Metrics for ENA, Section 1.4, Exercise 4d

analyze15.0ms (0.1%)

Memory

-13.5MiB live, 26.1MiB allocated

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	12.8%	87.2%	0%	0%	0%	0
0%	0%	12.8%	87.2%	0%	0%	0%	1
0%	0%	12.8%	87.2%	0%	0%	0%	2
50%	6.4%	6.4%	87.2%	0%	0%	0%	3
57.1%	6.4%	4.8%	87.2%	0%	1.6%	0%	4
69.2%	7.2%	3.2%	87.2%	0%	2.4%	0%	5
75%	7.2%	2.4%	87.2%	0%	3.2%	0%	6
82.6%	7.6%	1.6%	87.2%	0%	3.6%	0%	7
86.4%	7.6%	1.2%	87.2%	0%	4%	0%	8
90.7%	7.8%	0.8%	87.2%	0%	4.2%	0%	9
92.6%	7.8%	0.6%	87.2%	0%	4.4%	0%	10
95%	7.9%	0.4%	87.2%	0%	4.5%	0%	11
96.3%	8%	0.3%	87.2%	0%	4.5%	0%	12

Compiler

Compiled 24 to 18 computations (25% saved)

sample1.2s (12.4%)

Memory

5.6MiB live, 1 645.7MiB allocated

Samples

419.0ms	2 669×	1	valid
389.0ms	4 940×	0	valid
92.0ms	647×	2	valid
11.0ms	172×	0	invalid

Precisions

Click to see histograms. Total time spent on operations: 546.0ms

ival-mult: 153.0ms (28% of total)

ival-sub: 124.0ms (22.7% of total)

ival-<=: 96.0ms (17.6% of total)

ival-sqrt: 90.0ms (16.5% of total)

adjust: 41.0ms (7.5% of total)

ival-and: 22.0ms (4% of total)

exact: 17.0ms (3.1% of total)

ival-assert: 3.0ms (0.5% of total)

Bogosity

preprocess35.0ms (0.4%)

Memory

18.6MiB live, 55.6MiB allocated

Algorithm

2×	egg-herbie

Rules

176×	`accelerator-lowering-fma.f32`
176×	`accelerator-lowering-fma.f64`
148×	`sub-neg`
104×	`-lowering-.f32`
104×	`-lowering-.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	54
1	49	52
2	125	49
3	290	49
4	522	49
5	609	49
6	617	49
0	6	8
1	10	8
2	18	8
3	30	8
4	48	8
5	90	8
6	157	8
7	203	8
8	285	8
9	315	8
10	331	8
0	331	8

Stop Event

1×	iter limit
1×	saturated
1×	saturated

Calls

Call 1

Inputs
(- x (sqrt (- (* x x) eps)))

Outputs
(- x (sqrt (- (* x x) eps)))
(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))

Call 2

Inputs
(- x (sqrt (- (* x x) eps)))
(- (neg x) (sqrt (- (* (neg x) (neg x)) eps)))
(- x (sqrt (- (* x x) (neg eps))))
(neg (- (neg x) (sqrt (- (* (neg x) (neg x)) eps))))
(neg (- x (sqrt (- (* x x) (neg eps)))))
(- eps (sqrt (- (* eps eps) x)))

Outputs
(- x (sqrt (- (* x x) eps)))
(- (neg x) (sqrt (- (* (neg x) (neg x)) eps)))
(- (neg x) (sqrt (- (* x x) eps)))
(- x (sqrt (- (* x x) (neg eps))))
(- x (sqrt (+ (* x x) eps)))
(neg (- (neg x) (sqrt (- (* (neg x) (neg x)) eps))))
(+ x (sqrt (- (* x x) eps)))
(neg (- x (sqrt (- (* x x) (neg eps)))))
(- (sqrt (+ (* x x) eps)) x)
(- eps (sqrt (- (* eps eps) x)))

explain108.0ms (1.1%)

Memory

13.7MiB live, 242.7MiB allocated

FPErrors

Click to see full error table

Ground Truth	Example	Example	Subexpression
110	-	-	`(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))`
0	-	-	`eps`
0	-	-	`(sqrt.f64 (-.f64 (*.f64 x x) eps))`
0	-	-	`(-.f64 (*.f64 x x) eps)`
0	-	-	`(*.f64 x x)`
0	-	-	`x`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`-.f64`	`(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))`	cancellation	110	0

Confusion

	Predicted +	Predicted -
+	110	0
-	0	146

Precision

1.0

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	110	0	0
-	0	0	146

Precision?

1.0

Recall?

1.0

Freqs

test

number	freq
0	146
1	110

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

22.0ms	300×	0	valid
17.0ms	172×	1	valid
6.0ms	40×	2	valid

Compiler

Compiled 72 to 28 computations (61.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 26.0ms

ival-sqrt: 10.0ms (38.3% of total)

ival-sub: 7.0ms (26.8% of total)

ival-mult: 5.0ms (19.2% of total)

adjust: 3.0ms (11.5% of total)

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

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

eval0.0ms (0%)

Memory: 0.5MiB live, 0.5MiB allocated
Compiler: Compiled 2 to 2 computations (0% saved)

prune1.0ms (0%)

Memory

1.9MiB live, 1.9MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	60.4%	(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))

Compiler

Compiled 10 to 6 computations (40% saved)

simplify19.0ms (0.2%)

Memory

-37.8MiB live, 25.9MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

New	Metric	Program
✓	cost-diff	(*.f64 x x)
✓	cost-diff	(-.f64 (*.f64 x x) eps)
✓	cost-diff	(sqrt.f64 (-.f64 (*.f64 x x) eps))
✓	cost-diff	(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))

Rules

176×	`accelerator-lowering-fma.f32`
176×	`accelerator-lowering-fma.f64`
104×	`-lowering-.f32`
104×	`-lowering-.f64`
64×	`+-lowering-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	24
1	10	24
2	18	24
3	30	24
4	48	24
5	90	24
6	157	24
7	203	24
8	285	24
9	315	24
10	331	24
0	331	24

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

Inputs
(- x (sqrt (- (* x x) eps)))
x
(sqrt (- (* x x) eps))
(- (* x x) eps)
(* x x)
eps

Outputs
(- x (sqrt (- (* x x) eps)))
(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
x
(sqrt (- (* x x) eps))
(sqrt.f64 (-.f64 (*.f64 x x) eps))
(- (* x x) eps)
(-.f64 (*.f64 x x) eps)
(* x x)
(*.f64 x x)
eps

localize29.0ms (0.3%)

Memory

-14.8MiB live, 63.3MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(*.f64 x x)
✓	accuracy	100.0%	(-.f64 (*.f64 x x) eps)
✓	accuracy	100.0%	(sqrt.f64 (-.f64 (*.f64 x x) eps))
✓	accuracy	60.4%	(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))

Samples

11.0ms	86×	1	valid
8.0ms	150×	0	valid
3.0ms	20×	2	valid

Compiler

Compiled 26 to 8 computations (69.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 12.0ms

ival-sub: 4.0ms (34.6% of total)

ival-sqrt: 3.0ms (26% of total)

ival-mult: 3.0ms (26% of total)

adjust: 2.0ms (17.3% of total)

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

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

series8.0ms (0.1%)

Memory

18.4MiB live, 18.4MiB allocated

Counts

4 → 84

Calls

Call 1

Inputs
#<alt (- x (sqrt (- (* x x) eps)))>
#<alt (sqrt (- (* x x) eps))>
#<alt (- (* x x) eps)>
#<alt (* x x)>

Outputs
#<alt (* -1 (* (sqrt eps) (sqrt -1)))>
#<alt (- x (* (sqrt eps) (sqrt -1)))>
#<alt (- (* x (+ 1 (* -1/2 (* (sqrt (/ 1 eps)) (/ x (sqrt -1)))))) (* (sqrt eps) (sqrt -1)))>
#<alt (- (* x (+ 1 (* x (- (* 1/8 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))))))) (* (sqrt eps) (sqrt -1)))>
#<alt (* 1/2 (/ eps x))>
#<alt (/ (- (* 1/8 (/ (pow eps 2) (pow x 2))) (* -1/2 eps)) x)>
#<alt (/ (- (* 1/16 (/ (pow eps 3) (pow x 4))) (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2))))) x)>
#<alt (/ (- (* 1/2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) (pow x 6))) (+ (* -1/2 eps) (+ (* -1/8 (/ (pow eps 2) (pow x 2))) (* -1/16 (/ (pow eps 3) (pow x 4)))))) x)>
#<alt (* 2 x)>
#<alt (* -1 (* x (- (* 1/2 (/ eps (pow x 2))) 2)))>
#<alt (* -1 (* x (- (* 1/8 (/ (pow eps 2) (pow x 4))) (+ 2 (* -1/2 (/ eps (pow x 2)))))))>
#<alt (* -1 (* x (- (* 1/16 (/ (pow eps 3) (pow x 6))) (+ 2 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4))))))))>
#<alt (* 1/2 (/ eps x))>
#<alt (* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))>
#<alt (* eps (+ (* eps (+ (* 1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))>
#<alt (* eps (+ (* eps (+ (* eps (+ (* 5/128 (/ eps (pow x 7))) (* 1/16 (/ 1 (pow x 5))))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))>
#<alt (* -1 (* (sqrt eps) (sqrt -1)))>
#<alt (* eps (- (/ x eps) (* (sqrt (/ 1 eps)) (sqrt -1))))>
#<alt (* eps (- (+ (* -1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1))))>
#<alt (* eps (- (+ (* 1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (/ x eps)) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))>
#<alt (* (sqrt eps) (sqrt -1))>
#<alt (* -1 (* eps (- (* -1 (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))>
#<alt (* -1 (* eps (- (* -1 (/ (+ x (* 1/2 (* (sqrt (/ 1 eps)) (* (pow x 2) (sqrt -1))))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))>
#<alt (* -1 (* eps (- (* -1 (/ (+ x (* -1 (/ (- (* 1/8 (* (sqrt (/ 1 eps)) (* (pow x 4) (sqrt -1)))) (* 1/2 (* (sqrt eps) (* (pow x 2) (sqrt -1))))) eps))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))>
#<alt (* (sqrt eps) (sqrt -1))>
#<alt (+ (* 1/2 (* (sqrt (/ 1 eps)) (/ (pow x 2) (sqrt -1)))) (* (sqrt eps) (sqrt -1)))>
#<alt (+ (* (sqrt eps) (sqrt -1)) (* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))))))>
#<alt (+ (* (sqrt eps) (sqrt -1)) (* (pow x 2) (+ (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))) (* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3)))) (* 1/16 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 2) (pow (sqrt -1) 5)))))))))>
#<alt x>
#<alt (* x (+ 1 (* -1/2 (/ eps (pow x 2)))))>
#<alt (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4))))))>
#<alt (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/8 (/ (pow eps 2) (pow x 4))) (* -1/16 (/ (pow eps 3) (pow x 6)))))))>
#<alt (* -1 x)>
#<alt (* -1 (* x (+ 1 (* -1/2 (/ eps (pow x 2))))))>
#<alt (* -1 (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4)))))))>
#<alt (* -1 (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/8 (/ (pow eps 2) (pow x 4))) (* -1/16 (/ (pow eps 3) (pow x 6))))))))>
#<alt x>
#<alt (+ x (* -1/2 (/ eps x)))>
#<alt (+ x (* eps (- (* -1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))))>
#<alt (+ x (* eps (- (* eps (- (* -1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))))>
#<alt (* (sqrt eps) (sqrt -1))>
#<alt (* eps (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))>
#<alt (* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))>
#<alt (* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow eps 7))) (/ (pow x 6) (pow (sqrt -1) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))))>
#<alt (* -1 (* (sqrt eps) (sqrt -1)))>
#<alt (* -1 (* eps (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))>
#<alt (* -1 (* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (* (pow x 4) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))))>
#<alt (* -1 (* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (* (pow x 4) (sqrt -1)))) (+ (* 1/16 (* (sqrt (/ 1 (pow eps 7))) (* (pow x 6) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))))>
#<alt (* -1 eps)>
#<alt (- (pow x 2) eps)>
#<alt (- (pow x 2) eps)>
#<alt (- (pow x 2) eps)>
#<alt (pow x 2)>
#<alt (* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))>
#<alt (* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))>
#<alt (* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))>
#<alt (pow x 2)>
#<alt (* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))>
#<alt (* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))>
#<alt (* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))>
#<alt (pow x 2)>
#<alt (+ (* -1 eps) (pow x 2))>
#<alt (+ (* -1 eps) (pow x 2))>
#<alt (+ (* -1 eps) (pow x 2))>
#<alt (* -1 eps)>
#<alt (* eps (- (/ (pow x 2) eps) 1))>
#<alt (* eps (- (/ (pow x 2) eps) 1))>
#<alt (* eps (- (/ (pow x 2) eps) 1))>
#<alt (* -1 eps)>
#<alt (* -1 (* eps (+ 1 (* -1 (/ (pow x 2) eps)))))>
#<alt (* -1 (* eps (+ 1 (* -1 (/ (pow x 2) eps)))))>
#<alt (* -1 (* eps (+ 1 (* -1 (/ (pow x 2) eps)))))>
#<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

