ (* 1/1920 (cos (* 1/2 (+ eps (* 2 x))))) (/ (cos (* 1/2 (+ eps (* 2 x)))) (pow eps 4)))))
(* (pow eps 5) (+ (* -1/24 (/ (cos (* 1/2 (+ eps (* 2 x)))) (pow eps 2))) (+ (* 1/1920 (cos (* 1/2 (+ eps (* 2 x))))) (/ (cos (* 1/2 (+ eps (* 2 x)))) (pow eps 4)))))
(* 1/1920 (* (pow eps 5) (cos (* 1/2 (- (* 2 x) (* -1 eps))))))
(* -1 (* (pow eps 5) (+ (* -1/1920 (cos (* 1/2 (- (* 2 x) (* -1 eps))))) (* 1/24 (/ (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (pow eps 2))))))
(* -1 (* (pow eps 5) (+ (* -1 (/ (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (pow eps 4))) (+ (* -1/1920 (cos (* 1/2 (- (* 2 x) (* -1 eps))))) (* 1/24 (/ (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (pow eps 2)))))))
(* -1 (* (pow eps 5) (+ (* -1 (/ (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (pow eps 4))) (+ (* -1/1920 (cos (* 1/2 (- (* 2 x) (* -1 eps))))) (* 1/24 (/ (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (pow eps 2)))))))
(* 2 (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))
(+ (* -2 (* eps (* x (* (sin (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))) (* 2 (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))))
(+ (* 2 (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))) (* x (+ (* -2 (* eps (* (sin (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))) (* -1 (* eps (* x (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))))))
(+ (* 2 (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))) (* x (+ (* -2 (* eps (* (sin (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))) (* x (+ (* -1 (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))) (* 1/3 (* eps (* x (* (sin (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))))))))
(* 2 (* eps (* (cos (* 1/2 (+ eps (* 2 x)))) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))
(* 2 (* eps (* (cos (* 1/2 (+ eps (* 2 x)))) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))
(* 2 (* eps (* (cos (* 1/2 (+ eps (* 2 x)))) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))
(* 2 (* eps (* (cos (* 1/2 (+ eps (* 2 x)))) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))
(* 2 (* eps (* (cos (* 1/2 (- eps (* -2 x)))) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))
(* 2 (* eps (* (cos (* 1/2 (- eps (* -2 x)))) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))
(* 2 (* eps (* (cos (* 1/2 (- eps (* -2 x)))) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))
(* 2 (* eps (* (cos (* 1/2 (- eps (* -2 x)))) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))
(* 1/2 (* eps (cos x)))
(* eps (+ (* -1/4 (* eps (sin x))) (* 1/2 (cos x))))
(* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))
(* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (+ (* -1/48 (cos x)) (* 1/48 (* eps (sin x))))))))))
(* 1/3840 (* (pow eps 5) (cos (* 1/2 (+ eps (* 2 x))))))
(* (pow eps 5) (+ (* -1/48 (/ (cos (* 1/2 (+ eps (* 2 x)))) (pow eps 2))) (* 1/3840 (cos (* 1/2 (+ eps (* 2 x)))))))
(* (pow eps 5) (+ (* -1/48 (/ (cos (* 1/2 (+ eps (* 2 x)))) (pow eps 2))) (+ (* 1/3840 (cos (* 1/2 (+ eps (* 2 x))))) (* 1/2 (/ (cos (* 1/2 (+ eps (* 2 x)))) (pow eps 4))))))
(* (pow eps 5) (+ (* -1/48 (/ (cos (* 1/2 (+ eps (* 2 x)))) (pow eps 2))) (+ (* 1/3840 (cos (* 1/2 (+ eps (* 2 x))))) (* 1/2 (/ (cos (* 1/2 (+ eps (* 2 x)))) (pow eps 4))))))
(* 1/3840 (* (pow eps 5) (cos (* 1/2 (- (* 2 x) (* -1 eps))))))
(* -1 (* (pow eps 5) (+ (* -1/3840 (cos (* 1/2 (- (* 2 x) (* -1 eps))))) (* 1/48 (/ (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (pow eps 2))))))
(* -1 (* (pow eps 5) (+ (* -1/2 (/ (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (pow eps 4))) (+ (* -1/3840 (cos (* 1/2 (- (* 2 x) (* -1 eps))))) (* 1/48 (/ (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (pow eps 2)))))))
(* -1 (* (pow eps 5) (+ (* -1/2 (/ (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (pow eps 4))) (+ (* -1/3840 (cos (* 1/2 (- (* 2 x) (* -1 eps))))) (* 1/48 (/ (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (pow eps 2)))))))
(* eps (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))
(+ (* -1 (* eps (* x (* (sin (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))) (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))
(+ (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))) (* x (+ (* -1 (* eps (* (sin (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))) (* -1/2 (* eps (* x (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))))))
(+ (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))) (* x (+ (* -1 (* eps (* (sin (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))) (* x (+ (* -1/2 (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))) (* 1/6 (* eps (* x (* (sin (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))))))))
(* eps (* (cos (* 1/2 (+ eps (* 2 x)))) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))
(* eps (* (cos (* 1/2 (+ eps (* 2 x)))) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))
(* eps (* (cos (* 1/2 (+ eps (* 2 x)))) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))
(* eps (* (cos (* 1/2 (+ eps (* 2 x)))) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))
(* eps (* (cos (* 1/2 (- eps (* -2 x)))) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))
(* eps (* (cos (* 1/2 (- eps (* -2 x)))) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))
(* eps (* (cos (* 1/2 (- eps (* -2 x)))) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))
(* eps (* (cos (* 1/2 (- eps (* -2 x)))) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))
(* 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) (- (* 1/3840 (pow eps 2)) 1/48))))
(* 1/3840 (pow eps 5))
(* (pow eps 5) (- 1/3840 (* 1/48 (/ 1 (pow eps 2)))))
(* (pow eps 5) (- (+ 1/3840 (/ 1/2 (pow eps 4))) (* 1/48 (/ 1 (pow eps 2)))))
(* (pow eps 5) (- (+ 1/3840 (/ 1/2 (pow eps 4))) (* 1/48 (/ 1 (pow eps 2)))))
(* 1/3840 (pow eps 5))
(* -1 (* (pow eps 5) (- (* 1/48 (/ 1 (pow eps 2))) 1/3840)))
(* -1 (* (pow eps 5) (- (* 1/48 (/ 1 (pow eps 2))) (+ 1/3840 (/ 1/2 (pow eps 4))))))
(* -1 (* (pow eps 5) (- (* 1/48 (/ 1 (pow eps 2))) (+ 1/3840 (/ 1/2 (pow eps 4))))))
eps
(* eps (+ 1 (* -1/6 (pow eps 2))))
(* eps (+ 1 (* -1/6 (pow eps 2))))
(* eps (+ 1 (* -1/6 (pow eps 2))))
(* -1/6 (pow eps 3))
(* (pow eps 3) (- (/ 1 (pow eps 2)) 1/6))
(* (pow eps 3) (- (/ 1 (pow eps 2)) 1/6))
(* (pow eps 3) (- (/ 1 (pow eps 2)) 1/6))
(* -1/6 (pow eps 3))
(* -1 (* (pow eps 3) (- 1/6 (/ 1 (pow eps 2)))))
(* -1 (* (pow eps 3) (- 1/6 (/ 1 (pow eps 2)))))
(* -1 (* (pow eps 3) (- 1/6 (/ 1 (pow eps 2)))))
(* -1/6 (pow eps 2))
(* -1/6 (pow eps 2))
(* -1/6 (pow eps 2))
(* -1/6 (pow eps 2))
(* -1/6 (pow eps 2))
(* -1/6 (pow eps 2))
(* -1/6 (pow eps 2))
(* -1/6 (pow eps 2))
(* -1/6 (pow eps 2))
(* -1/6 (pow eps 2))
(* -1/6 (pow eps 2))
(* -1/6 (pow eps 2))
(* -1/6 eps)
(* -1/6 eps)
(* -1/6 eps)
(* -1/6 eps)
(* -1/6 eps)
(* -1/6 eps)
(* -1/6 eps)
(* -1/6 eps)
(* -1/6 eps)
(* -1/6 eps)
(* -1/6 eps)
(* -1/6 eps)
(* eps (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))))
(* eps (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))))
(* eps (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))))
(* eps (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))))
(* eps (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))))
(* eps (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))))
(* eps (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))))
(* eps (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))))
(* eps (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))))
(* eps (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))))
(* eps (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))))
(* eps (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))))
eps
(+ eps (* -1/2 (* eps (pow x 2))))
(+ eps (* (pow x 2) (+ (* -1/2 eps) (* 1/24 (* eps (pow x 2))))))
(+ eps (* (pow x 2) (+ (* -1/2 eps) (* (pow x 2) (+ (* -1/720 (* eps (pow x 2))) (* 1/24 eps))))))
(* -1/720 (* eps (pow x 6)))
(* (pow x 6) (+ (* -1/720 eps) (* 1/24 (/ eps (pow x 2)))))
(* (pow x 6) (+ (* -1/2 (/ eps (pow x 4))) (+ (* -1/720 eps) (* 1/24 (/ eps (pow x 2))))))
(* (pow x 6) (+ (* -1/2 (/ eps (pow x 4))) (+ (* -1/720 eps) (+ (* 1/24 (/ eps (pow x 2))) (/ eps (pow x 6))))))
(* -1/720 (* eps (pow x 6)))
(* (pow x 6) (+ (* -1/720 eps) (* 1/24 (/ eps (pow x 2)))))
(* (pow x 6) (+ (* -1/2 (/ eps (pow x 4))) (+ (* -1/720 eps) (* 1/24 (/ eps (pow x 2))))))
(* (pow x 6) (+ (* -1/2 (/ eps (pow x 4))) (+ (* -1/720 eps) (+ (* 1/24 (/ eps (pow x 2))) (/ eps (pow x 6))))))
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)))
(* -1/720 (pow x 6))
(* (pow x 6) (- (* 1/24 (/ 1 (pow x 2))) 1/720))
(* (pow x 6) (- (* 1/24 (/ 1 (pow x 2))) (+ 1/720 (/ 1/2 (pow x 4)))))
(* (pow x 6) (- (+ (* 1/24 (/ 1 (pow x 2))) (/ 1 (pow x 6))) (+ 1/720 (/ 1/2 (pow x 4)))))
(* -1/720 (pow x 6))
(* (pow x 6) (- (* 1/24 (/ 1 (pow x 2))) 1/720))
(* (pow x 6) (- (* 1/24 (/ 1 (pow x 2))) (+ 1/720 (/ 1/2 (pow x 4)))))
(* (pow x 6) (- (+ (* 1/24 (/ 1 (pow x 2))) (/ 1 (pow x 6))) (+ 1/720 (/ 1/2 (pow x 4)))))
(* -1/2 x)
(* x (- (* 1/24 (pow x 2)) 1/2))
(* x (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))
(* x (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))
(* -1/720 (pow x 5))
(* (pow x 5) (- (* 1/24 (/ 1 (pow x 2))) 1/720))
(* (pow x 5) (- (* 1/24 (/ 1 (pow x 2))) (+ 1/720 (/ 1/2 (pow x 4)))))
(* (pow x 5) (- (* 1/24 (/ 1 (pow x 2))) (+ 1/720 (/ 1/2 (pow x 4)))))
(* -1/720 (pow x 5))
(* -1 (* (pow x 5) (- 1/720 (* 1/24 (/ 1 (pow x 2))))))
(* -1 (* (pow x 5) (- (+ 1/720 (/ 1/2 (pow x 4))) (* 1/24 (/ 1 (pow x 2))))))
(* -1 (* (pow x 5) (- (+ 1/720 (/ 1/2 (pow x 4))) (* 1/24 (/ 1 (pow x 2))))))
-1/2
(- (* 1/24 (pow x 2)) 1/2)
(- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)
(- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)
(* -1/720 (pow x 4))
(* (pow x 4) (- (* 1/24 (/ 1 (pow x 2))) 1/720))
(* (pow x 4) (- (* 1/24 (/ 1 (pow x 2))) (+ 1/720 (/ 1/2 (pow x 4)))))
(* (pow x 4) (- (* 1/24 (/ 1 (pow x 2))) (+ 1/720 (/ 1/2 (pow x 4)))))
(* -1/720 (pow x 4))
(* (pow x 4) (- (* 1/24 (/ 1 (pow x 2))) 1/720))
(* (pow x 4) (- (* 1/24 (/ 1 (pow x 2))) (+ 1/720 (/ 1/2 (pow x 4)))))
(* (pow x 4) (- (* 1/24 (/ 1 (pow x 2))) (+ 1/720 (/ 1/2 (pow x 4)))))
(* eps (cos x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/8 (* eps (cos x)))))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/8 (cos x)) (* 1/48 (* eps (sin x)))))))))
(* eps (cos (* 1/2 (+ eps (* 2 x)))))
(* eps (cos (* 1/2 (+ eps (* 2 x)))))
(* eps (cos (* 1/2 (+ eps (* 2 x)))))
(* eps (cos (* 1/2 (+ eps (* 2 x)))))
(* eps (cos (* 1/2 (- (* 2 x) (* -1 eps)))))
(* eps (cos (* 1/2 (- (* 2 x) (* -1 eps)))))
(* eps (cos (* 1/2 (- (* 2 x) (* -1 eps)))))
(* eps (cos (* 1/2 (- (* 2 x) (* -1 eps)))))
(* eps (cos (* 1/2 eps)))
(+ (* -1 (* eps (* x (sin (* 1/2 eps))))) (* eps (cos (* 1/2 eps))))
(+ (* eps (cos (* 1/2 eps))) (* x (+ (* -1 (* eps (sin (* 1/2 eps)))) (* -1/2 (* eps (* x (cos (* 1/2 eps))))))))
(+ (* eps (cos (* 1/2 eps))) (* x (+ (* -1 (* eps (sin (* 1/2 eps)))) (* x (+ (* -1/2 (* eps (cos (* 1/2 eps)))) (* 1/6 (* eps (* x (sin (* 1/2 eps))))))))))
(* eps (cos (* 1/2 (+ eps (* 2 x)))))
(* eps (cos (* 1/2 (+ eps (* 2 x)))))
(* eps (cos (* 1/2 (+ eps (* 2 x)))))
(* eps (cos (* 1/2 (+ eps (* 2 x)))))
(* eps (cos (* 1/2 (- eps (* -2 x)))))
(* eps (cos (* 1/2 (- eps (* -2 x)))))
(* eps (cos (* 1/2 (- eps (* -2 x)))))
(* eps (cos (* 1/2 (- eps (* -2 x)))))
(* 1/2 (* eps (cos x)))
(* eps (+ (* -1/4 (* eps (sin x))) (* 1/2 (cos x))))
(* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* -1/16 (* eps (cos x)))))))
(* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (* 1/96 (* eps (sin x)))))))))
(* 1/2 (* eps (cos (* 1/2 (+ eps (* 2 x))))))
(* 1/2 (* eps (cos (* 1/2 (+ eps (* 2 x))))))
(* 1/2 (* eps (cos (* 1/2 (+ eps (* 2 x))))))
(* 1/2 (* eps (cos (* 1/2 (+ eps (* 2 x))))))
(* 1/2 (* eps (cos (* 1/2 (- (* 2 x) (* -1 eps))))))
(* 1/2 (* eps (cos (* 1/2 (- (* 2 x) (* -1 eps))))))
(* 1/2 (* eps (cos (* 1/2 (- (* 2 x) (* -1 eps))))))
(* 1/2 (* eps (cos (* 1/2 (- (* 2 x) (* -1 eps))))))
(* 1/2 (* eps (cos (* 1/2 eps))))
(+ (* -1/2 (* eps (* x (sin (* 1/2 eps))))) (* 1/2 (* eps (cos (* 1/2 eps)))))
(+ (* 1/2 (* eps (cos (* 1/2 eps)))) (* x (+ (* -1/2 (* eps (sin (* 1/2 eps)))) (* -1/4 (* eps (* x (cos (* 1/2 eps))))))))
(+ (* 1/2 (* eps (cos (* 1/2 eps)))) (* x (+ (* -1/2 (* eps (sin (* 1/2 eps)))) (* x (+ (* -1/4 (* eps (cos (* 1/2 eps)))) (* 1/12 (* eps (* x (sin (* 1/2 eps))))))))))
(* 1/2 (* eps (cos (* 1/2 (+ eps (* 2 x))))))
(* 1/2 (* eps (cos (* 1/2 (+ eps (* 2 x))))))
(* 1/2 (* eps (cos (* 1/2 (+ eps (* 2 x))))))
(* 1/2 (* eps (cos (* 1/2 (+ eps (* 2 x))))))
(* 1/2 (* eps (cos (* 1/2 (- eps (* -2 x))))))
(* 1/2 (* eps (cos (* 1/2 (- eps (* -2 x))))))
(* 1/2 (* eps (cos (* 1/2 (- eps (* -2 x))))))
(* 1/2 (* eps (cos (* 1/2 (- eps (* -2 x))))))
(* 1/2 eps)
(* 1/2 eps)
(* 1/2 eps)
(* 1/2 eps)
(* 1/2 eps)
(* 1/2 eps)
(* 1/2 eps)
(* 1/2 eps)
(* 1/2 eps)
(* 1/2 eps)
(* 1/2 eps)
(* 1/2 eps)
eps
(+ eps (* 2 x))
(+ eps (* 2 x))
(+ eps (* 2 x))
(* 2 x)
(* x (+ 2 (/ eps x)))
(* x (+ 2 (/ eps x)))
(* x (+ 2 (/ eps x)))
(* 2 x)
(* -1 (* x (- (* -1 (/ eps x)) 2)))
(* -1 (* x (- (* -1 (/ eps x)) 2)))
(* -1 (* x (- (* -1 (/ eps x)) 2)))
(* 2 x)
(+ eps (* 2 x))
(+ eps (* 2 x))
(+ eps (* 2 x))
eps
(* eps (+ 1 (* 2 (/ x eps))))
(* eps (+ 1 (* 2 (/ x eps))))
(* eps (+ 1 (* 2 (/ x eps))))
eps
(* -1 (* eps (- (* -2 (/ x eps)) 1)))
(* -1 (* eps (- (* -2 (/ x eps)) 1)))
(* -1 (* eps (- (* -2 (/ x eps)) 1)))
(* 1/3840 eps)
(* 1/3840 eps)
(* 1/3840 eps)
(* 1/3840 eps)
(* 1/3840 eps)
(* 1/3840 eps)
(* 1/3840 eps)
(* 1/3840 eps)
(* 1/3840 eps)
(* 1/3840 eps)
(* 1/3840 eps)
(* 1/3840 eps)
(cos (* 1/2 eps))
(+ (cos (* 1/2 eps)) (* -1 (* x (sin (* 1/2 eps)))))
(+ (cos (* 1/2 eps)) (* x (- (* -1/2 (* x (cos (* 1/2 eps)))) (sin (* 1/2 eps)))))
(+ (cos (* 1/2 eps)) (* x (- (* x (+ (* -1/2 (cos (* 1/2 eps))) (* 1/6 (* x (sin (* 1/2 eps)))))) (sin (* 1/2 eps)))))
(cos (* 1/2 (+ eps (* 2 x))))
(cos (* 1/2 (+ eps (* 2 x))))
(cos (* 1/2 (+ eps (* 2 x))))
(cos (* 1/2 (+ eps (* 2 x))))
(cos (* 1/2 (- eps (* -2 x))))
(cos (* 1/2 (- eps (* -2 x))))
(cos (* 1/2 (- eps (* -2 x))))
(cos (* 1/2 (- eps (* -2 x))))
(cos x)
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* eps (- (* -1/8 (* eps (cos x))) (* 1/2 (sin x)))))
(+ (cos x) (* eps (- (* eps (+ (* -1/8 (cos x)) (* 1/48 (* eps (sin x))))) (* 1/2 (sin x)))))
(cos (* 1/2 (+ eps (* 2 x))))
(cos (* 1/2 (+ eps (* 2 x))))
(cos (* 1/2 (+ eps (* 2 x))))
(cos (* 1/2 (+ eps (* 2 x))))
(cos (* 1/2 (- (* 2 x) (* -1 eps))))
(cos (* 1/2 (- (* 2 x) (* -1 eps))))
(cos (* 1/2 (- (* 2 x) (* -1 eps))))
(cos (* 1/2 (- (* 2 x) (* -1 eps))))
1/24
(+ 1/24 (* -1/720 (pow x 2)))
(+ 1/24 (* -1/720 (pow x 2)))
(+ 1/24 (* -1/720 (pow x 2)))
(* -1/720 (pow x 2))
(* (pow x 2) (- (* 1/24 (/ 1 (pow x 2))) 1/720))
(* (pow x 2) (- (* 1/24 (/ 1 (pow x 2))) 1/720))
(* (pow x 2) (- (* 1/24 (/ 1 (pow x 2))) 1/720))
(* -1/720 (pow x 2))
(* (pow x 2) (- (* 1/24 (/ 1 (pow x 2))) 1/720))
(* (pow x 2) (- (* 1/24 (/ 1 (pow x 2))) 1/720))
(* (pow x 2) (- (* 1/24 (/ 1 (pow x 2))) 1/720))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)