21 calls:

Time	Variable		Point	Expression
1.0ms	x	@	inf	(- x (sqrt (- (* x x) eps)))
1.0ms	eps	@	inf	(- x (sqrt (- (* x x) eps)))
1.0ms	eps	@	0	(- x (sqrt (- (* x x) eps)))
1.0ms	x	@	0	(- x (sqrt (- (* x x) eps)))
1.0ms	eps	@	-inf	(- x (sqrt (- (* x x) eps)))

rewrite386.0ms (3.8%)

Memory

-7.6MiB live, 384.8MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

4 146×	`accelerator-lowering-fma.f32`
4 146×	`accelerator-lowering-fma.f64`
3 310×	`-lowering-.f32`
3 310×	`-lowering-.f64`
2 470×	`pow-lowering-pow.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	22
1	38	22
2	306	22
3	3595	22
0	8551	22

Stop Event

1×	iter limit
1×	node limit

Counts

4 → 224

Calls

Call 1

Inputs
(- x (sqrt (- (* x x) eps)))
(sqrt (- (* x x) eps))
(- (* x x) eps)
(* x x)

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

simplify716.0ms (7.1%)

Memory

13.7MiB live, 684.5MiB allocated

Algorithm

1×	egg-herbie

Rules

11 222×	`accelerator-lowering-fma.f32`
11 222×	`accelerator-lowering-fma.f64`
4 906×	`-lowering-.f32`
4 906×	`-lowering-.f64`
3 416×	`+-lowering-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	257	1257
1	784	1238
2	2594	1200
3	6944	1197
0	8091	1129

Stop Event

1×	iter limit
1×	node limit

Counts

84 → 84

Calls

Call 1

Inputs
(* -1 (* (sqrt eps) (sqrt -1)))
(- x (* (sqrt eps) (sqrt -1)))
(- (* x (+ 1 (* -1/2 (* (sqrt (/ 1 eps)) (/ x (sqrt -1)))))) (* (sqrt eps) (sqrt -1)))
(- (* x (+ 1 (* x (- (* 1/8 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))))))) (* (sqrt eps) (sqrt -1)))
(* 1/2 (/ eps x))
(/ (- (* 1/8 (/ (pow eps 2) (pow x 2))) (* -1/2 eps)) x)
(/ (- (* 1/16 (/ (pow eps 3) (pow x 4))) (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2))))) x)
(/ (- (* 1/2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) (pow x 6))) (+ (* -1/2 eps) (+ (* -1/8 (/ (pow eps 2) (pow x 2))) (* -1/16 (/ (pow eps 3) (pow x 4)))))) x)
(* 2 x)
(* -1 (* x (- (* 1/2 (/ eps (pow x 2))) 2)))
(* -1 (* x (- (* 1/8 (/ (pow eps 2) (pow x 4))) (+ 2 (* -1/2 (/ eps (pow x 2)))))))
(* -1 (* x (- (* 1/16 (/ (pow eps 3) (pow x 6))) (+ 2 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4))))))))
(* 1/2 (/ eps x))
(* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))
(* eps (+ (* eps (+ (* 1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))
(* eps (+ (* eps (+ (* eps (+ (* 5/128 (/ eps (pow x 7))) (* 1/16 (/ 1 (pow x 5))))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))
(* -1 (* (sqrt eps) (sqrt -1)))
(* eps (- (/ x eps) (* (sqrt (/ 1 eps)) (sqrt -1))))
(* eps (- (+ (* -1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1))))
(* eps (- (+ (* 1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (/ x eps)) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* (sqrt eps) (sqrt -1))
(* -1 (* eps (- (* -1 (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* -1 (* eps (- (* -1 (/ (+ x (* 1/2 (* (sqrt (/ 1 eps)) (* (pow x 2) (sqrt -1))))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* -1 (* eps (- (* -1 (/ (+ x (* -1 (/ (- (* 1/8 (* (sqrt (/ 1 eps)) (* (pow x 4) (sqrt -1)))) (* 1/2 (* (sqrt eps) (* (pow x 2) (sqrt -1))))) eps))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* (sqrt eps) (sqrt -1))
(+ (* 1/2 (* (sqrt (/ 1 eps)) (/ (pow x 2) (sqrt -1)))) (* (sqrt eps) (sqrt -1)))
(+ (* (sqrt eps) (sqrt -1)) (* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))))))
(+ (* (sqrt eps) (sqrt -1)) (* (pow x 2) (+ (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))) (* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3)))) (* 1/16 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 2) (pow (sqrt -1) 5)))))))))
x
(* x (+ 1 (* -1/2 (/ eps (pow x 2)))))
(* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4))))))
(* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/8 (/ (pow eps 2) (pow x 4))) (* -1/16 (/ (pow eps 3) (pow x 6)))))))
(* -1 x)
(* -1 (* x (+ 1 (* -1/2 (/ eps (pow x 2))))))
(* -1 (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4)))))))
(* -1 (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/8 (/ (pow eps 2) (pow x 4))) (* -1/16 (/ (pow eps 3) (pow x 6))))))))
x
(+ x (* -1/2 (/ eps x)))
(+ x (* eps (- (* -1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))))
(+ x (* eps (- (* eps (- (* -1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))))
(* (sqrt eps) (sqrt -1))
(* eps (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))
(* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow eps 7))) (/ (pow x 6) (pow (sqrt -1) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))))
(* -1 (* (sqrt eps) (sqrt -1)))
(* -1 (* eps (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* -1 (* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (* (pow x 4) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))))
(* -1 (* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (* (pow x 4) (sqrt -1)))) (+ (* 1/16 (* (sqrt (/ 1 (pow eps 7))) (* (pow x 6) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))))
(* -1 eps)
(- (pow x 2) eps)
(- (pow x 2) eps)
(- (pow x 2) eps)
(pow x 2)
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))
(pow x 2)
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))
(pow x 2)
(+ (* -1 eps) (pow x 2))
(+ (* -1 eps) (pow x 2))
(+ (* -1 eps) (pow x 2))
(* -1 eps)
(* eps (- (/ (pow x 2) eps) 1))
(* eps (- (/ (pow x 2) eps) 1))
(* eps (- (/ (pow x 2) eps) 1))
(* -1 eps)
(* -1 (* eps (+ 1 (* -1 (/ (pow x 2) eps)))))
(* -1 (* eps (+ 1 (* -1 (/ (pow x 2) eps)))))
(* -1 (* eps (+ 1 (* -1 (/ (pow x 2) eps)))))
(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 (* (sqrt eps) (sqrt -1)))
(*.f64 (sqrt.f64 eps) (neg.f64 (sqrt.f64 #s(literal -1 binary64))))
(- x (* (sqrt eps) (sqrt -1)))
(fma.f64 (sqrt.f64 eps) (neg.f64 (sqrt.f64 #s(literal -1 binary64))) x)
(- (* x (+ 1 (* -1/2 (* (sqrt (/ 1 eps)) (/ x (sqrt -1)))))) (* (sqrt eps) (sqrt -1)))
(-.f64 (fma.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (/.f64 x (sqrt.f64 #s(literal -1 binary64)))) (.f64 #s(literal -1/2 binary64) x) x) (*.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64))))
(- (* x (+ 1 (* x (- (* 1/8 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))))))) (* (sqrt eps) (sqrt -1)))
(-.f64 (fma.f64 (.f64 x x) (fma.f64 #s(literal -1/2 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64))) (.f64 #s(literal -1/8 binary64) (/.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 eps (.f64 eps eps)))) (.f64 x x)) (sqrt.f64 #s(literal -1 binary64))))) x) (*.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64))))
(* 1/2 (/ eps x))
(/.f64 (*.f64 eps #s(literal 1/2 binary64)) x)
(/ (- (* 1/8 (/ (pow eps 2) (pow x 2))) (* -1/2 eps)) x)
(/.f64 (fma.f64 eps #s(literal 1/2 binary64) (/.f64 (.f64 #s(literal 1/8 binary64) (.f64 eps eps)) (*.f64 x x))) x)
(/ (- (* 1/16 (/ (pow eps 3) (pow x 4))) (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2))))) x)
(/.f64 (fma.f64 #s(literal 1/8 binary64) (/.f64 (.f64 eps eps) (.f64 x x)) (fma.f64 (.f64 eps (.f64 eps eps)) (/.f64 #s(literal 1/16 binary64) (.f64 (.f64 x x) (.f64 x x))) (.f64 eps #s(literal 1/2 binary64)))) x)
(/ (- (* 1/2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) (pow x 6))) (+ (* -1/2 eps) (+ (* -1/8 (/ (pow eps 2) (pow x 2))) (* -1/16 (/ (pow eps 3) (pow x 4)))))) x)
(/.f64 (fma.f64 #s(literal 1/2 binary64) (fma.f64 (pow.f64 eps #s(literal 4 binary64)) (/.f64 #s(literal 5/64 binary64) (pow.f64 x #s(literal 6 binary64))) eps) (fma.f64 #s(literal 1/8 binary64) (/.f64 (.f64 eps eps) (.f64 x x)) (/.f64 (.f64 (.f64 eps (.f64 eps eps)) #s(literal 1/16 binary64)) (.f64 (.f64 x x) (.f64 x x))))) x)
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* -1 (* x (- (* 1/2 (/ eps (pow x 2))) 2)))
(.f64 x (fma.f64 eps (/.f64 #s(literal -1/2 binary64) (.f64 x x)) #s(literal 2 binary64)))
(* -1 (* x (- (* 1/8 (/ (pow eps 2) (pow x 4))) (+ 2 (* -1/2 (/ eps (pow x 2)))))))
(.f64 (neg.f64 x) (fma.f64 eps (/.f64 #s(literal 1/2 binary64) (.f64 x x)) (fma.f64 (.f64 eps #s(literal 1/8 binary64)) (/.f64 eps (.f64 (.f64 x x) (.f64 x x))) #s(literal -2 binary64))))
(* -1 (* x (- (* 1/16 (/ (pow eps 3) (pow x 6))) (+ 2 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4))))))))
(.f64 (fma.f64 (.f64 eps (.f64 eps eps)) (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 6 binary64))) (fma.f64 eps (/.f64 #s(literal 1/2 binary64) (.f64 x x)) (fma.f64 (.f64 eps #s(literal 1/8 binary64)) (/.f64 eps (.f64 (.f64 x x) (.f64 x x))) #s(literal -2 binary64)))) (neg.f64 x))
(* 1/2 (/ eps x))
(/.f64 (*.f64 eps #s(literal 1/2 binary64)) x)
(* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))
(/.f64 (fma.f64 eps #s(literal 1/2 binary64) (/.f64 (.f64 #s(literal 1/8 binary64) (.f64 eps eps)) (*.f64 x x))) x)
(* eps (+ (* eps (+ (* 1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))
(.f64 eps (fma.f64 eps (fma.f64 eps (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 5 binary64))) (/.f64 #s(literal 1/8 binary64) (.f64 x (*.f64 x x)))) (/.f64 #s(literal 1/2 binary64) x)))
(* eps (+ (* eps (+ (* eps (+ (* 5/128 (/ eps (pow x 7))) (* 1/16 (/ 1 (pow x 5))))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))
(.f64 eps (fma.f64 eps (fma.f64 eps (fma.f64 eps (/.f64 #s(literal 5/128 binary64) (pow.f64 x #s(literal 7 binary64))) (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 5 binary64)))) (/.f64 #s(literal 1/8 binary64) (.f64 x (*.f64 x x)))) (/.f64 #s(literal 1/2 binary64) x)))
(* -1 (* (sqrt eps) (sqrt -1)))
(*.f64 (sqrt.f64 eps) (neg.f64 (sqrt.f64 #s(literal -1 binary64))))
(* eps (- (/ x eps) (* (sqrt (/ 1 eps)) (sqrt -1))))
(.f64 eps (-.f64 (/.f64 x eps) (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)))))
(* eps (- (+ (* -1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1))))
(.f64 eps (-.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 eps (.f64 eps eps)))) (/.f64 (.f64 (.f64 x x) #s(literal -1/2 binary64)) (sqrt.f64 #s(literal -1 binary64))) (/.f64 x eps)) (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)))))
(* eps (- (+ (* 1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (/ x eps)) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(.f64 eps (fma.f64 #s(literal -1/8 binary64) (.f64 (.f64 (.f64 x x) (.f64 x x)) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 5 binary64)))) (sqrt.f64 #s(literal -1 binary64)))) (-.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 eps (.f64 eps eps)))) (/.f64 (.f64 (.f64 x x) #s(literal -1/2 binary64)) (sqrt.f64 #s(literal -1 binary64))) (/.f64 x eps)) (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))))))
(* (sqrt eps) (sqrt -1))
(*.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64)))
(* -1 (* eps (- (* -1 (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(*.f64 eps (fma.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (/.f64 x eps)))
(* -1 (* eps (- (* -1 (/ (+ x (* 1/2 (* (sqrt (/ 1 eps)) (* (pow x 2) (sqrt -1))))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(.f64 eps (fma.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (/.f64 (fma.f64 #s(literal 1/2 binary64) (.f64 (sqrt.f64 #s(literal -1 binary64)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (.f64 x x))) x) eps)))
(* -1 (* eps (- (* -1 (/ (+ x (* -1 (/ (- (* 1/8 (* (sqrt (/ 1 eps)) (* (pow x 4) (sqrt -1)))) (* 1/2 (* (sqrt eps) (* (pow x 2) (sqrt -1))))) eps))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(.f64 eps (fma.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (/.f64 (-.f64 x (/.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) (fma.f64 #s(literal 1/8 binary64) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (.f64 (.f64 x x) (.f64 x x))) (.f64 #s(literal -1/2 binary64) (.f64 (sqrt.f64 eps) (*.f64 x x))))) eps)) eps)))
(* (sqrt eps) (sqrt -1))
(*.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64)))
(+ (* 1/2 (* (sqrt (/ 1 eps)) (/ (pow x 2) (sqrt -1)))) (* (sqrt eps) (sqrt -1)))
(fma.f64 (.f64 x x) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64)))) (*.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64))))
(+ (* (sqrt eps) (sqrt -1)) (* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))))))
(fma.f64 (.f64 x x) (fma.f64 #s(literal 1/8 binary64) (/.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 eps (.f64 eps eps)))) (.f64 x x)) (sqrt.f64 #s(literal -1 binary64))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64))))) (*.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64))))
(+ (* (sqrt eps) (sqrt -1)) (* (pow x 2) (+ (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))) (* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3)))) (* 1/16 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 2) (pow (sqrt -1) 5)))))))))
(fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 eps (.f64 eps eps)))) (/.f64 #s(literal 1/8 binary64) (sqrt.f64 #s(literal -1 binary64))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 5 binary64)))) (/.f64 (.f64 (.f64 x x) #s(literal 1/16 binary64)) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64))))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64))))) (*.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64))))
x
(* x (+ 1 (* -1/2 (/ eps (pow x 2)))))
(fma.f64 (.f64 eps #s(literal -1/2 binary64)) (/.f64 x (.f64 x x)) x)
(* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4))))))
(fma.f64 x (fma.f64 (.f64 eps #s(literal -1/8 binary64)) (/.f64 eps (.f64 (.f64 x x) (.f64 x x))) (/.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 x x))) x)
(* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/8 (/ (pow eps 2) (pow x 4))) (* -1/16 (/ (pow eps 3) (pow x 6)))))))
(fma.f64 x (fma.f64 (.f64 eps (.f64 eps eps)) (/.f64 #s(literal -1/16 binary64) (pow.f64 x #s(literal 6 binary64))) (fma.f64 (.f64 eps #s(literal -1/8 binary64)) (/.f64 eps (.f64 (.f64 x x) (.f64 x x))) (/.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 x x)))) x)
(* -1 x)
(neg.f64 x)
(* -1 (* x (+ 1 (* -1/2 (/ eps (pow x 2))))))
(.f64 x (fma.f64 eps (/.f64 #s(literal 1/2 binary64) (.f64 x x)) #s(literal -1 binary64)))
(* -1 (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4)))))))
(.f64 x (fma.f64 #s(literal 1/8 binary64) (/.f64 (.f64 eps eps) (.f64 (.f64 x x) (.f64 x x))) (fma.f64 eps (/.f64 #s(literal 1/2 binary64) (.f64 x x)) #s(literal -1 binary64))))
(* -1 (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/8 (/ (pow eps 2) (pow x 4))) (* -1/16 (/ (pow eps 3) (pow x 6))))))))
(neg.f64 (fma.f64 x (fma.f64 (.f64 eps (.f64 eps eps)) (/.f64 #s(literal -1/16 binary64) (pow.f64 x #s(literal 6 binary64))) (fma.f64 (.f64 eps #s(literal -1/8 binary64)) (/.f64 eps (.f64 (.f64 x x) (.f64 x x))) (/.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 x x)))) x))
x
(+ x (* -1/2 (/ eps x)))
(fma.f64 eps (/.f64 #s(literal -1/2 binary64) x) x)
(+ x (* eps (- (* -1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))))
(fma.f64 eps (fma.f64 eps (/.f64 #s(literal -1/8 binary64) (.f64 x (.f64 x x))) (/.f64 #s(literal -1/2 binary64) x)) x)
(+ x (* eps (- (* eps (- (* -1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))))
(fma.f64 eps (fma.f64 eps (fma.f64 eps (/.f64 #s(literal -1/16 binary64) (pow.f64 x #s(literal 5 binary64))) (/.f64 #s(literal -1/8 binary64) (.f64 x (.f64 x x)))) (/.f64 #s(literal -1/2 binary64) x)) x)
(* (sqrt eps) (sqrt -1))
(*.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64)))
(* eps (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))
(.f64 eps (fma.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (/.f64 (.f64 #s(literal 1/2 binary64) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 eps (.f64 eps eps)))) (.f64 x x))) (sqrt.f64 #s(literal -1 binary64)))))
(* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(.f64 eps (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 eps (.f64 eps eps)))) (/.f64 (.f64 (.f64 x x) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal -1 binary64))) (fma.f64 #s(literal 1/8 binary64) (.f64 (.f64 (.f64 x x) (.f64 x x)) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 5 binary64)))) (sqrt.f64 #s(literal -1 binary64)))) (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))))))
(* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow eps 7))) (/ (pow x 6) (pow (sqrt -1) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))))
(.f64 eps (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 eps (.f64 eps eps)))) (/.f64 (.f64 (.f64 x x) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal -1 binary64))) (fma.f64 #s(literal 1/16 binary64) (/.f64 (.f64 (pow.f64 x #s(literal 6 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 7 binary64))))) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64))) (fma.f64 #s(literal 1/8 binary64) (.f64 (.f64 (.f64 x x) (.f64 x x)) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 5 binary64)))) (sqrt.f64 #s(literal -1 binary64)))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)))))))
(* -1 (* (sqrt eps) (sqrt -1)))
(*.f64 (sqrt.f64 eps) (neg.f64 (sqrt.f64 #s(literal -1 binary64))))
(* -1 (* eps (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(neg.f64 (.f64 eps (.f64 (sqrt.f64 #s(literal -1 binary64)) (fma.f64 #s(literal 1/2 binary64) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 eps (.f64 eps eps)))) (.f64 x x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))))))
(* -1 (* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (* (pow x 4) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))))
(.f64 (fma.f64 (sqrt.f64 #s(literal -1 binary64)) (fma.f64 #s(literal -1/8 binary64) (.f64 (.f64 (.f64 x x) (.f64 x x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 5 binary64))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))) (.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 eps (.f64 eps eps)))) (.f64 x x)) (*.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 1/2 binary64)))) (neg.f64 eps))
(* -1 (* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (* (pow x 4) (sqrt -1)))) (+ (* 1/16 (* (sqrt (/ 1 (pow eps 7))) (* (pow x 6) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))))
(neg.f64 (.f64 eps (fma.f64 (sqrt.f64 #s(literal -1 binary64)) (fma.f64 (.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 5 binary64))))) (.f64 (.f64 x x) (.f64 x x)) (.f64 #s(literal 1/16 binary64) (.f64 (pow.f64 x #s(literal 6 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 7 binary64))))))) (.f64 (sqrt.f64 #s(literal -1 binary64)) (fma.f64 #s(literal 1/2 binary64) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 eps (.f64 eps eps)))) (.f64 x x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)))))))
(* -1 eps)
(neg.f64 eps)
(- (pow x 2) eps)
(-.f64 (*.f64 x x) eps)
(- (pow x 2) eps)
(-.f64 (*.f64 x x) eps)
(- (pow x 2) eps)
(-.f64 (*.f64 x x) eps)
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))
(.f64 x (fma.f64 x (/.f64 eps (.f64 x (neg.f64 x))) x))
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))
(.f64 x (fma.f64 x (/.f64 eps (.f64 x (neg.f64 x))) x))
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))
(.f64 x (fma.f64 x (/.f64 eps (.f64 x (neg.f64 x))) x))
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))
(.f64 x (fma.f64 x (/.f64 eps (.f64 x (neg.f64 x))) x))
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))
(.f64 x (fma.f64 x (/.f64 eps (.f64 x (neg.f64 x))) x))
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))
(.f64 x (fma.f64 x (/.f64 eps (.f64 x (neg.f64 x))) x))
(pow x 2)
(*.f64 x x)
(+ (* -1 eps) (pow x 2))
(-.f64 (*.f64 x x) eps)
(+ (* -1 eps) (pow x 2))
(-.f64 (*.f64 x x) eps)
(+ (* -1 eps) (pow x 2))
(-.f64 (*.f64 x x) eps)
(* -1 eps)
(neg.f64 eps)
(* eps (- (/ (pow x 2) eps) 1))
(*.f64 eps (fma.f64 x (/.f64 x eps) #s(literal -1 binary64)))
(* eps (- (/ (pow x 2) eps) 1))
(*.f64 eps (fma.f64 x (/.f64 x eps) #s(literal -1 binary64)))
(* eps (- (/ (pow x 2) eps) 1))
(*.f64 eps (fma.f64 x (/.f64 x eps) #s(literal -1 binary64)))
(* -1 eps)
(neg.f64 eps)
(* -1 (* eps (+ 1 (* -1 (/ (pow x 2) eps)))))
(*.f64 eps (fma.f64 x (/.f64 x eps) #s(literal -1 binary64)))
(* -1 (* eps (+ 1 (* -1 (/ (pow x 2) eps)))))
(*.f64 eps (fma.f64 x (/.f64 x eps) #s(literal -1 binary64)))
(* -1 (* eps (+ 1 (* -1 (/ (pow x 2) eps)))))
(*.f64 eps (fma.f64 x (/.f64 x eps) #s(literal -1 binary64)))
(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)