Outputs
(* 1/2 eps)
(*.f64 #s(literal 1/2 binary64) eps)
(+ x (* 1/2 eps))
(fma.f64 #s(literal 1/2 binary64) eps x)
(+ x (* 1/2 eps))
(fma.f64 #s(literal 1/2 binary64) eps x)
(+ x (* 1/2 eps))
(fma.f64 #s(literal 1/2 binary64) eps x)
x
(* x (+ 1 (* 1/2 (/ eps x))))
(fma.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 eps x) x) x)
(* x (+ 1 (* 1/2 (/ eps x))))
(fma.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 eps x) x) x)
(* x (+ 1 (* 1/2 (/ eps x))))
(fma.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 eps x) x) x)
x
(* -1 (* x (- (* -1/2 (/ eps x)) 1)))
(neg.f64 (*.f64 x (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) #s(literal -1 binary64))))
(* -1 (* x (- (* -1/2 (/ eps x)) 1)))
(neg.f64 (*.f64 x (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) #s(literal -1 binary64))))
(* -1 (* x (- (* -1/2 (/ eps x)) 1)))
(neg.f64 (*.f64 x (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) #s(literal -1 binary64))))
x
(+ x (* 1/2 eps))
(fma.f64 #s(literal 1/2 binary64) eps x)
(+ x (* 1/2 eps))
(fma.f64 #s(literal 1/2 binary64) eps x)
(+ x (* 1/2 eps))
(fma.f64 #s(literal 1/2 binary64) eps x)
(* 1/2 eps)
(*.f64 #s(literal 1/2 binary64) eps)
(* eps (+ 1/2 (/ x eps)))
(*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)))
(* eps (+ 1/2 (/ x eps)))
(*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)))
(* eps (+ 1/2 (/ x eps)))
(*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)))
(* 1/2 eps)
(*.f64 #s(literal 1/2 binary64) eps)
(* -1 (* eps (- (* -1 (/ x eps)) 1/2)))
(*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)))
(* -1 (* eps (- (* -1 (/ x eps)) 1/2)))
(*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)))
(* -1 (* eps (- (* -1 (/ x eps)) 1/2)))
(*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)))
(* eps (cos x))
(*.f64 eps (cos.f64 x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(.f64 eps (fma.f64 #s(literal -1/2 binary64) (.f64 eps (sin.f64 x)) (cos.f64 x)))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* 2 (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x)))))))))
(.f64 eps (fma.f64 eps (fma.f64 eps (.f64 (cos.f64 x) #s(literal -1/6 binary64)) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) (cos.f64 x)))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* 1/24 (* eps (sin x))) (* 2 (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))))
(.f64 eps (fma.f64 eps (fma.f64 eps (.f64 (cos.f64 x) #s(literal -1/6 binary64)) (.f64 (sin.f64 x) (+.f64 #s(literal -1/2 binary64) (.f64 eps (*.f64 eps #s(literal 1/24 binary64)))))) (cos.f64 x)))
(* 1/1920 (* (pow eps 5) (cos (* 1/2 (+ eps (* 2 x))))))
(.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (.f64 #s(literal 1/1920 binary64) (pow.f64 eps #s(literal 5 binary64))))
(* (pow eps 5) (+ (* -1/24 (/ (cos (* 1/2 (+ eps (* 2 x)))) (pow eps 2))) (* 1/1920 (cos (* 1/2 (+ eps (* 2 x)))))))
(.f64 (pow.f64 eps #s(literal 5 binary64)) (fma.f64 #s(literal 1/1920 binary64) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (/.f64 #s(literal -1/24 binary64) (*.f64 eps eps)))))
(* (pow eps 5) (+ (* -1/24 (/ (cos (* 1/2 (+ eps (* 2 x)))) (pow eps 2))) (+ (* 1/1920 (cos (* 1/2 (+ eps (* 2 x))))) (/ (cos (* 1/2 (+ eps (* 2 x)))) (pow eps 4)))))
(.f64 (pow.f64 eps #s(literal 5 binary64)) (fma.f64 #s(literal 1/1920 binary64) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (fma.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (/.f64 #s(literal -1/24 binary64) (.f64 eps eps)) (/.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (pow.f64 eps #s(literal 4 binary64))))))
(* (pow eps 5) (+ (* -1/24 (/ (cos (* 1/2 (+ eps (* 2 x)))) (pow eps 2))) (+ (* 1/1920 (cos (* 1/2 (+ eps (* 2 x))))) (/ (cos (* 1/2 (+ eps (* 2 x)))) (pow eps 4)))))
(.f64 (pow.f64 eps #s(literal 5 binary64)) (fma.f64 #s(literal 1/1920 binary64) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (fma.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (/.f64 #s(literal -1/24 binary64) (.f64 eps eps)) (/.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (pow.f64 eps #s(literal 4 binary64))))))
(* 1/1920 (* (pow eps 5) (cos (* 1/2 (- (* 2 x) (* -1 eps))))))
(.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (.f64 #s(literal 1/1920 binary64) (pow.f64 eps #s(literal 5 binary64))))
(* -1 (* (pow eps 5) (+ (* -1/1920 (cos (* 1/2 (- (* 2 x) (* -1 eps))))) (* 1/24 (/ (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (pow eps 2))))))
(.f64 (pow.f64 eps #s(literal 5 binary64)) (fma.f64 #s(literal 1/1920 binary64) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (/.f64 #s(literal -1/24 binary64) (*.f64 eps eps)))))
(* -1 (* (pow eps 5) (+ (* -1 (/ (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (pow eps 4))) (+ (* -1/1920 (cos (* 1/2 (- (* 2 x) (* -1 eps))))) (* 1/24 (/ (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (pow eps 2)))))))
(.f64 (pow.f64 eps #s(literal 5 binary64)) (fma.f64 #s(literal 1/1920 binary64) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (fma.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (/.f64 #s(literal -1/24 binary64) (.f64 eps eps)) (/.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (pow.f64 eps #s(literal 4 binary64))))))
(* -1 (* (pow eps 5) (+ (* -1 (/ (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (pow eps 4))) (+ (* -1/1920 (cos (* 1/2 (- (* 2 x) (* -1 eps))))) (* 1/24 (/ (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (pow eps 2)))))))
(.f64 (pow.f64 eps #s(literal 5 binary64)) (fma.f64 #s(literal 1/1920 binary64) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (fma.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (/.f64 #s(literal -1/24 binary64) (.f64 eps eps)) (/.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (pow.f64 eps #s(literal 4 binary64))))))
(* 2 (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))
(.f64 (.f64 (.f64 eps #s(literal 2 binary64)) (fma.f64 eps (.f64 eps (fma.f64 (.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64))) #s(literal 1/2 binary64))) (cos.f64 (.f64 #s(literal 1/2 binary64) eps)))
(+ (* -2 (* eps (* x (* (sin (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))) (* 2 (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))))
(.f64 (fma.f64 eps (.f64 eps (fma.f64 (.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64))) #s(literal 1/2 binary64)) (fma.f64 (.f64 eps #s(literal -2 binary64)) (.f64 x (sin.f64 (.f64 #s(literal 1/2 binary64) eps))) (.f64 (.f64 eps #s(literal 2 binary64)) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)))))
(+ (* 2 (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))) (* x (+ (* -2 (* eps (* (sin (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))) (* -1 (* eps (* x (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))))))
(fma.f64 x (.f64 (fma.f64 eps (.f64 eps (fma.f64 (.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64))) #s(literal 1/2 binary64)) (fma.f64 (.f64 eps #s(literal -2 binary64)) (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (neg.f64 (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (.f64 eps x))))) (.f64 (.f64 (.f64 eps #s(literal 2 binary64)) (fma.f64 eps (.f64 eps (fma.f64 (.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64))) #s(literal 1/2 binary64))) (cos.f64 (.f64 #s(literal 1/2 binary64) eps))))
(+ (* 2 (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))) (* x (+ (* -2 (* eps (* (sin (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))) (* x (+ (* -1 (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))) (* 1/3 (* eps (* x (* (sin (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))))))))
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(.f64 #s(literal 1/2 binary64) (.f64 eps (cos.f64 x)))
(* eps (+ (* -1/4 (* eps (sin x))) (* 1/2 (cos x))))
(.f64 eps (fma.f64 #s(literal 1/2 binary64) (cos.f64 x) (.f64 (*.f64 eps (sin.f64 x)) #s(literal -1/4 binary64))))
(* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* -1/16 (* eps (cos x)))))))
(.f64 eps (fma.f64 (cos.f64 x) (fma.f64 eps (.f64 eps #s(literal -1/16 binary64)) #s(literal 1/2 binary64)) (.f64 (.f64 eps (sin.f64 x)) #s(literal -1/4 binary64))))
(* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (* 1/96 (* eps (sin x)))))))))
(.f64 eps (fma.f64 eps (fma.f64 (sin.f64 x) (fma.f64 eps (.f64 eps #s(literal 1/96 binary64)) #s(literal -1/4 binary64)) (.f64 eps (.f64 (cos.f64 x) #s(literal -1/16 binary64)))) (*.f64 #s(literal 1/2 binary64) (cos.f64 x))))
(* 1/2 (* eps (cos (* 1/2 (+ eps (* 2 x))))))
(.f64 (.f64 #s(literal 1/2 binary64) eps) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))
(* 1/2 (* eps (cos (* 1/2 (+ eps (* 2 x))))))
(.f64 (.f64 #s(literal 1/2 binary64) eps) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))
(* 1/2 (* eps (cos (* 1/2 (+ eps (* 2 x))))))
(.f64 (.f64 #s(literal 1/2 binary64) eps) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))
(* 1/2 (* eps (cos (* 1/2 (+ eps (* 2 x))))))
(.f64 (.f64 #s(literal 1/2 binary64) eps) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))
(* 1/2 (* eps (cos (* 1/2 (- (* 2 x) (* -1 eps))))))
(.f64 (.f64 #s(literal 1/2 binary64) eps) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))
(* 1/2 (* eps (cos (* 1/2 (- (* 2 x) (* -1 eps))))))
(.f64 (.f64 #s(literal 1/2 binary64) eps) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))
(* 1/2 (* eps (cos (* 1/2 (- (* 2 x) (* -1 eps))))))
(.f64 (.f64 #s(literal 1/2 binary64) eps) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))
(* 1/2 (* eps (cos (* 1/2 (- (* 2 x) (* -1 eps))))))
(.f64 (.f64 #s(literal 1/2 binary64) eps) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))