eval67.0ms (0.7%)

Memory: 5.1MiB live, 80.0MiB allocated
Compiler: Compiled 9 601 to 1 050 computations (89.1% saved)

prune80.0ms (0.8%)

Memory

-34.0MiB live, 87.6MiB allocated

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	294	14	308
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	295	14	309

Accuracy

99.6%

Counts

309 → 14

Alt Table

Click to see full alt table

Status	Accuracy	Program
	59.6%	(fma.f64 (sqrt.f64 (sqrt.f64 (-.f64 (.f64 x x) eps))) (neg.f64 (sqrt.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)))) x)
▶	60.2%	(fma.f64 (sqrt.f64 x) (sqrt.f64 x) (neg.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps))))
	43.0%	(/.f64 (fma.f64 eps #s(literal 1/2 binary64) (/.f64 (.f64 #s(literal 1/8 binary64) (.f64 eps eps)) (*.f64 x x))) x)
	33.6%	(/.f64 (fma.f64 #s(literal 1/8 binary64) (/.f64 (.f64 eps eps) (.f64 x x)) (fma.f64 (.f64 eps (.f64 eps eps)) (/.f64 #s(literal 1/16 binary64) (.f64 (.f64 x x) (.f64 x x))) (.f64 eps #s(literal 1/2 binary64)))) x)
	60.0%	(/.f64 (-.f64 (fma.f64 x x eps) (.f64 x x)) (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))))
▶	45.6%	(/.f64 (*.f64 eps #s(literal 1/2 binary64)) x)
▶	60.3%	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))))
	6.7%	(-.f64 x (fma.f64 eps (/.f64 #s(literal -1/2 binary64) x) x))
	60.0%	(-.f64 x (/.f64 (-.f64 (.f64 x x) eps) (sqrt.f64 (-.f64 (.f64 x x) eps))))
▶	60.4%	(-.f64 x (sqrt.f64 (fma.f64 x x (neg.f64 eps))))
	56.2%	(-.f64 x (sqrt.f64 (neg.f64 eps)))
	3.7%	(-.f64 x (neg.f64 x))
▶	4.3%	(-.f64 x x)
	31.0%	(.f64 eps (fma.f64 eps (fma.f64 eps (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 5 binary64))) (/.f64 #s(literal 1/8 binary64) (.f64 x (*.f64 x x)))) (/.f64 #s(literal 1/2 binary64) x)))

Compiler

Compiled 394 to 220 computations (44.2% saved)

simplify67.0ms (0.7%)

Memory

3.4MiB live, 78.6MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 15 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(sqrt.f64 (-.f64 (*.f64 x x) eps))
✓	cost-diff	0	(neg.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)))
✓	cost-diff	0	(sqrt.f64 x)
✓	cost-diff	1600	(fma.f64 (sqrt.f64 x) (sqrt.f64 x) (neg.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps))))
✓	cost-diff	0	(sqrt.f64 (-.f64 (*.f64 x x) eps))
✓	cost-diff	0	(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
✓	cost-diff	0	(/.f64 #s(literal 1 binary64) (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))
✓	cost-diff	1408	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))))
✓	cost-diff	0	(*.f64 eps #s(literal 1/2 binary64))
✓	cost-diff	0	(/.f64 (*.f64 eps #s(literal 1/2 binary64)) x)
✓	cost-diff	192	(-.f64 x x)
✓	cost-diff	0	(neg.f64 eps)
✓	cost-diff	0	(fma.f64 x x (neg.f64 eps))
✓	cost-diff	0	(sqrt.f64 (fma.f64 x x (neg.f64 eps)))
✓	cost-diff	0	(-.f64 x (sqrt.f64 (fma.f64 x x (neg.f64 eps))))

Rules

680×	`accelerator-lowering-fma.f32`
680×	`accelerator-lowering-fma.f64`
584×	`-lowering-.f32`
584×	`-lowering-.f64`
286×	`times-frac`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	112
1	40	112
2	83	112
3	140	112
4	247	112
5	397	112
6	548	112
7	836	112
8	1129	112
9	1438	112
10	1485	112
11	1534	112
12	1566	112
13	1566	112
0	1566	112

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

Inputs
(- x (sqrt (+ (* x x) (neg eps))))
x
(sqrt (+ (* x x) (neg eps)))
(+ (* x x) (neg eps))
(neg eps)
eps
(- x x)
x
(/ (* eps 1/2) x)
(* eps 1/2)
eps
1/2
x
(/ 1 (/ 1 (- x (sqrt (- (* x x) eps)))))
1
(/ 1 (- x (sqrt (- (* x x) eps))))
(- x (sqrt (- (* x x) eps)))
x
(sqrt (- (* x x) eps))
(- (* x x) eps)
(* x x)
eps
(+ (* (sqrt x) (sqrt x)) (neg (sqrt (- (* x x) eps))))
(sqrt x)
x
(neg (sqrt (- (* x x) eps)))
(sqrt (- (* x x) eps))
(- (* x x) eps)
(* x x)
eps

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

localize98.0ms (1%)

Memory

-14.9MiB live, 223.4MiB allocated

Localize:

Found 15 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(neg.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)))
✓	accuracy	100.0%	(-.f64 (*.f64 x x) eps)
✓	accuracy	100.0%	(sqrt.f64 (-.f64 (*.f64 x x) eps))
✓	accuracy	60.2%	(fma.f64 (sqrt.f64 x) (sqrt.f64 x) (neg.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps))))
✓	accuracy	100.0%	(sqrt.f64 (-.f64 (*.f64 x x) eps))
✓	accuracy	99.6%	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))))
✓	accuracy	99.6%	(/.f64 #s(literal 1 binary64) (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))
✓	accuracy	60.4%	(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
✓	accuracy	100.0%	(/.f64 (*.f64 eps #s(literal 1/2 binary64)) x)
✓	accuracy	100.0%	(*.f64 eps #s(literal 1/2 binary64))
✓	accuracy	100.0%	(-.f64 x x)
✓	accuracy	100.0%	(fma.f64 x x (neg.f64 eps))
✓	accuracy	100.0%	(neg.f64 eps)
✓	accuracy	100.0%	(sqrt.f64 (fma.f64 x x (neg.f64 eps)))
✓	accuracy	60.4%	(-.f64 x (sqrt.f64 (fma.f64 x x (neg.f64 eps))))

Samples

30.0ms	86×	1	valid
28.0ms	150×	0	valid
6.0ms	14×	2	valid
4.0ms	5×	3	valid
1.0ms	1×	4	valid

Compiler

Compiled 124 to 23 computations (81.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 48.0ms

ival-mult: 13.0ms (27.2% of total)

ival-div: 9.0ms (18.8% of total)

ival-sqrt: 8.0ms (16.7% of total)

ival-sub: 7.0ms (14.6% of total)

ival-add: 4.0ms (8.4% of total)

adjust: 3.0ms (6.3% of total)

ival-neg: 3.0ms (6.3% of total)

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

exact: 0.0ms (0% of total)

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

series19.0ms (0.2%)

Memory

6.1MiB live, 44.6MiB allocated

Counts

15 → 312

Calls

Call 1

Inputs
#<alt (- x (sqrt (+ (* x x) (neg eps))))>
#<alt (sqrt (+ (* x x) (neg eps)))>
#<alt (+ (* x x) (neg eps))>
#<alt (neg eps)>
#<alt (- x x)>
#<alt (/ (* eps 1/2) x)>
#<alt (* eps 1/2)>
#<alt (/ 1 (/ 1 (- x (sqrt (- (* x x) eps)))))>
#<alt (/ 1 (- x (sqrt (- (* x x) eps))))>
#<alt (- x (sqrt (- (* x x) eps)))>
#<alt (sqrt (- (* x x) eps))>
#<alt (+ (* (sqrt x) (sqrt x)) (neg (sqrt (- (* x x) eps))))>
#<alt (sqrt x)>
#<alt (neg (sqrt (- (* x x) eps)))>
#<alt (- (* x x) eps)>