(* 1/2 (* eps (cos (* 1/2 eps))))
(.f64 (.f64 #s(literal 1/2 binary64) eps) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)))
(+ (* -1/2 (* eps (* x (sin (* 1/2 eps))))) (* 1/2 (* eps (cos (* 1/2 eps)))))
(.f64 eps (fma.f64 #s(literal -1/2 binary64) (.f64 x (sin.f64 (.f64 #s(literal 1/2 binary64) eps))) (.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)))))
(+ (* 1/2 (* eps (cos (* 1/2 eps)))) (* x (+ (* -1/2 (* eps (sin (* 1/2 eps)))) (* -1/4 (* eps (* x (cos (* 1/2 eps))))))))
(fma.f64 x (.f64 eps (fma.f64 (.f64 x (cos.f64 (.f64 #s(literal 1/2 binary64) eps))) #s(literal -1/4 binary64) (.f64 #s(literal -1/2 binary64) (sin.f64 (.f64 #s(literal 1/2 binary64) eps))))) (.f64 (.f64 #s(literal 1/2 binary64) eps) (cos.f64 (.f64 #s(literal 1/2 binary64) eps))))
(+ (* 1/2 (* eps (cos (* 1/2 eps)))) (* x (+ (* -1/2 (* eps (sin (* 1/2 eps)))) (* x (+ (* -1/4 (* eps (cos (* 1/2 eps)))) (* 1/12 (* eps (* x (sin (* 1/2 eps))))))))))
(fma.f64 (.f64 x x) (.f64 eps (fma.f64 (.f64 x (sin.f64 (.f64 #s(literal 1/2 binary64) eps))) #s(literal 1/12 binary64) (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) #s(literal -1/4 binary64)))) (.f64 eps (fma.f64 #s(literal -1/2 binary64) (.f64 x (sin.f64 (.f64 #s(literal 1/2 binary64) eps))) (.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps))))))
(* 1/2 (* eps (cos (* 1/2 (+ eps (* 2 x))))))
(.f64 (.f64 #s(literal 1/2 binary64) eps) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))
(* 1/2 (* eps (cos (* 1/2 (+ eps (* 2 x))))))
(.f64 (.f64 #s(literal 1/2 binary64) eps) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))
(* 1/2 (* eps (cos (* 1/2 (+ eps (* 2 x))))))
(.f64 (.f64 #s(literal 1/2 binary64) eps) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))
(* 1/2 (* eps (cos (* 1/2 (+ eps (* 2 x))))))
(.f64 (.f64 #s(literal 1/2 binary64) eps) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))
(* 1/2 (* eps (cos (* 1/2 (- eps (* -2 x))))))
(.f64 (.f64 #s(literal 1/2 binary64) eps) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))
(* 1/2 (* eps (cos (* 1/2 (- eps (* -2 x))))))
(.f64 (.f64 #s(literal 1/2 binary64) eps) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))
(* 1/2 (* eps (cos (* 1/2 (- eps (* -2 x))))))
(.f64 (.f64 #s(literal 1/2 binary64) eps) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))
(* 1/2 (* eps (cos (* 1/2 (- eps (* -2 x))))))
(.f64 (.f64 #s(literal 1/2 binary64) eps) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))
(* 1/2 eps)
(*.f64 #s(literal 1/2 binary64) eps)
(* 1/2 eps)
(*.f64 #s(literal 1/2 binary64) eps)
(* 1/2 eps)
(*.f64 #s(literal 1/2 binary64) eps)
(* 1/2 eps)
(*.f64 #s(literal 1/2 binary64) eps)
(* 1/2 eps)
(*.f64 #s(literal 1/2 binary64) eps)
(* 1/2 eps)
(*.f64 #s(literal 1/2 binary64) eps)
(* 1/2 eps)
(*.f64 #s(literal 1/2 binary64) eps)
(* 1/2 eps)
(*.f64 #s(literal 1/2 binary64) eps)
(* 1/2 eps)
(*.f64 #s(literal 1/2 binary64) eps)
(* 1/2 eps)
(*.f64 #s(literal 1/2 binary64) eps)
(* 1/2 eps)
(*.f64 #s(literal 1/2 binary64) eps)
(* 1/2 eps)
(*.f64 #s(literal 1/2 binary64) eps)
eps
(+ eps (* 2 x))
(fma.f64 x #s(literal 2 binary64) eps)
(+ eps (* 2 x))
(fma.f64 x #s(literal 2 binary64) eps)
(+ eps (* 2 x))
(fma.f64 x #s(literal 2 binary64) eps)
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* x (+ 2 (/ eps x)))
(*.f64 x (+.f64 (/.f64 eps x) #s(literal 2 binary64)))
(* x (+ 2 (/ eps x)))
(*.f64 x (+.f64 (/.f64 eps x) #s(literal 2 binary64)))
(* x (+ 2 (/ eps x)))
(*.f64 x (+.f64 (/.f64 eps x) #s(literal 2 binary64)))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* -1 (* x (- (* -1 (/ eps x)) 2)))
(*.f64 x (+.f64 (/.f64 eps x) #s(literal 2 binary64)))
(* -1 (* x (- (* -1 (/ eps x)) 2)))
(*.f64 x (+.f64 (/.f64 eps x) #s(literal 2 binary64)))
(* -1 (* x (- (* -1 (/ eps x)) 2)))
(*.f64 x (+.f64 (/.f64 eps x) #s(literal 2 binary64)))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(+ eps (* 2 x))
(fma.f64 x #s(literal 2 binary64) eps)
(+ eps (* 2 x))
(fma.f64 x #s(literal 2 binary64) eps)
(+ eps (* 2 x))
(fma.f64 x #s(literal 2 binary64) eps)
eps
(* eps (+ 1 (* 2 (/ x eps))))
(fma.f64 eps (/.f64 (*.f64 x #s(literal 2 binary64)) eps) eps)
(* eps (+ 1 (* 2 (/ x eps))))
(fma.f64 eps (/.f64 (*.f64 x #s(literal 2 binary64)) eps) eps)
(* eps (+ 1 (* 2 (/ x eps))))
(fma.f64 eps (/.f64 (*.f64 x #s(literal 2 binary64)) eps) eps)
eps
(* -1 (* eps (- (* -2 (/ x eps)) 1)))
(fma.f64 eps (/.f64 (*.f64 x #s(literal 2 binary64)) eps) eps)
(* -1 (* eps (- (* -2 (/ x eps)) 1)))
(fma.f64 eps (/.f64 (*.f64 x #s(literal 2 binary64)) eps) eps)
(* -1 (* eps (- (* -2 (/ x eps)) 1)))
(fma.f64 eps (/.f64 (*.f64 x #s(literal 2 binary64)) eps) eps)
(* 1/3840 eps)
(*.f64 eps #s(literal 1/3840 binary64))
(* 1/3840 eps)
(*.f64 eps #s(literal 1/3840 binary64))
(* 1/3840 eps)
(*.f64 eps #s(literal 1/3840 binary64))
(* 1/3840 eps)
(*.f64 eps #s(literal 1/3840 binary64))
(* 1/3840 eps)
(*.f64 eps #s(literal 1/3840 binary64))
(* 1/3840 eps)
(*.f64 eps #s(literal 1/3840 binary64))
(* 1/3840 eps)
(*.f64 eps #s(literal 1/3840 binary64))
(* 1/3840 eps)
(*.f64 eps #s(literal 1/3840 binary64))
(* 1/3840 eps)
(*.f64 eps #s(literal 1/3840 binary64))
(* 1/3840 eps)
(*.f64 eps #s(literal 1/3840 binary64))
(* 1/3840 eps)
(*.f64 eps #s(literal 1/3840 binary64))
(* 1/3840 eps)
(*.f64 eps #s(literal 1/3840 binary64))
(cos (* 1/2 eps))
(cos.f64 (*.f64 #s(literal 1/2 binary64) eps))
(+ (cos (* 1/2 eps)) (* -1 (* x (sin (* 1/2 eps)))))
(fma.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (neg.f64 x) (cos.f64 (.f64 #s(literal 1/2 binary64) eps)))
(+ (cos (* 1/2 eps)) (* x (- (* -1/2 (* x (cos (* 1/2 eps)))) (sin (* 1/2 eps)))))
(fma.f64 x (-.f64 (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (.f64 x #s(literal -1/2 binary64))) (sin.f64 (.f64 #s(literal 1/2 binary64) eps))) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)))
(+ (cos (* 1/2 eps)) (* x (- (* x (+ (* -1/2 (cos (* 1/2 eps))) (* 1/6 (* x (sin (* 1/2 eps)))))) (sin (* 1/2 eps)))))
(fma.f64 x (fma.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (fma.f64 x (.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64)) (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (.f64 x #s(literal -1/2 binary64)))) (cos.f64 (.f64 #s(literal 1/2 binary64) eps)))
(cos (* 1/2 (+ eps (* 2 x))))
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(cos (* 1/2 (+ eps (* 2 x))))
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(cos (* 1/2 (+ eps (* 2 x))))
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(cos (* 1/2 (+ eps (* 2 x))))
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(cos (* 1/2 (- eps (* -2 x))))
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(cos (* 1/2 (- eps (* -2 x))))
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(cos (* 1/2 (- eps (* -2 x))))
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(cos (* 1/2 (- eps (* -2 x))))
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(cos x)
(cos.f64 x)
(+ (cos x) (* -1/2 (* eps (sin x))))
(fma.f64 #s(literal -1/2 binary64) (*.f64 eps (sin.f64 x)) (cos.f64 x))
(+ (cos x) (* eps (- (* -1/8 (* eps (cos x))) (* 1/2 (sin x)))))
(fma.f64 (fma.f64 eps (.f64 eps #s(literal -1/8 binary64)) #s(literal 1 binary64)) (cos.f64 x) (.f64 #s(literal -1/2 binary64) (*.f64 eps (sin.f64 x))))
(+ (cos x) (* eps (- (* eps (+ (* -1/8 (cos x)) (* 1/48 (* eps (sin x))))) (* 1/2 (sin x)))))
(fma.f64 eps (fma.f64 eps (.f64 (cos.f64 x) #s(literal -1/8 binary64)) (.f64 (sin.f64 x) (fma.f64 eps (*.f64 eps #s(literal 1/48 binary64)) #s(literal -1/2 binary64)))) (cos.f64 x))
(cos (* 1/2 (+ eps (* 2 x))))
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(cos (* 1/2 (+ eps (* 2 x))))
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(cos (* 1/2 (+ eps (* 2 x))))
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(cos (* 1/2 (+ eps (* 2 x))))
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(cos (* 1/2 (- (* 2 x) (* -1 eps))))
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(cos (* 1/2 (- (* 2 x) (* -1 eps))))
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(cos (* 1/2 (- (* 2 x) (* -1 eps))))
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(cos (* 1/2 (- (* 2 x) (* -1 eps))))
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
1/24
#s(literal 1/24 binary64)
(+ 1/24 (* -1/720 (pow x 2)))
(fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64))
(+ 1/24 (* -1/720 (pow x 2)))
(fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64))
(+ 1/24 (* -1/720 (pow x 2)))
(fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64))
(* -1/720 (pow x 2))
(.f64 x (.f64 x #s(literal -1/720 binary64)))
(* (pow x 2) (- (* 1/24 (/ 1 (pow x 2))) 1/720))
(.f64 x (.f64 x (+.f64 #s(literal -1/720 binary64) (/.f64 #s(literal 1/24 binary64) (*.f64 x x)))))
(* (pow x 2) (- (* 1/24 (/ 1 (pow x 2))) 1/720))
(.f64 x (.f64 x (+.f64 #s(literal -1/720 binary64) (/.f64 #s(literal 1/24 binary64) (*.f64 x x)))))
(* (pow x 2) (- (* 1/24 (/ 1 (pow x 2))) 1/720))
(.f64 x (.f64 x (+.f64 #s(literal -1/720 binary64) (/.f64 #s(literal 1/24 binary64) (*.f64 x x)))))
(* -1/720 (pow x 2))
(.f64 x (.f64 x #s(literal -1/720 binary64)))
(* (pow x 2) (- (* 1/24 (/ 1 (pow x 2))) 1/720))
(.f64 x (.f64 x (+.f64 #s(literal -1/720 binary64) (/.f64 #s(literal 1/24 binary64) (*.f64 x x)))))
(* (pow x 2) (- (* 1/24 (/ 1 (pow x 2))) 1/720))
(.f64 x (.f64 x (+.f64 #s(literal -1/720 binary64) (/.f64 #s(literal 1/24 binary64) (*.f64 x x)))))
(* (pow x 2) (- (* 1/24 (/ 1 (pow x 2))) 1/720))
(.f64 x (.f64 x (+.f64 #s(literal -1/720 binary64) (/.f64 #s(literal 1/24 binary64) (*.f64 x x)))))
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)