Outputs
#<alt (* -1 (* (sqrt eps) (sqrt -1)))>
#<alt (- x (* (sqrt eps) (sqrt -1)))>
#<alt (- (* x (+ 1 (* -1/2 (* (sqrt (/ 1 eps)) (/ x (sqrt -1)))))) (* (sqrt eps) (sqrt -1)))>
#<alt (- (* x (+ 1 (* x (- (* 1/8 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))))))) (* (sqrt eps) (sqrt -1)))>
#<alt (* 1/2 (/ eps x))>
#<alt (/ (- (* 1/8 (/ (pow eps 2) (pow x 2))) (* -1/2 eps)) x)>
#<alt (/ (- (* 1/16 (/ (pow eps 3) (pow x 4))) (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2))))) x)>
#<alt (/ (- (* 1/2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) (pow x 6))) (+ (* -1/2 eps) (+ (* -1/8 (/ (pow eps 2) (pow x 2))) (* -1/16 (/ (pow eps 3) (pow x 4)))))) x)>
#<alt (* 2 x)>
#<alt (* -1 (* x (- (* 1/2 (/ eps (pow x 2))) 2)))>
#<alt (* -1 (* x (- (* 1/8 (/ (pow eps 2) (pow x 4))) (+ 2 (* -1/2 (/ eps (pow x 2)))))))>
#<alt (* -1 (* x (- (* 1/16 (/ (pow eps 3) (pow x 6))) (+ 2 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4))))))))>
#<alt (* 1/2 (/ eps x))>
#<alt (* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))>
#<alt (* eps (+ (* eps (+ (* 1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))>
#<alt (* eps (+ (* eps (+ (* eps (+ (* 5/128 (/ eps (pow x 7))) (* 1/16 (/ 1 (pow x 5))))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))>
#<alt (* -1 (* (sqrt eps) (sqrt -1)))>
#<alt (* eps (- (/ x eps) (* (sqrt (/ 1 eps)) (sqrt -1))))>
#<alt (* eps (- (+ (* -1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1))))>
#<alt (* eps (- (+ (* 1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (/ x eps)) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))>
#<alt (* (sqrt eps) (sqrt -1))>
#<alt (* -1 (* eps (- (* -1 (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))>
#<alt (* -1 (* eps (- (* -1 (/ (+ x (* 1/2 (* (sqrt (/ 1 eps)) (* (pow x 2) (sqrt -1))))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))>
#<alt (* -1 (* eps (- (* -1 (/ (+ x (* -1 (/ (- (* 1/8 (* (sqrt (/ 1 eps)) (* (pow x 4) (sqrt -1)))) (* 1/2 (* (sqrt eps) (* (pow x 2) (sqrt -1))))) eps))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))>
#<alt (* (sqrt eps) (sqrt -1))>
#<alt (+ (* 1/2 (* (sqrt (/ 1 eps)) (/ (pow x 2) (sqrt -1)))) (* (sqrt eps) (sqrt -1)))>
#<alt (+ (* (sqrt eps) (sqrt -1)) (* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))))))>
#<alt (+ (* (sqrt eps) (sqrt -1)) (* (pow x 2) (+ (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))) (* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3)))) (* 1/16 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 2) (pow (sqrt -1) 5)))))))))>
#<alt x>
#<alt (* x (+ 1 (* -1/2 (/ eps (pow x 2)))))>
#<alt (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4))))))>
#<alt (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/8 (/ (pow eps 2) (pow x 4))) (* -1/16 (/ (pow eps 3) (pow x 6)))))))>
#<alt (* -1 x)>
#<alt (* -1 (* x (+ 1 (* -1/2 (/ eps (pow x 2))))))>
#<alt (* -1 (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4)))))))>
#<alt (* -1 (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/8 (/ (pow eps 2) (pow x 4))) (* -1/16 (/ (pow eps 3) (pow x 6))))))))>
#<alt x>
#<alt (+ x (* -1/2 (/ eps x)))>
#<alt (+ x (* eps (- (* -1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))))>
#<alt (+ x (* eps (- (* eps (- (* -1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))))>
#<alt (* (sqrt eps) (sqrt -1))>
#<alt (* eps (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))>
#<alt (* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))>
#<alt (* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow eps 7))) (/ (pow x 6) (pow (sqrt -1) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))))>
#<alt (* -1 (* (sqrt eps) (sqrt -1)))>
#<alt (* -1 (* eps (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))>
#<alt (* -1 (* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (* (pow x 4) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))))>
#<alt (* -1 (* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (* (pow x 4) (sqrt -1)))) (+ (* 1/16 (* (sqrt (/ 1 (pow eps 7))) (* (pow x 6) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))))>
#<alt (* -1 eps)>
#<alt (- (pow x 2) eps)>
#<alt (- (pow x 2) eps)>
#<alt (- (pow x 2) eps)>
#<alt (pow x 2)>
#<alt (* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))>
#<alt (* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))>
#<alt (* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))>
#<alt (pow x 2)>
#<alt (* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))>
#<alt (* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))>
#<alt (* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))>
#<alt (pow x 2)>
#<alt (+ (* -1 eps) (pow x 2))>
#<alt (+ (* -1 eps) (pow x 2))>
#<alt (+ (* -1 eps) (pow x 2))>
#<alt (* -1 eps)>
#<alt (* eps (- (/ (pow x 2) eps) 1))>
#<alt (* eps (- (/ (pow x 2) eps) 1))>
#<alt (* eps (- (/ (pow x 2) eps) 1))>
#<alt (* -1 eps)>
#<alt (* -1 (* eps (+ 1 (* -1 (/ (pow x 2) eps)))))>
#<alt (* -1 (* eps (+ 1 (* -1 (/ (pow x 2) eps)))))>
#<alt (* -1 (* eps (+ 1 (* -1 (/ (pow x 2) eps)))))>
#<alt (* -1 eps)>
#<alt (* -1 eps)>
#<alt (* -1 eps)>
#<alt (* -1 eps)>
#<alt (* -1 eps)>
#<alt (* -1 eps)>
#<alt (* -1 eps)>
#<alt (* -1 eps)>
#<alt (* -1 eps)>
#<alt (* -1 eps)>
#<alt (* -1 eps)>
#<alt (* -1 eps)>
#<alt 0>
#<alt 0>
#<alt 0>
#<alt 0>
#<alt 0>
#<alt 0>
#<alt 0>
#<alt 0>
#<alt 0>
#<alt 0>
#<alt 0>
#<alt 0>
#<alt (* 1/2 (/ eps x))>
#<alt (* 1/2 (/ eps x))>
#<alt (* 1/2 (/ eps x))>
#<alt (* 1/2 (/ eps x))>
#<alt (* 1/2 (/ eps x))>
#<alt (* 1/2 (/ eps x))>
#<alt (* 1/2 (/ eps x))>
#<alt (* 1/2 (/ eps x))>
#<alt (* 1/2 (/ eps x))>
#<alt (* 1/2 (/ eps x))>
#<alt (* 1/2 (/ eps x))>
#<alt (* 1/2 (/ eps x))>
#<alt (* 1/2 (/ eps x))>
#<alt (* 1/2 (/ eps x))>
#<alt (* 1/2 (/ eps x))>
#<alt (* 1/2 (/ eps x))>
#<alt (* 1/2 (/ eps x))>
#<alt (* 1/2 (/ eps x))>
#<alt (* 1/2 (/ eps x))>
#<alt (* 1/2 (/ eps x))>
#<alt (* 1/2 (/ eps x))>
#<alt (* 1/2 (/ eps x))>
#<alt (* 1/2 (/ eps x))>
#<alt (* 1/2 (/ eps x))>
#<alt (* 1/2 eps)>
#<alt (* 1/2 eps)>
#<alt (* 1/2 eps)>
#<alt (* 1/2 eps)>
#<alt (* 1/2 eps)>
#<alt (* 1/2 eps)>
#<alt (* 1/2 eps)>
#<alt (* 1/2 eps)>
#<alt (* 1/2 eps)>
#<alt (* 1/2 eps)>
#<alt (* 1/2 eps)>
#<alt (* 1/2 eps)>
#<alt (* -1 (* (sqrt eps) (sqrt -1)))>
#<alt (- x (* (sqrt eps) (sqrt -1)))>
#<alt (- (* x (+ 1 (* -1/2 (* (sqrt (/ 1 eps)) (/ x (sqrt -1)))))) (* (sqrt eps) (sqrt -1)))>
#<alt (- (* x (+ 1 (* x (- (* 1/8 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))))))) (* (sqrt eps) (sqrt -1)))>
#<alt (* 1/2 (/ eps x))>
#<alt (/ (- (* 1/8 (/ (pow eps 2) (pow x 2))) (* -1/2 eps)) x)>
#<alt (/ (- (* 1/16 (/ (pow eps 3) (pow x 4))) (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2))))) x)>
#<alt (/ (- (* 1/2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) (pow x 6))) (+ (* -1/2 eps) (+ (* -1/8 (/ (pow eps 2) (pow x 2))) (* -1/16 (/ (pow eps 3) (pow x 4)))))) x)>
#<alt (* 2 x)>
#<alt (* -1 (* x (- (* 1/2 (/ eps (pow x 2))) 2)))>
#<alt (* -1 (* x (- (+ (* 1/8 (/ (pow eps 2) (pow x 4))) (* 1/2 (/ eps (pow x 2)))) 2)))>
#<alt (* -1 (* x (- (+ (* 1/16 (/ (pow eps 3) (pow x 6))) (+ (* 1/8 (/ (pow eps 2) (pow x 4))) (* 1/2 (/ eps (pow x 2))))) 2)))>
#<alt (* 1/2 (/ eps x))>
#<alt (* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))>
#<alt (* eps (+ (* eps (+ (* 1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))>
#<alt (* eps (+ (* eps (+ (* eps (+ (* 5/128 (/ eps (pow x 7))) (* 1/16 (/ 1 (pow x 5))))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))>
#<alt (* -1 (* (sqrt eps) (sqrt -1)))>
#<alt (* eps (- (/ x eps) (* (sqrt (/ 1 eps)) (sqrt -1))))>
#<alt (* eps (- (+ (* -1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1))))>
#<alt (* eps (- (+ (* 1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (/ x eps)) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))>
#<alt (* (sqrt eps) (sqrt -1))>
#<alt (* -1 (* eps (- (* -1 (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))>
#<alt (* -1 (* eps (- (* -1 (/ (+ x (* 1/2 (* (sqrt (/ 1 eps)) (* (pow x 2) (sqrt -1))))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))>
#<alt (* -1 (* eps (- (* -1 (/ (+ x (* -1 (/ (- (* 1/8 (* (sqrt (/ 1 eps)) (* (pow x 4) (sqrt -1)))) (* 1/2 (* (sqrt eps) (* (pow x 2) (sqrt -1))))) eps))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))>
#<alt (* -1 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1))))>
#<alt (+ (* -1 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))) (* -1 (/ x (* eps (pow (sqrt -1) 2)))))>
#<alt (+ (* -1 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))) (* x (- (* -1 (* x (+ (* -1/2 (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3)))) (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3)))))) (/ 1 (* eps (pow (sqrt -1) 2))))))>
#<alt (+ (* -1 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))) (* x (- (* x (- (* x (- (* 1/2 (/ 1 (* (pow eps 2) (pow (sqrt -1) 4)))) (* (sqrt (/ 1 eps)) (/ (+ (* -1/2 (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3)))) (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3)))) (sqrt -1))))) (+ (* -1/2 (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3)))) (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3)))))) (/ 1 (* eps (pow (sqrt -1) 2))))))>
#<alt (* 2 (/ x eps))>
#<alt (* x (- (* 2 (/ 1 eps)) (* 1/2 (/ 1 (pow x 2)))))>
#<alt (* x (- (+ (* -1 (/ (+ (* -1/8 eps) (* 1/4 eps)) (pow x 4))) (* 2 (/ 1 eps))) (* 1/2 (/ 1 (pow x 2)))))>
#<alt (* x (- (+ (* -1 (/ (+ (* -1/4 (* eps (+ (* -1/8 eps) (* 1/4 eps)))) (+ (* -1/16 (pow eps 2)) (* 2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) (pow eps 2))))) (pow x 6))) (* 2 (/ 1 eps))) (+ (* -1/8 (/ eps (pow x 4))) (+ (* 1/4 (/ eps (pow x 4))) (* 1/2 (/ 1 (pow x 2)))))))>
#<alt (/ 1/2 x)>
#<alt (* -1 (/ (- (* -1/8 (/ eps (pow x 2))) 1/2) x))>
#<alt (* -1 (/ (- (* -1/16 (/ (pow eps 2) (pow x 4))) (+ 1/2 (* 1/8 (/ eps (pow x 2))))) x))>
#<alt (* -1 (/ (- (* -1 (/ (+ (* 1/128 (pow eps 3)) (* 1/32 (pow eps 3))) (pow x 6))) (+ 1/2 (+ (* 1/16 (/ (pow eps 2) (pow x 4))) (* 1/8 (/ eps (pow x 2)))))) x))>
#<alt (* 2 (/ x eps))>
#<alt (/ (+ (* -1/2 (/ eps x)) (* 2 x)) eps)>
#<alt (/ (+ (* 2 x) (* eps (- (* -1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))) eps)>
#<alt (/ (+ (* 2 x) (* eps (- (* eps (- (* -1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))) eps)>
#<alt (* -1 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1))))>
#<alt (/ (+ (* -1 (* (sqrt eps) (/ 1 (sqrt -1)))) (* -1 (/ x (pow (sqrt -1) 2)))) eps)>
#<alt (/ (- (+ (* -1 (* (sqrt eps) (/ 1 (sqrt -1)))) (* -1 (/ (+ (* -1/2 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3)))) (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3)))) (pow eps 2)))) (/ x (pow (sqrt -1) 2))) eps)>
#<alt (/ (- (+ (* -1 (* (sqrt eps) (/ 1 (sqrt -1)))) (* -1 (/ (+ (* -1/2 (/ (* (pow eps 2) (pow x 3)) (pow (sqrt -1) 4))) (* (sqrt eps) (/ (* x (+ (* -1/2 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3)))) (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3))))) (sqrt -1)))) (pow eps 3)))) (+ (* -1/2 (* (sqrt (/ 1 eps)) (/ (pow x 2) (pow (sqrt -1) 3)))) (+ (* (sqrt (/ 1 eps)) (/ (pow x 2) (pow (sqrt -1) 3))) (/ x (pow (sqrt -1) 2))))) eps)>
#<alt (* (sqrt (/ 1 eps)) (sqrt -1))>
#<alt (* -1 (/ (+ (* -1 x) (* -1 (* (sqrt eps) (sqrt -1)))) eps))>
#<alt (* -1 (/ (+ (* -1 (* (sqrt eps) (sqrt -1))) (* -1 (/ (- (+ (* -1/2 (* (sqrt eps) (* (pow x 2) (sqrt -1)))) (* (sqrt eps) (* (pow x 2) (sqrt -1)))) (* -1 (* eps x))) eps))) eps))>
#<alt (* -1 (/ (+ (* -1 (* (sqrt eps) (sqrt -1))) (* -1 (/ (- (* -1 (/ (- (+ (* -1/2 (* eps (pow x 3))) (* (sqrt (/ 1 eps)) (* x (* (sqrt -1) (+ (* -1/2 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))) (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))))))) (+ (* -1/2 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))) (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1))))) eps)) (* -1 (* eps x))) eps))) eps))>
#<alt (* -1 (* (sqrt eps) (sqrt -1)))>
#<alt (- x (* (sqrt eps) (sqrt -1)))>
#<alt (- (* x (+ 1 (* -1/2 (* (sqrt (/ 1 eps)) (/ x (sqrt -1)))))) (* (sqrt eps) (sqrt -1)))>
#<alt (- (* x (+ 1 (* x (- (* 1/8 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))))))) (* (sqrt eps) (sqrt -1)))>
#<alt (* 1/2 (/ eps x))>
#<alt (/ (- (* 1/8 (/ (pow eps 2) (pow x 2))) (* -1/2 eps)) x)>
#<alt (/ (- (* 1/16 (/ (pow eps 3) (pow x 4))) (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2))))) x)>
#<alt (/ (- (* 1/2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) (pow x 6))) (+ (* -1/2 eps) (+ (* -1/8 (/ (pow eps 2) (pow x 2))) (* -1/16 (/ (pow eps 3) (pow x 4)))))) x)>
#<alt (* 2 x)>
#<alt (* -1 (* x (- (* 1/2 (/ eps (pow x 2))) 2)))>
#<alt (* -1 (* x (- (* 1/8 (/ (pow eps 2) (pow x 4))) (+ 2 (* -1/2 (/ eps (pow x 2)))))))>
#<alt (* -1 (* x (- (* 1/16 (/ (pow eps 3) (pow x 6))) (+ 2 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4))))))))>
#<alt (* 1/2 (/ eps x))>
#<alt (* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))>
#<alt (* eps (+ (* eps (+ (* 1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))>
#<alt (* eps (+ (* eps (+ (* eps (+ (* 5/128 (/ eps (pow x 7))) (* 1/16 (/ 1 (pow x 5))))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))>
#<alt (* -1 (* (sqrt eps) (sqrt -1)))>
#<alt (* eps (- (/ x eps) (* (sqrt (/ 1 eps)) (sqrt -1))))>
#<alt (* eps (- (+ (* -1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1))))>
#<alt (* eps (- (+ (* 1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (/ x eps)) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))>
#<alt (* (sqrt eps) (sqrt -1))>
#<alt (* -1 (* eps (- (* -1 (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))>
#<alt (* -1 (* eps (- (* -1 (/ (+ x (* 1/2 (* (sqrt (/ 1 eps)) (* (pow x 2) (sqrt -1))))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))>
#<alt (* -1 (* eps (- (* -1 (/ (+ x (* -1 (/ (- (* 1/8 (* (sqrt (/ 1 eps)) (* (pow x 4) (sqrt -1)))) (* 1/2 (* (sqrt eps) (* (pow x 2) (sqrt -1))))) eps))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))>
#<alt (* (sqrt eps) (sqrt -1))>
#<alt (+ (* 1/2 (* (sqrt (/ 1 eps)) (/ (pow x 2) (sqrt -1)))) (* (sqrt eps) (sqrt -1)))>
#<alt (+ (* (sqrt eps) (sqrt -1)) (* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))))))>
#<alt (+ (* (sqrt eps) (sqrt -1)) (* (pow x 2) (+ (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))) (* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3)))) (* 1/16 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 2) (pow (sqrt -1) 5)))))))))>
#<alt x>
#<alt (* x (+ 1 (* -1/2 (/ eps (pow x 2)))))>
#<alt (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4))))))>
#<alt (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/8 (/ (pow eps 2) (pow x 4))) (* -1/16 (/ (pow eps 3) (pow x 6)))))))>
#<alt (* -1 x)>
#<alt (* -1 (* x (+ 1 (* -1/2 (/ eps (pow x 2))))))>
#<alt (* -1 (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4)))))))>
#<alt (* -1 (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/8 (/ (pow eps 2) (pow x 4))) (* -1/16 (/ (pow eps 3) (pow x 6))))))))>
#<alt x>
#<alt (+ x (* -1/2 (/ eps x)))>
#<alt (+ x (* eps (- (* -1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))))>
#<alt (+ x (* eps (- (* eps (- (* -1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))))>
#<alt (* (sqrt eps) (sqrt -1))>
#<alt (* eps (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))>
#<alt (* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))>
#<alt (* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow eps 7))) (/ (pow x 6) (pow (sqrt -1) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))))>
#<alt (* -1 (* (sqrt eps) (sqrt -1)))>
#<alt (* -1 (* eps (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))>
#<alt (* -1 (* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (* (pow x 4) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))))>
#<alt (* -1 (* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (* (pow x 4) (sqrt -1)))) (+ (* 1/16 (* (sqrt (/ 1 (pow eps 7))) (* (pow x 6) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))))>
#<alt (* -1 (* (sqrt eps) (sqrt -1)))>
#<alt (- x (* (sqrt eps) (sqrt -1)))>
#<alt (- (* x (+ 1 (* -1/2 (* (sqrt (/ 1 eps)) (/ x (sqrt -1)))))) (* (sqrt eps) (sqrt -1)))>
#<alt (- (* x (+ 1 (* x (- (* 1/8 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))))))) (* (sqrt eps) (sqrt -1)))>
#<alt (* 1/2 (/ eps x))>
#<alt (/ (- (* 1/8 (/ (pow eps 2) (pow x 2))) (* -1/2 eps)) x)>
#<alt (/ (- (* 1/16 (/ (pow eps 3) (pow x 4))) (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2))))) x)>
#<alt (/ (- (* 1/2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) (pow x 6))) (+ (* -1/2 eps) (+ (* -1/8 (/ (pow eps 2) (pow x 2))) (* -1/16 (/ (pow eps 3) (pow x 4)))))) x)>
#<alt (* -1 (* x (- (pow (sqrt -1) 2) 1)))>
#<alt (* -1 (* x (- (+ (* 1/2 (/ eps (pow x 2))) (pow (sqrt -1) 2)) 1)))>
#<alt (* -1 (* x (- (+ (* 1/8 (/ (pow eps 2) (pow x 4))) (pow (sqrt -1) 2)) (+ 1 (* -1/2 (/ eps (pow x 2)))))))>
#<alt (* -1 (* x (- (+ (* 1/16 (/ (pow eps 3) (pow x 6))) (pow (sqrt -1) 2)) (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4))))))))>
#<alt (* 1/2 (/ eps x))>
#<alt (* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))>
#<alt (* eps (+ (* eps (+ (* 1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))>
#<alt (* eps (+ (* eps (+ (* eps (+ (* 5/128 (/ eps (pow x 7))) (* 1/16 (/ 1 (pow x 5))))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))>
#<alt (* -1 (* (sqrt eps) (sqrt -1)))>
#<alt (* eps (- (/ x eps) (* (sqrt (/ 1 eps)) (sqrt -1))))>
#<alt (* eps (- (+ (* -1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1))))>
#<alt (* eps (- (+ (* 1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (/ x eps)) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))>
#<alt (* (sqrt eps) (sqrt -1))>
#<alt (* -1 (* eps (- (* -1 (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))>
#<alt (* -1 (* eps (- (* -1 (/ (+ x (* 1/2 (* (sqrt (/ 1 eps)) (* (pow x 2) (sqrt -1))))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))>
#<alt (* -1 (* eps (- (* -1 (/ (+ x (* -1 (/ (- (* 1/8 (* (sqrt (/ 1 eps)) (* (pow x 4) (sqrt -1)))) (* 1/2 (* (sqrt eps) (* (pow x 2) (sqrt -1))))) eps))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (* -1 (* (sqrt x) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt x) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt x) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt x) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt eps) (sqrt -1)))>
#<alt (- (* -1/2 (* (sqrt (/ 1 eps)) (/ (pow x 2) (sqrt -1)))) (* (sqrt eps) (sqrt -1)))>
#<alt (- (* (pow x 2) (- (* 1/8 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))))) (* (sqrt eps) (sqrt -1)))>
#<alt (- (* (pow x 2) (- (* (pow x 2) (- (* -1/16 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 2) (pow (sqrt -1) 5)))) (* -1/8 (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3)))))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))))) (* (sqrt eps) (sqrt -1)))>
#<alt (* -1 x)>
#<alt (* x (- (* 1/2 (/ eps (pow x 2))) 1))>
#<alt (* x (- (* 1/8 (/ (pow eps 2) (pow x 4))) (+ 1 (* -1/2 (/ eps (pow x 2))))))>
#<alt (* x (- (* 1/16 (/ (pow eps 3) (pow x 6))) (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4)))))))>
#<alt x>
#<alt (* -1 (* x (- (* 1/2 (/ eps (pow x 2))) 1)))>
#<alt (* -1 (* x (- (* 1/8 (/ (pow eps 2) (pow x 4))) (+ 1 (* -1/2 (/ eps (pow x 2)))))))>
#<alt (* -1 (* x (- (* 1/16 (/ (pow eps 3) (pow x 6))) (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4))))))))>
#<alt (* -1 x)>
#<alt (- (* 1/2 (/ eps x)) x)>
#<alt (- (* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))) x)>
#<alt (- (* eps (+ (* eps (+ (* 1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))) x)>
#<alt (* -1 (* (sqrt eps) (sqrt -1)))>
#<alt (* eps (- (* -1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))>
#<alt (* eps (- (* 1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))>
#<alt (* eps (- (* -1/16 (* (sqrt (/ 1 (pow eps 7))) (/ (pow x 6) (pow (sqrt -1) 5)))) (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))))>
#<alt (* (sqrt eps) (sqrt -1))>
#<alt (* -1 (* eps (- (* -1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))>
#<alt (* -1 (* eps (- (* 1/8 (* (sqrt (/ 1 (pow eps 5))) (* (pow x 4) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))))>
#<alt (* -1 (* eps (- (* -1/16 (* (sqrt (/ 1 (pow eps 7))) (* (pow x 6) (sqrt -1)))) (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (* (pow x 4) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))))>
#<alt (* -1 eps)>
#<alt (- (pow x 2) eps)>
#<alt (- (pow x 2) eps)>
#<alt (- (pow x 2) eps)>
#<alt (pow x 2)>
#<alt (* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))>
#<alt (* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))>
#<alt (* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))>
#<alt (pow x 2)>
#<alt (* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))>
#<alt (* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))>
#<alt (* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))>
#<alt (pow x 2)>
#<alt (+ (* -1 eps) (pow x 2))>
#<alt (+ (* -1 eps) (pow x 2))>
#<alt (+ (* -1 eps) (pow x 2))>
#<alt (* -1 eps)>
#<alt (* eps (- (/ (pow x 2) eps) 1))>
#<alt (* eps (- (/ (pow x 2) eps) 1))>
#<alt (* eps (- (/ (pow x 2) eps) 1))>
#<alt (* -1 eps)>
#<alt (* -1 (* eps (+ 1 (* -1 (/ (pow x 2) eps)))))>
#<alt (* -1 (* eps (+ 1 (* -1 (/ (pow x 2) eps)))))>
#<alt (* -1 (* eps (+ 1 (* -1 (/ (pow x 2) eps)))))>