eval176.0ms (1.3%)

Memory: -18.8MiB live, 215.0MiB allocated
Compiler: Compiled 31 239 to 2 696 computations (91.4% saved)

prune100.0ms (0.7%)

Memory

19.4MiB live, 220.7MiB allocated

Pruning

14 alts after pruning (10 fresh and 4 done)

	Pruned	Kept	Total
New	983	8	991
Fresh	5	2	7
Picked	3	2	5
Done	0	2	2
Total	991	14	1 005

Accuracy

100.0%

Counts

1 005 → 14

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.1%	(fma.f64 (.f64 eps (.f64 x x)) (fma.f64 x (*.f64 x #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) eps)
	60.6%	(-.f64 (-.f64 (sin.f64 (+.f64 x eps)) x) (.f64 (.f64 x x) (.f64 x (fma.f64 (.f64 x x) #s(literal 1/120 binary64) #s(literal -1/6 binary64)))))
✓	60.6%	(-.f64 (sin.f64 (+.f64 x eps)) (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) (.f64 x (*.f64 x x)) x))
	98.4%	(.f64 (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) eps)
	99.9%	(.f64 (.f64 (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64))) (fma.f64 (fma.f64 eps (.f64 eps #s(literal -1/8 binary64)) #s(literal 1 binary64)) (cos.f64 x) (.f64 #s(literal -1/2 binary64) (.f64 eps (sin.f64 x))))) #s(literal 2 binary64))
▶	100.0%	(.f64 (.f64 (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 eps (*.f64 eps #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64))) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) #s(literal 2 binary64))
▶	99.9%	(.f64 (.f64 (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64))) (cos.f64 (*.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
	99.7%	(.f64 (.f64 (.f64 #s(literal 1/2 binary64) eps) (cos.f64 (.f64 (*.f64 x (+.f64 (/.f64 eps x) #s(literal 2 binary64))) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
✓	99.1%	(.f64 eps (fma.f64 x (.f64 x (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) #s(literal -1/2 binary64))) #s(literal 1 binary64)))
▶	98.9%	(.f64 eps (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)))
	99.1%	(.f64 eps (+.f64 (.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) #s(literal -1/2 binary64))) #s(literal 1 binary64)))
▶	99.7%	(*.f64 eps (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))
✓	99.3%	(*.f64 eps (cos.f64 x))
✓	98.4%	eps

Compiler

Compiled 411 to 263 computations (36% saved)

simplify482.0ms (3.4%)

Memory

13.1MiB live, 605.8MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 18 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))
✓	cost-diff	0	(.f64 (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64))) (cos.f64 (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64))))
✓	cost-diff	128	(.f64 (.f64 (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64))) (cos.f64 (*.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
✓	cost-diff	320	(*.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64))
✓	cost-diff	0	(fma.f64 #s(literal 1/2 binary64) eps x)
✓	cost-diff	0	(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
✓	cost-diff	0	(*.f64 eps (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))
✓	cost-diff	0	(fma.f64 x (*.f64 x #s(literal 1/24 binary64)) #s(literal -1/2 binary64))
✓	cost-diff	0	(*.f64 x x)
✓	cost-diff	0	(.f64 eps (.f64 x x))
✓	cost-diff	0	(fma.f64 (.f64 eps (.f64 x x)) (fma.f64 x (*.f64 x #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) eps)
✓	cost-diff	0	(*.f64 x #s(literal -1/2 binary64))
✓	cost-diff	0	(fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))
✓	cost-diff	0	(.f64 eps (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)))
✓	cost-diff	0	(fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64))
✓	cost-diff	0	(.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 eps (*.f64 eps #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))
✓	cost-diff	0	(.f64 (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64))) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))
✓	cost-diff	128	(.f64 (.f64 (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 eps (*.f64 eps #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64))) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) #s(literal 2 binary64))

Rules

20 966×	`accelerator-lowering-fma.f32`
20 966×	`accelerator-lowering-fma.f64`
5 458×	`+-lowering-+.f64`
5 458×	`+-lowering-+.f32`
4 048×	`-lowering-.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	43	267
1	123	267
2	337	267
3	986	263
4	1963	263
5	3638	263
6	4759	263
7	5948	263
8	6063	263
9	6178	263
10	6537	263
0	8614	233

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

Inputs
(* (* (* eps (+ (* (* eps eps) (+ (* eps (* eps 1/3840)) -1/48)) 1/2)) (cos (+ (* 1/2 eps) x))) 2)
(* (* eps (+ (* (* eps eps) (+ (* eps (* eps 1/3840)) -1/48)) 1/2)) (cos (+ (* 1/2 eps) x)))
(* eps (+ (* (* eps eps) (+ (* eps (* eps 1/3840)) -1/48)) 1/2))
eps
(+ (* (* eps eps) (+ (* eps (* eps 1/3840)) -1/48)) 1/2)
(* eps eps)
(+ (* eps (* eps 1/3840)) -1/48)
(* eps 1/3840)
1/3840
-1/48
1/2
(cos (+ (* 1/2 eps) x))
(+ (* 1/2 eps) x)
x
2
(* eps (+ (* x (* x -1/2)) 1))
eps
(+ (* x (* x -1/2)) 1)
x
(* x -1/2)
-1/2
1
(+ (* (* eps (* x x)) (+ (* x (* x 1/24)) -1/2)) eps)
(* eps (* x x))
eps
(* x x)
x
(+ (* x (* x 1/24)) -1/2)
(* x 1/24)
1/24
-1/2
(* eps (cos (+ (* 1/2 eps) x)))
eps
(cos (+ (* 1/2 eps) x))
(+ (* 1/2 eps) x)
1/2
x
(* (* (* eps (+ (* eps (* eps -1/48)) 1/2)) (cos (* (+ x (+ x eps)) 1/2))) 2)
(* (* eps (+ (* eps (* eps -1/48)) 1/2)) (cos (* (+ x (+ x eps)) 1/2)))
(* eps (+ (* eps (* eps -1/48)) 1/2))
eps
(+ (* eps (* eps -1/48)) 1/2)
(* eps -1/48)
-1/48
1/2
(cos (* (+ x (+ x eps)) 1/2))
(* (+ x (+ x eps)) 1/2)
(+ x (+ x eps))
x
(+ x eps)
2

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

localize133.0ms (0.9%)

Memory

-1.3MiB live, 276.9MiB allocated

Localize:

Found 18 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(.f64 (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64))) (cos.f64 (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64))))
✓	accuracy	100.0%	(cos.f64 (*.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)))
✓	accuracy	99.6%	(+.f64 x (+.f64 x eps))
✓	accuracy	99.4%	(*.f64 eps #s(literal -1/48 binary64))
✓	accuracy	100.0%	(fma.f64 #s(literal 1/2 binary64) eps x)
✓	accuracy	100.0%	(*.f64 eps (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))
✓	accuracy	100.0%	(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
✓	accuracy	100.0%	(fma.f64 x (*.f64 x #s(literal 1/24 binary64)) #s(literal -1/2 binary64))
✓	accuracy	100.0%	(*.f64 x x)
✓	accuracy	99.9%	(.f64 eps (.f64 x x))
✓	accuracy	99.4%	(*.f64 x #s(literal 1/24 binary64))
✓	accuracy	100.0%	(fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))
✓	accuracy	100.0%	(*.f64 x #s(literal -1/2 binary64))
✓	accuracy	100.0%	(.f64 eps (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)))
✓	accuracy	100.0%	(fma.f64 eps (*.f64 eps #s(literal 1/3840 binary64)) #s(literal -1/48 binary64))
✓	accuracy	100.0%	(.f64 (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64))) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))
✓	accuracy	100.0%	(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
✓	accuracy	99.8%	(*.f64 eps #s(literal 1/3840 binary64))

Samples

80.0ms

256×

valid

Compiler

Compiled 248 to 45 computations (81.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 58.0ms

ival-mult: 34.0ms (58.2% of total)

ival-add: 10.0ms (17.1% of total)

const: 10.0ms (17.1% of total)

ival-cos: 4.0ms (6.9% of total)

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

exact: 0.0ms (0% of total)

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

series40.0ms (0.3%)

Memory

-32.3MiB live, 59.4MiB allocated

Counts

24 → 444

Calls

Call 1

Inputs
#<alt (* (* (* eps (+ (* (* eps eps) (+ (* eps (* eps 1/3840)) -1/48)) 1/2)) (cos (+ (* 1/2 eps) x))) 2)>
#<alt (* (* eps (+ (* (* eps eps) (+ (* eps (* eps 1/3840)) -1/48)) 1/2)) (cos (+ (* 1/2 eps) x)))>
#<alt (* eps (+ (* (* eps eps) (+ (* eps (* eps 1/3840)) -1/48)) 1/2))>
#<alt (+ (* (* eps eps) (+ (* eps (* eps 1/3840)) -1/48)) 1/2)>
#<alt (* eps (+ (* x (* x -1/2)) 1))>
#<alt (+ (* x (* x -1/2)) 1)>
#<alt (* x -1/2)>
#<alt (+ (* (* eps (* x x)) (+ (* x (* x 1/24)) -1/2)) eps)>
#<alt (* eps (* x x))>
#<alt (* x x)>
#<alt (+ (* x (* x 1/24)) -1/2)>
#<alt (* eps (cos (+ (* 1/2 eps) x)))>
#<alt (cos (+ (* 1/2 eps) x))>
#<alt (+ (* 1/2 eps) x)>
#<alt (* (+ x (+ x eps)) 1/2)>
#<alt (* (* (* eps (+ (* eps (* eps -1/48)) 1/2)) (cos (* (+ x (+ x eps)) 1/2))) 2)>
#<alt (* (* eps (+ (* eps (* eps -1/48)) 1/2)) (cos (* (+ x (+ x eps)) 1/2)))>
#<alt (* eps (+ (* eps (* eps -1/48)) 1/2))>
#<alt (* eps 1/3840)>
#<alt (+ (* eps (* eps 1/3840)) -1/48)>
#<alt (* x 1/24)>
#<alt (* eps -1/48)>
#<alt (+ x (+ x eps))>
#<alt (cos (* (+ x (+ x eps)) 1/2))>

Outputs
#<alt (* eps (cos x))>
#<alt (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))>
#<alt (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* 2 (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x)))))))))>
#<alt (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* 1/24 (* eps (sin x))) (* 2 (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))))>
#<alt (* 1/1920 (* (pow eps 5) (cos (+ x (* 1/2 eps)))))>
#<alt (* (pow eps 5) (+ (* -1/24 (/ (cos (+ x (* 1/2 eps))) (pow eps 2))) (* 1/1920 (cos (+ x (* 1/2 eps))))))>
#<alt (* (pow eps 5) (+ (* -1/24 (/ (cos (+ x (* 1/2 eps))) (pow eps 2))) (+ (* 1/1920 (cos (+ x (* 1/2 eps)))) (/ (cos (+ x (* 1/2 eps))) (pow eps 4)))))>
#<alt (* (pow eps 5) (+ (* -1/24 (/ (cos (+ x (* 1/2 eps))) (pow eps 2))) (+ (* 1/1920 (cos (+ x (* 1/2 eps)))) (/ (cos (+ x (* 1/2 eps))) (pow eps 4)))))>
#<alt (* 1/1920 (* (pow eps 5) (cos (- x (* -1/2 eps)))))>
#<alt (* -1 (* (pow eps 5) (+ (* -1/1920 (cos (- x (* -1/2 eps)))) (* 1/24 (/ (cos (- x (* -1/2 eps))) (pow eps 2))))))>
#<alt (* -1 (* (pow eps 5) (+ (* -1 (/ (cos (- x (* -1/2 eps))) (pow eps 4))) (+ (* -1/1920 (cos (- x (* -1/2 eps)))) (* 1/24 (/ (cos (- x (* -1/2 eps))) (pow eps 2)))))))>
#<alt (* -1 (* (pow eps 5) (+ (* -1 (/ (cos (- x (* -1/2 eps))) (pow eps 4))) (+ (* -1/1920 (cos (- x (* -1/2 eps)))) (* 1/24 (/ (cos (- x (* -1/2 eps))) (pow eps 2)))))))>
#<alt (* 2 (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))>
#<alt (+ (* -2 (* eps (* x (* (sin (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))) (* 2 (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))))>
#<alt (+ (* 2 (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))) (* x (+ (* -2 (* eps (* (sin (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))) (* -1 (* eps (* x (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))))))>
#<alt (+ (* 2 (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))) (* x (+ (* -2 (* eps (* (sin (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))) (* x (+ (* -1 (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))) (* 1/3 (* eps (* x (* (sin (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))))))))>
#<alt (* 2 (* eps (* (cos (+ x (* 1/2 eps))) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))>
#<alt (* 2 (* eps (* (cos (+ x (* 1/2 eps))) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))>
#<alt (* 2 (* eps (* (cos (+ x (* 1/2 eps))) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))>
#<alt (* 2 (* eps (* (cos (+ x (* 1/2 eps))) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))>
#<alt (* 2 (* eps (* (cos (- (* 1/2 eps) (* -1 x))) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))>
#<alt (* 2 (* eps (* (cos (- (* 1/2 eps) (* -1 x))) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))>
#<alt (* 2 (* eps (* (cos (- (* 1/2 eps) (* -1 x))) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))>
#<alt (* 2 (* eps (* (cos (- (* 1/2 eps) (* -1 x))) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))>
#<alt (* 1/2 (* eps (cos x)))>
#<alt (* eps (+ (* -1/4 (* eps (sin x))) (* 1/2 (cos x))))>
#<alt (* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))>
#<alt (* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (+ (* -1/48 (cos x)) (* 1/48 (* eps (sin x))))))))))>
#<alt (* 1/3840 (* (pow eps 5) (cos (+ x (* 1/2 eps)))))>
#<alt (* (pow eps 5) (+ (* -1/48 (/ (cos (+ x (* 1/2 eps))) (pow eps 2))) (* 1/3840 (cos (+ x (* 1/2 eps))))))>
#<alt (* (pow eps 5) (+ (* -1/48 (/ (cos (+ x (* 1/2 eps))) (pow eps 2))) (+ (* 1/3840 (cos (+ x (* 1/2 eps)))) (* 1/2 (/ (cos (+ x (* 1/2 eps))) (pow eps 4))))))>
#<alt (* (pow eps 5) (+ (* -1/48 (/ (cos (+ x (* 1/2 eps))) (pow eps 2))) (+ (* 1/3840 (cos (+ x (* 1/2 eps)))) (* 1/2 (/ (cos (+ x (* 1/2 eps))) (pow eps 4))))))>
#<alt (* 1/3840 (* (pow eps 5) (cos (- x (* -1/2 eps)))))>
#<alt (* -1 (* (pow eps 5) (+ (* -1/3840 (cos (- x (* -1/2 eps)))) (* 1/48 (/ (cos (- x (* -1/2 eps))) (pow eps 2))))))>
#<alt (* -1 (* (pow eps 5) (+ (* -1/2 (/ (cos (- x (* -1/2 eps))) (pow eps 4))) (+ (* -1/3840 (cos (- x (* -1/2 eps)))) (* 1/48 (/ (cos (- x (* -1/2 eps))) (pow eps 2)))))))>
#<alt (* -1 (* (pow eps 5) (+ (* -1/2 (/ (cos (- x (* -1/2 eps))) (pow eps 4))) (+ (* -1/3840 (cos (- x (* -1/2 eps)))) (* 1/48 (/ (cos (- x (* -1/2 eps))) (pow eps 2)))))))>
#<alt (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))>
#<alt (+ (* -1 (* eps (* x (* (sin (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))) (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))>
#<alt (+ (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))) (* x (+ (* -1 (* eps (* (sin (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))) (* -1/2 (* eps (* x (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))))))>
#<alt (+ (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))) (* x (+ (* -1 (* eps (* (sin (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))) (* x (+ (* -1/2 (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))) (* 1/6 (* eps (* x (* (sin (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))))))))>
#<alt (* eps (* (cos (+ x (* 1/2 eps))) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))>
#<alt (* eps (* (cos (+ x (* 1/2 eps))) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))>
#<alt (* eps (* (cos (+ x (* 1/2 eps))) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))>
#<alt (* eps (* (cos (+ x (* 1/2 eps))) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))>
#<alt (* eps (* (cos (- (* 1/2 eps) (* -1 x))) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))>
#<alt (* eps (* (cos (- (* 1/2 eps) (* -1 x))) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))>
#<alt (* eps (* (cos (- (* 1/2 eps) (* -1 x))) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))>
#<alt (* eps (* (cos (- (* 1/2 eps) (* -1 x))) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))>
#<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) (- (* 1/3840 (pow eps 2)) 1/48))))>
#<alt (* 1/3840 (pow eps 5))>
#<alt (* (pow eps 5) (- 1/3840 (* 1/48 (/ 1 (pow eps 2)))))>
#<alt (* (pow eps 5) (- (+ 1/3840 (/ 1/2 (pow eps 4))) (* 1/48 (/ 1 (pow eps 2)))))>
#<alt (* (pow eps 5) (- (+ 1/3840 (/ 1/2 (pow eps 4))) (* 1/48 (/ 1 (pow eps 2)))))>
#<alt (* 1/3840 (pow eps 5))>
#<alt (* -1 (* (pow eps 5) (- (* 1/48 (/ 1 (pow eps 2))) 1/3840)))>
#<alt (* -1 (* (pow eps 5) (- (* 1/48 (/ 1 (pow eps 2))) (+ 1/3840 (/ 1/2 (pow eps 4))))))>
#<alt (* -1 (* (pow eps 5) (- (* 1/48 (/ 1 (pow eps 2))) (+ 1/3840 (/ 1/2 (pow eps 4))))))>
#<alt 1/2>
#<alt (+ 1/2 (* -1/48 (pow eps 2)))>
#<alt (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))>
#<alt (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))>
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#<alt (* 1/24 x)>
#<alt (* 1/24 x)>
#<alt (* 1/24 x)>
#<alt (* 1/24 x)>
#<alt (* 1/24 x)>
#<alt (* 1/24 x)>
#<alt (* -1/48 eps)>
#<alt (* -1/48 eps)>
#<alt (* -1/48 eps)>
#<alt (* -1/48 eps)>
#<alt (* -1/48 eps)>
#<alt (* -1/48 eps)>
#<alt (* -1/48 eps)>
#<alt (* -1/48 eps)>
#<alt (* -1/48 eps)>
#<alt (* -1/48 eps)>
#<alt (* -1/48 eps)>
#<alt (* -1/48 eps)>
#<alt eps>
#<alt (+ eps (* 2 x))>
#<alt (+ eps (* 2 x))>
#<alt (+ eps (* 2 x))>
#<alt (* 2 x)>
#<alt (* x (+ 2 (/ eps x)))>
#<alt (* x (+ 2 (/ eps x)))>
#<alt (* x (+ 2 (/ eps x)))>
#<alt (* 2 x)>
#<alt (* -1 (* x (- (* -1 (/ eps x)) 2)))>
#<alt (* -1 (* x (- (* -1 (/ eps x)) 2)))>
#<alt (* -1 (* x (- (* -1 (/ eps x)) 2)))>
#<alt (* 2 x)>
#<alt (+ eps (* 2 x))>
#<alt (+ eps (* 2 x))>
#<alt (+ eps (* 2 x))>
#<alt eps>
#<alt (* eps (+ 1 (* 2 (/ x eps))))>
#<alt (* eps (+ 1 (* 2 (/ x eps))))>
#<alt (* eps (+ 1 (* 2 (/ x eps))))>
#<alt eps>
#<alt (* -1 (* eps (- (* -2 (/ x eps)) 1)))>
#<alt (* -1 (* eps (- (* -2 (/ x eps)) 1)))>
#<alt (* -1 (* eps (- (* -2 (/ x eps)) 1)))>
#<alt (cos (* 1/2 eps))>
#<alt (+ (cos (* 1/2 eps)) (* -1 (* x (sin (* 1/2 eps)))))>
#<alt (+ (cos (* 1/2 eps)) (* x (- (* -1/2 (* x (cos (* 1/2 eps)))) (sin (* 1/2 eps)))))>
#<alt (+ (cos (* 1/2 eps)) (* x (- (* x (+ (* -1/2 (cos (* 1/2 eps))) (* 1/6 (* x (sin (* 1/2 eps)))))) (sin (* 1/2 eps)))))>
#<alt (cos (* 1/2 (+ eps (* 2 x))))>
#<alt (cos (* 1/2 (+ eps (* 2 x))))>
#<alt (cos (* 1/2 (+ eps (* 2 x))))>
#<alt (cos (* 1/2 (+ eps (* 2 x))))>
#<alt (cos (* 1/2 (- eps (* -2 x))))>
#<alt (cos (* 1/2 (- eps (* -2 x))))>
#<alt (cos (* 1/2 (- eps (* -2 x))))>
#<alt (cos (* 1/2 (- eps (* -2 x))))>
#<alt (cos x)>
#<alt (+ (cos x) (* -1/2 (* eps (sin x))))>
#<alt (+ (cos x) (* eps (- (* -1/8 (* eps (cos x))) (* 1/2 (sin x)))))>
#<alt (+ (cos x) (* eps (- (* eps (+ (* -1/8 (cos x)) (* 1/48 (* eps (sin x))))) (* 1/2 (sin x)))))>
#<alt (cos (* 1/2 (+ eps (* 2 x))))>
#<alt (cos (* 1/2 (+ eps (* 2 x))))>
#<alt (cos (* 1/2 (+ eps (* 2 x))))>
#<alt (cos (* 1/2 (+ eps (* 2 x))))>
#<alt (cos (* 1/2 (- (* 2 x) (* -1 eps))))>
#<alt (cos (* 1/2 (- (* 2 x) (* -1 eps))))>
#<alt (cos (* 1/2 (- (* 2 x) (* -1 eps))))>
#<alt (cos (* 1/2 (- (* 2 x) (* -1 eps))))>