Calls

78 calls:

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

rewrite124.0ms (1.2%)

Memory

22.0MiB live, 140.9MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

538×	`accelerator-lowering-fma.f32`
538×	`accelerator-lowering-fma.f64`
402×	`-lowering-.f32`
402×	`-lowering-.f64`
306×	`/-lowering-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	84
1	130	84
0	888	84

Stop Event

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

Counts

15 → 356

Calls

Call 1

Inputs
(- x (sqrt (+ (* x x) (neg eps))))
(sqrt (+ (* x x) (neg eps)))
(+ (* x x) (neg eps))
(neg eps)
(- x x)
(/ (* eps 1/2) x)
(* eps 1/2)
(/ 1 (/ 1 (- x (sqrt (- (* x x) eps)))))
(/ 1 (- x (sqrt (- (* x x) eps))))
(- x (sqrt (- (* x x) eps)))
(sqrt (- (* x x) eps))
(+ (* (sqrt x) (sqrt x)) (neg (sqrt (- (* x x) eps))))
(sqrt x)
(neg (sqrt (- (* x x) eps)))
(- (* x x) eps)

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

simplify369.0ms (3.7%)

Memory

8.5MiB live, 683.7MiB allocated

Algorithm

1×	egg-herbie

Rules

7 830×	`accelerator-lowering-fma.f32`
7 830×	`accelerator-lowering-fma.f64`
5 704×	`-lowering-.f32`
5 704×	`-lowering-.f64`
2 206×	`+-lowering-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	478	4837
1	1486	4685
2	5149	4612
0	8380	4376