Calls

111 calls:

Time	Variable		Point	Expression
3.0ms	x	@	-inf	(* (* (* eps (+ (* (* eps eps) (+ (* eps (* eps 1/3840)) -1/48)) 1/2)) (cos (+ (* 1/2 eps) x))) 2)
1.0ms	x	@	inf	(* (* (* eps (+ (* eps (* eps -1/48)) 1/2)) (cos (* (+ x (+ x eps)) 1/2))) 2)
1.0ms	x	@	inf	(* (* (* eps (+ (* (* eps eps) (+ (* eps (* eps 1/3840)) -1/48)) 1/2)) (cos (+ (* 1/2 eps) x))) 2)
1.0ms	eps	@	0	(+ (* (* eps (* x x)) (+ (* x (* x 1/24)) -1/2)) eps)
1.0ms	x	@	-inf	(* (* (* eps (+ (* eps (* eps -1/48)) 1/2)) (cos (* (+ x (+ x eps)) 1/2))) 2)

rewrite373.0ms (2.6%)

Memory

42.2MiB live, 746.7MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

6 066×	`accelerator-lowering-fma.f32`
6 066×	`accelerator-lowering-fma.f64`
4 184×	`/-lowering-/.f32`
4 184×	`/-lowering-/.f64`
4 130×	`-lowering-.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	43	225
1	236	225
2	1810	225
0	8618	198

Stop Event

1×	iter limit
1×	node limit

Counts

24 → 598

Calls

Call 1

Inputs
(* (* (* eps (+ (* (* eps eps) (+ (* eps (* eps 1/3840)) -1/48)) 1/2)) (cos (+ (* 1/2 eps) x))) 2)
(* (* eps (+ (* (* eps eps) (+ (* eps (* eps 1/3840)) -1/48)) 1/2)) (cos (+ (* 1/2 eps) x)))
(* eps (+ (* (* eps eps) (+ (* eps (* eps 1/3840)) -1/48)) 1/2))
(+ (* (* eps eps) (+ (* eps (* eps 1/3840)) -1/48)) 1/2)
(* eps (+ (* x (* x -1/2)) 1))
(+ (* x (* x -1/2)) 1)
(* x -1/2)
(+ (* (* eps (* x x)) (+ (* x (* x 1/24)) -1/2)) eps)
(* eps (* x x))
(* x x)
(+ (* x (* x 1/24)) -1/2)
(* eps (cos (+ (* 1/2 eps) x)))
(cos (+ (* 1/2 eps) x))
(+ (* 1/2 eps) x)
(* (+ x (+ x eps)) 1/2)
(* (* (* eps (+ (* eps (* eps -1/48)) 1/2)) (cos (* (+ x (+ x eps)) 1/2))) 2)
(* (* eps (+ (* eps (* eps -1/48)) 1/2)) (cos (* (+ x (+ x eps)) 1/2)))
(* eps (+ (* eps (* eps -1/48)) 1/2))
(* eps 1/3840)
(+ (* eps (* eps 1/3840)) -1/48)
(* x 1/24)
(* eps -1/48)
(+ x (+ x eps))
(cos (* (+ x (+ x eps)) 1/2))

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

simplify427.0ms (3%)

Memory

-28.5MiB live, 528.5MiB allocated

Algorithm

1×	egg-herbie

Rules

10 602×	`accelerator-lowering-fma.f32`
10 602×	`accelerator-lowering-fma.f64`
7 056×	`-lowering-.f32`
7 056×	`-lowering-.f64`
2 782×	`+-lowering-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	409	5211
1	1346	5100
2	4604	4891
0	8183	4448

Stop Event

1×	iter limit
1×	node limit

Counts

444 → 444

Calls

Call 1

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

Outputs
(* eps (cos x))
(*.f64 eps (cos.f64 x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x)))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* 2 (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x)))))))))
(.f64 eps (fma.f64 eps (fma.f64 eps (.f64 (cos.f64 x) #s(literal -1/6 binary64)) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) (cos.f64 x)))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* 1/24 (* eps (sin x))) (* 2 (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))))
(.f64 eps (fma.f64 eps (fma.f64 (sin.f64 x) (+.f64 #s(literal -1/2 binary64) (.f64 eps (.f64 eps #s(literal 1/24 binary64)))) (.f64 eps (*.f64 (cos.f64 x) #s(literal -1/6 binary64)))) (cos.f64 x)))
(* 1/1920 (* (pow eps 5) (cos (+ x (* 1/2 eps)))))
(.f64 (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (.f64 #s(literal 1/1920 binary64) (pow.f64 eps #s(literal 5 binary64))))
(* (pow eps 5) (+ (* -1/24 (/ (cos (+ x (* 1/2 eps))) (pow eps 2))) (* 1/1920 (cos (+ x (* 1/2 eps))))))
(.f64 (pow.f64 eps #s(literal 5 binary64)) (fma.f64 #s(literal -1/24 binary64) (/.f64 (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (.f64 eps eps)) (*.f64 #s(literal 1/1920 binary64) (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))))
(* (pow eps 5) (+ (* -1/24 (/ (cos (+ x (* 1/2 eps))) (pow eps 2))) (+ (* 1/1920 (cos (+ x (* 1/2 eps)))) (/ (cos (+ x (* 1/2 eps))) (pow eps 4)))))
(.f64 (pow.f64 eps #s(literal 5 binary64)) (fma.f64 #s(literal 1/1920 binary64) (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (fma.f64 #s(literal -1/24 binary64) (/.f64 (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (.f64 eps eps)) (/.f64 (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (pow.f64 eps #s(literal 4 binary64))))))
(* (pow eps 5) (+ (* -1/24 (/ (cos (+ x (* 1/2 eps))) (pow eps 2))) (+ (* 1/1920 (cos (+ x (* 1/2 eps)))) (/ (cos (+ x (* 1/2 eps))) (pow eps 4)))))
(.f64 (pow.f64 eps #s(literal 5 binary64)) (fma.f64 #s(literal 1/1920 binary64) (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (fma.f64 #s(literal -1/24 binary64) (/.f64 (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (.f64 eps eps)) (/.f64 (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (pow.f64 eps #s(literal 4 binary64))))))
(* 1/1920 (* (pow eps 5) (cos (- x (* -1/2 eps)))))
(.f64 (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (.f64 #s(literal 1/1920 binary64) (pow.f64 eps #s(literal 5 binary64))))
(* -1 (* (pow eps 5) (+ (* -1/1920 (cos (- x (* -1/2 eps)))) (* 1/24 (/ (cos (- x (* -1/2 eps))) (pow eps 2))))))
(.f64 (pow.f64 eps #s(literal 5 binary64)) (fma.f64 #s(literal -1/24 binary64) (/.f64 (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (.f64 eps eps)) (*.f64 #s(literal 1/1920 binary64) (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))))
(* -1 (* (pow eps 5) (+ (* -1 (/ (cos (- x (* -1/2 eps))) (pow eps 4))) (+ (* -1/1920 (cos (- x (* -1/2 eps)))) (* 1/24 (/ (cos (- x (* -1/2 eps))) (pow eps 2)))))))
(.f64 (pow.f64 eps #s(literal 5 binary64)) (fma.f64 #s(literal 1/1920 binary64) (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (fma.f64 #s(literal -1/24 binary64) (/.f64 (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (.f64 eps eps)) (/.f64 (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (pow.f64 eps #s(literal 4 binary64))))))
(* -1 (* (pow eps 5) (+ (* -1 (/ (cos (- x (* -1/2 eps))) (pow eps 4))) (+ (* -1/1920 (cos (- x (* -1/2 eps)))) (* 1/24 (/ (cos (- x (* -1/2 eps))) (pow eps 2)))))))
(.f64 (pow.f64 eps #s(literal 5 binary64)) (fma.f64 #s(literal 1/1920 binary64) (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (fma.f64 #s(literal -1/24 binary64) (/.f64 (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (.f64 eps eps)) (/.f64 (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (pow.f64 eps #s(literal 4 binary64))))))
(* 2 (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))
(.f64 (.f64 (.f64 eps #s(literal 2 binary64)) (fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64))) (cos.f64 (.f64 eps #s(literal 1/2 binary64))))
(+ (* -2 (* eps (* x (* (sin (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))) (* 2 (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))))
(.f64 (fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)) (fma.f64 (.f64 eps #s(literal -2 binary64)) (.f64 x (sin.f64 (.f64 eps #s(literal 1/2 binary64)))) (.f64 (.f64 eps #s(literal 2 binary64)) (cos.f64 (*.f64 eps #s(literal 1/2 binary64))))))
(+ (* 2 (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))) (* x (+ (* -2 (* eps (* (sin (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))) (* -1 (* eps (* x (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))))))
(fma.f64 x (.f64 (fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)) (fma.f64 (.f64 eps #s(literal -2 binary64)) (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (neg.f64 (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 eps x))))) (.f64 (.f64 (.f64 eps #s(literal 2 binary64)) (fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64))) (cos.f64 (.f64 eps #s(literal 1/2 binary64)))))
(+ (* 2 (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))) (* x (+ (* -2 (* eps (* (sin (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))) (* x (+ (* -1 (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))) (* 1/3 (* eps (* x (* (sin (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))))))))
(fma.f64 (fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)) (fma.f64 #s(literal 2 binary64) (.f64 eps (cos.f64 (.f64 eps #s(literal 1/2 binary64)))) (.f64 (.f64 eps #s(literal -2 binary64)) (.f64 x (sin.f64 (.f64 eps #s(literal 1/2 binary64)))))) (.f64 (.f64 (fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)) (fma.f64 (.f64 eps #s(literal 1/3 binary64)) (.f64 x (sin.f64 (.f64 eps #s(literal 1/2 binary64)))) (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (neg.f64 eps)))) (.f64 x x)))
(* 2 (* eps (* (cos (+ x (* 1/2 eps))) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))
(.f64 (.f64 (.f64 eps #s(literal 2 binary64)) (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x))) (fma.f64 (.f64 eps eps) (fma.f64 eps (*.f64 eps #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))
(* 2 (* eps (* (cos (+ x (* 1/2 eps))) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))
(.f64 (.f64 (.f64 eps #s(literal 2 binary64)) (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x))) (fma.f64 (.f64 eps eps) (fma.f64 eps (*.f64 eps #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))
(* 2 (* eps (* (cos (+ x (* 1/2 eps))) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))
(.f64 (.f64 (.f64 eps #s(literal 2 binary64)) (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x))) (fma.f64 (.f64 eps eps) (fma.f64 eps (*.f64 eps #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))
(* 2 (* eps (* (cos (+ x (* 1/2 eps))) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))
(.f64 (.f64 (.f64 eps #s(literal 2 binary64)) (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x))) (fma.f64 (.f64 eps eps) (fma.f64 eps (*.f64 eps #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))
(* 2 (* eps (* (cos (- (* 1/2 eps) (* -1 x))) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))
(.f64 (.f64 (.f64 eps #s(literal 2 binary64)) (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x))) (fma.f64 (.f64 eps eps) (fma.f64 eps (*.f64 eps #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))
(* 2 (* eps (* (cos (- (* 1/2 eps) (* -1 x))) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))
(.f64 (.f64 (.f64 eps #s(literal 2 binary64)) (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x))) (fma.f64 (.f64 eps eps) (fma.f64 eps (*.f64 eps #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))
(* 2 (* eps (* (cos (- (* 1/2 eps) (* -1 x))) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))
(.f64 (.f64 (.f64 eps #s(literal 2 binary64)) (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x))) (fma.f64 (.f64 eps eps) (fma.f64 eps (*.f64 eps #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))
(* 2 (* eps (* (cos (- (* 1/2 eps) (* -1 x))) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))
(.f64 (.f64 (.f64 eps #s(literal 2 binary64)) (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x))) (fma.f64 (.f64 eps eps) (fma.f64 eps (*.f64 eps #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))
(* 1/2 (* eps (cos x)))
(.f64 (cos.f64 x) (.f64 eps #s(literal 1/2 binary64)))
(* eps (+ (* -1/4 (* eps (sin x))) (* 1/2 (cos x))))
(.f64 eps (fma.f64 eps (.f64 (sin.f64 x) #s(literal -1/4 binary64)) (*.f64 (cos.f64 x) #s(literal 1/2 binary64))))
(* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))
(.f64 eps (fma.f64 eps (fma.f64 eps (.f64 (cos.f64 x) #s(literal -1/12 binary64)) (.f64 (sin.f64 x) #s(literal -1/4 binary64))) (.f64 (cos.f64 x) #s(literal 1/2 binary64))))
(* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (+ (* -1/48 (cos x)) (* 1/48 (* eps (sin x))))))))))
(.f64 eps (fma.f64 eps (fma.f64 eps (fma.f64 eps (.f64 (sin.f64 x) #s(literal 1/48 binary64)) (.f64 (cos.f64 x) #s(literal -1/12 binary64))) (.f64 (sin.f64 x) #s(literal -1/4 binary64))) (*.f64 (cos.f64 x) #s(literal 1/2 binary64))))
(* 1/3840 (* (pow eps 5) (cos (+ x (* 1/2 eps)))))
(.f64 (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (.f64 (pow.f64 eps #s(literal 5 binary64)) #s(literal 1/3840 binary64)))
(* (pow eps 5) (+ (* -1/48 (/ (cos (+ x (* 1/2 eps))) (pow eps 2))) (* 1/3840 (cos (+ x (* 1/2 eps))))))
(.f64 (pow.f64 eps #s(literal 5 binary64)) (fma.f64 #s(literal -1/48 binary64) (/.f64 (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (.f64 eps eps)) (*.f64 (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) #s(literal 1/3840 binary64))))
(* (pow eps 5) (+ (* -1/48 (/ (cos (+ x (* 1/2 eps))) (pow eps 2))) (+ (* 1/3840 (cos (+ x (* 1/2 eps)))) (* 1/2 (/ (cos (+ x (* 1/2 eps))) (pow eps 4))))))
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(* (pow eps 2) (- 1/3840 (* 1/48 (/ 1 (pow eps 2)))))
(.f64 (.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (/.f64 #s(literal -1/48 binary64) (*.f64 eps eps))))
(* (pow eps 2) (- 1/3840 (* 1/48 (/ 1 (pow eps 2)))))
(.f64 (.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (/.f64 #s(literal -1/48 binary64) (*.f64 eps eps))))
(* (pow eps 2) (- 1/3840 (* 1/48 (/ 1 (pow eps 2)))))
(.f64 (.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (/.f64 #s(literal -1/48 binary64) (*.f64 eps eps))))
(* 1/3840 (pow eps 2))
(.f64 eps (.f64 eps #s(literal 1/3840 binary64)))
(* (pow eps 2) (- 1/3840 (* 1/48 (/ 1 (pow eps 2)))))
(.f64 (.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (/.f64 #s(literal -1/48 binary64) (*.f64 eps eps))))
(* (pow eps 2) (- 1/3840 (* 1/48 (/ 1 (pow eps 2)))))
(.f64 (.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (/.f64 #s(literal -1/48 binary64) (*.f64 eps eps))))
(* (pow eps 2) (- 1/3840 (* 1/48 (/ 1 (pow eps 2)))))
(.f64 (.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (/.f64 #s(literal -1/48 binary64) (*.f64 eps eps))))
(* 1/24 x)
(*.f64 x #s(literal 1/24 binary64))
(* 1/24 x)
(*.f64 x #s(literal 1/24 binary64))
(* 1/24 x)
(*.f64 x #s(literal 1/24 binary64))
(* 1/24 x)
(*.f64 x #s(literal 1/24 binary64))
(* 1/24 x)
(*.f64 x #s(literal 1/24 binary64))
(* 1/24 x)
(*.f64 x #s(literal 1/24 binary64))
(* 1/24 x)
(*.f64 x #s(literal 1/24 binary64))
(* 1/24 x)
(*.f64 x #s(literal 1/24 binary64))
(* 1/24 x)
(*.f64 x #s(literal 1/24 binary64))
(* 1/24 x)
(*.f64 x #s(literal 1/24 binary64))
(* 1/24 x)
(*.f64 x #s(literal 1/24 binary64))
(* 1/24 x)
(*.f64 x #s(literal 1/24 binary64))
(* -1/48 eps)
(*.f64 eps #s(literal -1/48 binary64))
(* -1/48 eps)
(*.f64 eps #s(literal -1/48 binary64))
(* -1/48 eps)
(*.f64 eps #s(literal -1/48 binary64))
(* -1/48 eps)
(*.f64 eps #s(literal -1/48 binary64))
(* -1/48 eps)
(*.f64 eps #s(literal -1/48 binary64))
(* -1/48 eps)
(*.f64 eps #s(literal -1/48 binary64))
(* -1/48 eps)
(*.f64 eps #s(literal -1/48 binary64))
(* -1/48 eps)
(*.f64 eps #s(literal -1/48 binary64))
(* -1/48 eps)
(*.f64 eps #s(literal -1/48 binary64))
(* -1/48 eps)
(*.f64 eps #s(literal -1/48 binary64))
(* -1/48 eps)
(*.f64 eps #s(literal -1/48 binary64))
(* -1/48 eps)
(*.f64 eps #s(literal -1/48 binary64))
eps
(+ eps (* 2 x))
(fma.f64 x #s(literal 2 binary64) eps)
(+ eps (* 2 x))
(fma.f64 x #s(literal 2 binary64) eps)
(+ eps (* 2 x))
(fma.f64 x #s(literal 2 binary64) eps)
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* x (+ 2 (/ eps x)))
(*.f64 x (+.f64 #s(literal 2 binary64) (/.f64 eps x)))
(* x (+ 2 (/ eps x)))
(*.f64 x (+.f64 #s(literal 2 binary64) (/.f64 eps x)))
(* x (+ 2 (/ eps x)))
(*.f64 x (+.f64 #s(literal 2 binary64) (/.f64 eps x)))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* -1 (* x (- (* -1 (/ eps x)) 2)))
(*.f64 x (+.f64 #s(literal 2 binary64) (/.f64 eps x)))
(* -1 (* x (- (* -1 (/ eps x)) 2)))
(*.f64 x (+.f64 #s(literal 2 binary64) (/.f64 eps x)))
(* -1 (* x (- (* -1 (/ eps x)) 2)))
(*.f64 x (+.f64 #s(literal 2 binary64) (/.f64 eps x)))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(+ eps (* 2 x))
(fma.f64 x #s(literal 2 binary64) eps)
(+ eps (* 2 x))
(fma.f64 x #s(literal 2 binary64) eps)
(+ eps (* 2 x))
(fma.f64 x #s(literal 2 binary64) eps)
eps
(* eps (+ 1 (* 2 (/ x eps))))
(fma.f64 eps (/.f64 (*.f64 x #s(literal 2 binary64)) eps) eps)
(* eps (+ 1 (* 2 (/ x eps))))
(fma.f64 eps (/.f64 (*.f64 x #s(literal 2 binary64)) eps) eps)
(* eps (+ 1 (* 2 (/ x eps))))
(fma.f64 eps (/.f64 (*.f64 x #s(literal 2 binary64)) eps) eps)
eps
(* -1 (* eps (- (* -2 (/ x eps)) 1)))
(fma.f64 eps (/.f64 (*.f64 x #s(literal 2 binary64)) eps) eps)
(* -1 (* eps (- (* -2 (/ x eps)) 1)))
(fma.f64 eps (/.f64 (*.f64 x #s(literal 2 binary64)) eps) eps)
(* -1 (* eps (- (* -2 (/ x eps)) 1)))
(fma.f64 eps (/.f64 (*.f64 x #s(literal 2 binary64)) eps) eps)
(cos (* 1/2 eps))
(cos.f64 (*.f64 eps #s(literal 1/2 binary64)))
(+ (cos (* 1/2 eps)) (* -1 (* x (sin (* 1/2 eps)))))
(fma.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (neg.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64))))
(+ (cos (* 1/2 eps)) (* x (- (* -1/2 (* x (cos (* 1/2 eps)))) (sin (* 1/2 eps)))))
(fma.f64 x (-.f64 (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 x #s(literal -1/2 binary64))) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))) (cos.f64 (*.f64 eps #s(literal 1/2 binary64))))
(+ (cos (* 1/2 eps)) (* x (- (* x (+ (* -1/2 (cos (* 1/2 eps))) (* 1/6 (* x (sin (* 1/2 eps)))))) (sin (* 1/2 eps)))))
(fma.f64 x (fma.f64 x (.f64 #s(literal -1/2 binary64) (cos.f64 (.f64 eps #s(literal 1/2 binary64)))) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (fma.f64 x (.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64)))) (cos.f64 (.f64 eps #s(literal 1/2 binary64))))
(cos (* 1/2 (+ eps (* 2 x))))
(cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x))
(cos (* 1/2 (+ eps (* 2 x))))
(cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x))
(cos (* 1/2 (+ eps (* 2 x))))
(cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x))
(cos (* 1/2 (+ eps (* 2 x))))
(cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x))
(cos (* 1/2 (- eps (* -2 x))))
(cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x))
(cos (* 1/2 (- eps (* -2 x))))
(cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x))
(cos (* 1/2 (- eps (* -2 x))))
(cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x))
(cos (* 1/2 (- eps (* -2 x))))
(cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x))
(cos x)
(cos.f64 x)
(+ (cos x) (* -1/2 (* eps (sin x))))
(fma.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x))
(+ (cos x) (* eps (- (* -1/8 (* eps (cos x))) (* 1/2 (sin x)))))
(fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (.f64 (fma.f64 eps (*.f64 eps #s(literal -1/8 binary64)) #s(literal 1 binary64)) (cos.f64 x)))
(+ (cos x) (* eps (- (* eps (+ (* -1/8 (cos x)) (* 1/48 (* eps (sin x))))) (* 1/2 (sin x)))))
(fma.f64 eps (fma.f64 eps (.f64 (cos.f64 x) #s(literal -1/8 binary64)) (.f64 (sin.f64 x) (fma.f64 eps (*.f64 eps #s(literal 1/48 binary64)) #s(literal -1/2 binary64)))) (cos.f64 x))
(cos (* 1/2 (+ eps (* 2 x))))
(cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x))
(cos (* 1/2 (+ eps (* 2 x))))
(cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x))
(cos (* 1/2 (+ eps (* 2 x))))
(cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x))
(cos (* 1/2 (+ eps (* 2 x))))
(cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x))
(cos (* 1/2 (- (* 2 x) (* -1 eps))))
(cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x))
(cos (* 1/2 (- (* 2 x) (* -1 eps))))
(cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x))
(cos (* 1/2 (- (* 2 x) (* -1 eps))))
(cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x))
(cos (* 1/2 (- (* 2 x) (* -1 eps))))
(cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x))

eval189.0ms (1.3%)

Memory: 36.9MiB live, 189.7MiB allocated
Compiler: Compiled 32 241 to 2 975 computations (90.8% saved)

prune249.0ms (1.8%)

Memory

-17.2MiB live, 142.4MiB allocated

Pruning

12 alts after pruning (5 fresh and 7 done)

	Pruned	Kept	Total
New	1 150	2	1 152
Fresh	2	3	5
Picked	1	4	5
Done	1	3	4
Total	1 154	12	1 166

Accuracy

100.0%

Counts

1 166 → 12

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.1%	(fma.f64 (.f64 eps (.f64 x x)) (fma.f64 x (*.f64 x #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) eps)
	98.4%	(.f64 (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) eps)
✓	100.0%	(.f64 (.f64 (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 eps (*.f64 eps #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64))) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) #s(literal 2 binary64))
	99.9%	(.f64 (.f64 (.f64 eps (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/2 binary64))) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) #s(literal 2 binary64))
	99.9%	(.f64 (.f64 (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64))) (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (.f64 (fma.f64 eps (*.f64 eps #s(literal -1/8 binary64)) #s(literal 1 binary64)) (cos.f64 x)))) #s(literal 2 binary64))
	99.7%	(.f64 (.f64 (.f64 #s(literal 1/2 binary64) eps) (cos.f64 (.f64 (*.f64 x (+.f64 (/.f64 eps x) #s(literal 2 binary64))) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
✓	99.1%	(.f64 eps (fma.f64 x (.f64 x (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) #s(literal -1/2 binary64))) #s(literal 1 binary64)))
✓	98.9%	(.f64 eps (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)))
	99.1%	(.f64 eps (+.f64 (.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) #s(literal -1/2 binary64))) #s(literal 1 binary64)))
✓	99.7%	(*.f64 eps (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))
✓	99.3%	(*.f64 eps (cos.f64 x))
✓	98.4%	eps

Compiler

Compiled 598 to 245 computations (59% saved)

regimes44.0ms (0.3%)

Memory

-8.3MiB live, 30.2MiB allocated

Counts

29 → 1

Calls

Call 1

Inputs
eps
(.f64 eps (fma.f64 #s(literal -1/2 binary64) (.f64 x x) #s(literal 1 binary64)))
(.f64 eps (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)))
(.f64 (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) eps)
(fma.f64 eps (.f64 eps (.f64 eps #s(literal -1/6 binary64))) eps)
(fma.f64 (.f64 eps (.f64 x x)) (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal -1/2 binary64)) eps)
(fma.f64 (.f64 eps (.f64 x x)) (fma.f64 x (*.f64 x #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) eps)
(.f64 eps (fma.f64 x (.f64 x (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) #s(literal -1/2 binary64))) #s(literal 1 binary64)))
(.f64 eps (+.f64 (.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) #s(literal -1/2 binary64))) #s(literal 1 binary64)))
(sin.f64 eps)
(*.f64 eps (cos.f64 x))
(*.f64 eps (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))
(/.f64 (.f64 (.f64 eps eps) (cos.f64 x)) eps)
(.f64 (.f64 (.f64 #s(literal 1/2 binary64) eps) (cos.f64 (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
(.f64 (.f64 (.f64 eps (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/2 binary64))) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) #s(literal 2 binary64))
(-.f64 (sin.f64 (+.f64 x eps)) (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) (.f64 x (*.f64 x x)) x))
(-.f64 (-.f64 (sin.f64 (+.f64 x eps)) x) (.f64 (.f64 x x) (.f64 x (fma.f64 (.f64 x x) #s(literal 1/120 binary64) #s(literal -1/6 binary64)))))
(.f64 (.f64 (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64))) (cos.f64 (*.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
(.f64 (.f64 (.f64 #s(literal 1/2 binary64) eps) (cos.f64 (.f64 (*.f64 x (+.f64 (/.f64 eps x) #s(literal 2 binary64))) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
(.f64 (.f64 (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 eps (*.f64 eps #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64))) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) #s(literal 2 binary64))
(-.f64 (sin.f64 (+.f64 x eps)) (fma.f64 (fma.f64 x (.f64 x (fma.f64 (.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64))) #s(literal -1/6 binary64)) (.f64 x (.f64 x x)) x))
(.f64 (.f64 (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64))) (cos.f64 (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
(.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x)))
(.f64 (.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (cos.f64 (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
(.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (.f64 (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x))))
(.f64 (.f64 (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64))) (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (.f64 (fma.f64 eps (*.f64 eps #s(literal -1/8 binary64)) #s(literal 1 binary64)) (cos.f64 x)))) #s(literal 2 binary64))
(.f64 (.f64 (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64))) (fma.f64 (fma.f64 eps (.f64 eps #s(literal -1/8 binary64)) #s(literal 1 binary64)) (cos.f64 x) (.f64 #s(literal -1/2 binary64) (.f64 eps (sin.f64 x))))) #s(literal 2 binary64))
(.f64 (.f64 eps (fma.f64 #s(literal 1/2 binary64) (cos.f64 x) (.f64 eps (fma.f64 eps (.f64 (cos.f64 x) #s(literal -1/12 binary64)) (*.f64 (sin.f64 x) #s(literal -1/4 binary64)))))) #s(literal 2 binary64))

Outputs

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

Calls

3 calls:

27.0ms	x
8.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
8.0ms	eps

Results

Accuracy	Segments	Branch
100.0%	1	`x`
100.0%	1	`eps`
100.0%	1	`(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))`

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes17.0ms (0.1%)

Memory

21.1MiB live, 21.1MiB allocated

Counts

19 → 1

Calls

Call 1

Inputs
eps
(.f64 eps (fma.f64 #s(literal -1/2 binary64) (.f64 x x) #s(literal 1 binary64)))
(.f64 eps (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)))
(.f64 (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) eps)
(fma.f64 eps (.f64 eps (.f64 eps #s(literal -1/6 binary64))) eps)
(fma.f64 (.f64 eps (.f64 x x)) (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal -1/2 binary64)) eps)
(fma.f64 (.f64 eps (.f64 x x)) (fma.f64 x (*.f64 x #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) eps)
(.f64 eps (fma.f64 x (.f64 x (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) #s(literal -1/2 binary64))) #s(literal 1 binary64)))
(.f64 eps (+.f64 (.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) #s(literal -1/2 binary64))) #s(literal 1 binary64)))
(sin.f64 eps)
(*.f64 eps (cos.f64 x))
(*.f64 eps (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))
(/.f64 (.f64 (.f64 eps eps) (cos.f64 x)) eps)
(.f64 (.f64 (.f64 #s(literal 1/2 binary64) eps) (cos.f64 (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
(.f64 (.f64 (.f64 eps (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/2 binary64))) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) #s(literal 2 binary64))
(-.f64 (sin.f64 (+.f64 x eps)) (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) (.f64 x (*.f64 x x)) x))
(-.f64 (-.f64 (sin.f64 (+.f64 x eps)) x) (.f64 (.f64 x x) (.f64 x (fma.f64 (.f64 x x) #s(literal 1/120 binary64) #s(literal -1/6 binary64)))))
(.f64 (.f64 (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64))) (cos.f64 (*.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
(.f64 (.f64 (.f64 #s(literal 1/2 binary64) eps) (cos.f64 (.f64 (*.f64 x (+.f64 (/.f64 eps x) #s(literal 2 binary64))) #s(literal 1/2 binary64)))) #s(literal 2 binary64))

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

Calls

3 calls:

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

Results

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

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes31.0ms (0.2%)

Memory

-15.8MiB live, 21.4MiB allocated

Counts

14 → 1

Calls

Call 1

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

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

Calls

3 calls:

22.0ms	eps
4.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
4.0ms	x

Results

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

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes11.0ms (0.1%)

Memory

18.1MiB live, 18.1MiB allocated

Counts

11 → 1

Calls

Call 1

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

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

Calls

3 calls:

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

Results

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

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes16.0ms (0.1%)

Memory

-22.0MiB live, 17.4MiB allocated

Counts

10 → 1

Calls

Call 1

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

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

Calls

3 calls:

9.0ms	x
3.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
3.0ms	eps

Results

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

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes9.0ms (0.1%)

Memory

15.1MiB live, 15.1MiB allocated

Counts

8 → 1

Calls

Call 1

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

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

Calls

3 calls:

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

Results

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

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes8.0ms (0.1%)

Memory

12.5MiB live, 12.5MiB allocated

Counts

7 → 1

Calls

Call 1

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

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

Calls

3 calls:

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

Results

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

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes15.0ms (0.1%)

Memory

-29.9MiB live, 10.7MiB allocated

Counts

5 → 1

Calls

Call 1

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

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

Calls

3 calls:

10.0ms	x
2.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
2.0ms	eps

Results

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

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes4.0ms (0%)

Memory

7.1MiB live, 7.1MiB allocated

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts

1 → 1

Calls

Call 1

Inputs
eps

Outputs
eps

Calls

3 calls:

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

Results

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

Compiler

Compiled 15 to 10 computations (33.3% saved)

simplify8.0ms (0.1%)

Memory

10.4MiB live, 10.4MiB allocated

Algorithm

1×	egg-herbie

Rules

30×	`*-commutative_binary64`
2×	`+-commutative_binary64`
2×	`1-exp_binary64`
2×	`1-exp_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	40	107
1	59	107

Stop Event

1×

saturated

Calls

Call 1

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

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

soundness1.2s (8.2%)

Memory

-5.1MiB live, 844.8MiB allocated

Rules

16 678×	`accelerator-lowering-fma.f32`
16 678×	`accelerator-lowering-fma.f64`
12 524×	`accelerator-lowering-fma.f32`
12 524×	`accelerator-lowering-fma.f64`
12 218×	`accelerator-lowering-fma.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	40	212
1	216	208
2	1690	206
0	8241	181
0	403	4127
1	1269	3902
2	4009	3752
3	7933	3752
0	8032	3428
0	6	16
1	49	16
2	376	16
3	4763	16
0	8212	16
0	409	5211
1	1346	5100
2	4604	4891
0	8183	4448
0	107	496
1	314	496
2	775	489
3	2836	489
4	6173	489
0	8126	458
0	393	3354
1	1192	3234
2	3296	3198
0	8204	2943

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×	node limit
1×	iter limit
1×	node limit

Compiler

Compiled 366 to 209 computations (42.9% saved)

preprocess106.0ms (0.8%)

Memory: 6.0MiB live, 202.8MiB allocated
Compiler: Compiled 330 to 158 computations (52.1% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

Iter	Nodes	Cost
0	21	46
1	43	42
2	92	42
3	181	42
4	321	42
5	398	42
6	483	42
7	525	42
8	534	42
0	6	7
1	9	7
2	14	7
3	20	7
4	28	7
5	43	7
6	76	7
7	101	7
8	144	7
9	159	7
10	167	7
0	167	7

Iter	Nodes	Cost
0	6	18
1	9	18
2	14	18
3	20	18
4	28	18
5	43	18
6	76	18
7	101	18
8	144	18
9	159	18
10	167	18
0	167	18

Iter	Nodes	Cost
0	21	46
1	43	42
2	92	42
3	181	42
4	321	42
5	398	42
6	483	42
7	525	42
8	534	42
0	6	7
1	9	7
2	14	7
3	20	7
4	28	7
5	43	7
6	76	7
7	101	7
8	144	7
9	159	7
10	167	7
0	167	7

Iter	Nodes	Cost
0	6	18
1	9	18
2	14	18
3	20	18
4	28	18
5	43	18
6	76	18
7	101	18
8	144	18
9	159	18
10	167	18
0	167	18

analyze45.0ms (0.3%)

sample5.8s (40.9%)

preprocess24.0ms (0.2%)

explain120.0ms (0.9%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify8.0ms (0.1%)

localize29.0ms (0.2%)

series4.0ms (0%)

rewrite601.0ms (4.3%)

simplify413.0ms (2.9%)

eval36.0ms (0.3%)

prune36.0ms (0.3%)

simplify314.0ms (2.2%)

localize148.0ms (1.1%)

series27.0ms (0.2%)

rewrite413.0ms (2.9%)

simplify398.0ms (2.8%)

eval145.0ms (1%)

prune119.0ms (0.8%)

simplify739.0ms (5.2%)

localize199.0ms (1.4%)

series33.0ms (0.2%)

rewrite479.0ms (3.4%)

simplify395.0ms (2.8%)

eval176.0ms (1.3%)

prune100.0ms (0.7%)

simplify482.0ms (3.4%)

localize133.0ms (0.9%)

series40.0ms (0.3%)

rewrite373.0ms (2.6%)

simplify427.0ms (3%)

eval189.0ms (1.3%)

prune249.0ms (1.8%)

regimes44.0ms (0.3%)

regimes17.0ms (0.1%)

regimes31.0ms (0.2%)

regimes11.0ms (0.1%)

regimes16.0ms (0.1%)

regimes9.0ms (0.1%)

regimes8.0ms (0.1%)

regimes15.0ms (0.1%)

regimes4.0ms (0%)

simplify8.0ms (0.1%)

soundness1.2s (8.2%)

preprocess106.0ms (0.8%)

end0.0ms (0%)

Profiling

Iter	Nodes	Cost
0	21	46
1	43	42
2	92	42
3	181	42
4	321	42
5	398	42
6	483	42
7	525	42
8	534	42
0	6	7
1	9	7
2	14	7
3	20	7
4	28	7
5	43	7
6	76	7
7	101	7
8	144	7
9	159	7
10	167	7
0	167	7

Iter	Nodes	Cost
0	6	18
1	9	18
2	14	18
3	20	18
4	28	18
5	43	18
6	76	18
7	101	18
8	144	18
9	159	18
10	167	18
0	167	18