Stop Event

1×	iter limit
1×	node limit

Counts

312 → 312

Calls

Call 1

Inputs
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(- x (* (sqrt eps) (sqrt -1)))
(- (* x (+ 1 (* -1/2 (* (sqrt (/ 1 eps)) (/ x (sqrt -1)))))) (* (sqrt eps) (sqrt -1)))
(- (* x (+ 1 (* x (- (* 1/8 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))))))) (* (sqrt eps) (sqrt -1)))
(* 1/2 (/ eps x))
(/ (- (* 1/8 (/ (pow eps 2) (pow x 2))) (* -1/2 eps)) x)
(/ (- (* 1/16 (/ (pow eps 3) (pow x 4))) (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2))))) x)
(/ (- (* 1/2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) (pow x 6))) (+ (* -1/2 eps) (+ (* -1/8 (/ (pow eps 2) (pow x 2))) (* -1/16 (/ (pow eps 3) (pow x 4)))))) x)
(* 2 x)
(* -1 (* x (- (* 1/2 (/ eps (pow x 2))) 2)))
(* -1 (* x (- (* 1/8 (/ (pow eps 2) (pow x 4))) (+ 2 (* -1/2 (/ eps (pow x 2)))))))
(* -1 (* x (- (* 1/16 (/ (pow eps 3) (pow x 6))) (+ 2 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4))))))))
(* 1/2 (/ eps x))
(* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))
(* eps (+ (* eps (+ (* 1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))
(* eps (+ (* eps (+ (* eps (+ (* 5/128 (/ eps (pow x 7))) (* 1/16 (/ 1 (pow x 5))))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))
(* -1 (* (sqrt eps) (sqrt -1)))
(* eps (- (/ x eps) (* (sqrt (/ 1 eps)) (sqrt -1))))
(* eps (- (+ (* -1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1))))
(* eps (- (+ (* 1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (/ x eps)) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))
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(* -1 (* eps (- (* -1 (/ (+ x (* 1/2 (* (sqrt (/ 1 eps)) (* (pow x 2) (sqrt -1))))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
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(* (sqrt eps) (sqrt -1))
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x
(* x (+ 1 (* -1/2 (/ eps (pow x 2)))))
(* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4))))))
(* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/8 (/ (pow eps 2) (pow x 4))) (* -1/16 (/ (pow eps 3) (pow x 6)))))))
(* -1 x)
(* -1 (* x (+ 1 (* -1/2 (/ eps (pow x 2))))))
(* -1 (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4)))))))
(* -1 (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/8 (/ (pow eps 2) (pow x 4))) (* -1/16 (/ (pow eps 3) (pow x 6))))))))
x
(+ x (* -1/2 (/ eps x)))
(+ x (* eps (- (* -1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))))
(+ x (* eps (- (* eps (- (* -1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))))
(* (sqrt eps) (sqrt -1))
(* eps (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))
(* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow eps 7))) (/ (pow x 6) (pow (sqrt -1) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))))
(* -1 (* (sqrt eps) (sqrt -1)))
(* -1 (* eps (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* -1 (* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (* (pow x 4) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))))
(* -1 (* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (* (pow x 4) (sqrt -1)))) (+ (* 1/16 (* (sqrt (/ 1 (pow eps 7))) (* (pow x 6) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))))
(* -1 eps)
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(- (pow x 2) eps)
(pow x 2)
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))
(pow x 2)
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))
(pow x 2)
(+ (* -1 eps) (pow x 2))
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(+ (* -1 eps) (pow x 2))
(* -1 eps)
(* eps (- (/ (pow x 2) eps) 1))
(* eps (- (/ (pow x 2) eps) 1))
(* eps (- (/ (pow x 2) eps) 1))
(* -1 eps)
(* -1 (* eps (+ 1 (* -1 (/ (pow x 2) eps)))))
(* -1 (* eps (+ 1 (* -1 (/ (pow x 2) eps)))))
(* -1 (* eps (+ 1 (* -1 (/ (pow x 2) eps)))))
(* -1 eps)
(* -1 eps)
(* -1 eps)
(* -1 eps)
(* -1 eps)
(* -1 eps)
(* -1 eps)
(* -1 eps)
(* -1 eps)
(* -1 eps)
(* -1 eps)
(* -1 eps)
0
0
0
0
0
0
0
0
0
0
0
0
(* 1/2 (/ eps x))
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(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
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(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
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(* 1/2 (/ eps x))
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(* 1/2 (/ eps x))
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(* 1/2 eps)
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(* -1 (* (sqrt eps) (sqrt -1)))
(- x (* (sqrt eps) (sqrt -1)))
(- (* x (+ 1 (* -1/2 (* (sqrt (/ 1 eps)) (/ x (sqrt -1)))))) (* (sqrt eps) (sqrt -1)))
(- (* x (+ 1 (* x (- (* 1/8 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))))))) (* (sqrt eps) (sqrt -1)))
(* 1/2 (/ eps x))
(/ (- (* 1/8 (/ (pow eps 2) (pow x 2))) (* -1/2 eps)) x)
(/ (- (* 1/16 (/ (pow eps 3) (pow x 4))) (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2))))) x)
(/ (- (* 1/2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) (pow x 6))) (+ (* -1/2 eps) (+ (* -1/8 (/ (pow eps 2) (pow x 2))) (* -1/16 (/ (pow eps 3) (pow x 4)))))) x)
(* 2 x)
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(* -1 (* x (- (+ (* 1/8 (/ (pow eps 2) (pow x 4))) (* 1/2 (/ eps (pow x 2)))) 2)))
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(* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))
(* eps (+ (* eps (+ (* 1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))
(* eps (+ (* eps (+ (* eps (+ (* 5/128 (/ eps (pow x 7))) (* 1/16 (/ 1 (pow x 5))))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))
(* -1 (* (sqrt eps) (sqrt -1)))
(* eps (- (/ x eps) (* (sqrt (/ 1 eps)) (sqrt -1))))
(* eps (- (+ (* -1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1))))
(* eps (- (+ (* 1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (/ x eps)) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* (sqrt eps) (sqrt -1))
(* -1 (* eps (- (* -1 (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* -1 (* eps (- (* -1 (/ (+ x (* 1/2 (* (sqrt (/ 1 eps)) (* (pow x 2) (sqrt -1))))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* -1 (* eps (- (* -1 (/ (+ x (* -1 (/ (- (* 1/8 (* (sqrt (/ 1 eps)) (* (pow x 4) (sqrt -1)))) (* 1/2 (* (sqrt eps) (* (pow x 2) (sqrt -1))))) eps))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* -1 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1))))
(+ (* -1 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))) (* -1 (/ x (* eps (pow (sqrt -1) 2)))))
(+ (* -1 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))) (* x (- (* -1 (* x (+ (* -1/2 (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3)))) (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3)))))) (/ 1 (* eps (pow (sqrt -1) 2))))))
(+ (* -1 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))) (* x (- (* x (- (* x (- (* 1/2 (/ 1 (* (pow eps 2) (pow (sqrt -1) 4)))) (* (sqrt (/ 1 eps)) (/ (+ (* -1/2 (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3)))) (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3)))) (sqrt -1))))) (+ (* -1/2 (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3)))) (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3)))))) (/ 1 (* eps (pow (sqrt -1) 2))))))
(* 2 (/ x eps))
(* x (- (* 2 (/ 1 eps)) (* 1/2 (/ 1 (pow x 2)))))
(* x (- (+ (* -1 (/ (+ (* -1/8 eps) (* 1/4 eps)) (pow x 4))) (* 2 (/ 1 eps))) (* 1/2 (/ 1 (pow x 2)))))
(* x (- (+ (* -1 (/ (+ (* -1/4 (* eps (+ (* -1/8 eps) (* 1/4 eps)))) (+ (* -1/16 (pow eps 2)) (* 2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) (pow eps 2))))) (pow x 6))) (* 2 (/ 1 eps))) (+ (* -1/8 (/ eps (pow x 4))) (+ (* 1/4 (/ eps (pow x 4))) (* 1/2 (/ 1 (pow x 2)))))))
(/ 1/2 x)
(* -1 (/ (- (* -1/8 (/ eps (pow x 2))) 1/2) x))
(* -1 (/ (- (* -1/16 (/ (pow eps 2) (pow x 4))) (+ 1/2 (* 1/8 (/ eps (pow x 2))))) x))
(* -1 (/ (- (* -1 (/ (+ (* 1/128 (pow eps 3)) (* 1/32 (pow eps 3))) (pow x 6))) (+ 1/2 (+ (* 1/16 (/ (pow eps 2) (pow x 4))) (* 1/8 (/ eps (pow x 2)))))) x))
(* 2 (/ x eps))
(/ (+ (* -1/2 (/ eps x)) (* 2 x)) eps)
(/ (+ (* 2 x) (* eps (- (* -1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))) eps)
(/ (+ (* 2 x) (* eps (- (* eps (- (* -1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))) eps)
(* -1 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1))))
(/ (+ (* -1 (* (sqrt eps) (/ 1 (sqrt -1)))) (* -1 (/ x (pow (sqrt -1) 2)))) eps)
(/ (- (+ (* -1 (* (sqrt eps) (/ 1 (sqrt -1)))) (* -1 (/ (+ (* -1/2 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3)))) (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3)))) (pow eps 2)))) (/ x (pow (sqrt -1) 2))) eps)
(/ (- (+ (* -1 (* (sqrt eps) (/ 1 (sqrt -1)))) (* -1 (/ (+ (* -1/2 (/ (* (pow eps 2) (pow x 3)) (pow (sqrt -1) 4))) (* (sqrt eps) (/ (* x (+ (* -1/2 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3)))) (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3))))) (sqrt -1)))) (pow eps 3)))) (+ (* -1/2 (* (sqrt (/ 1 eps)) (/ (pow x 2) (pow (sqrt -1) 3)))) (+ (* (sqrt (/ 1 eps)) (/ (pow x 2) (pow (sqrt -1) 3))) (/ x (pow (sqrt -1) 2))))) eps)
(* (sqrt (/ 1 eps)) (sqrt -1))
(* -1 (/ (+ (* -1 x) (* -1 (* (sqrt eps) (sqrt -1)))) eps))
(* -1 (/ (+ (* -1 (* (sqrt eps) (sqrt -1))) (* -1 (/ (- (+ (* -1/2 (* (sqrt eps) (* (pow x 2) (sqrt -1)))) (* (sqrt eps) (* (pow x 2) (sqrt -1)))) (* -1 (* eps x))) eps))) eps))
(* -1 (/ (+ (* -1 (* (sqrt eps) (sqrt -1))) (* -1 (/ (- (* -1 (/ (- (+ (* -1/2 (* eps (pow x 3))) (* (sqrt (/ 1 eps)) (* x (* (sqrt -1) (+ (* -1/2 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))) (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))))))) (+ (* -1/2 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))) (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1))))) eps)) (* -1 (* eps x))) eps))) eps))
(* -1 (* (sqrt eps) (sqrt -1)))
(- x (* (sqrt eps) (sqrt -1)))
(- (* x (+ 1 (* -1/2 (* (sqrt (/ 1 eps)) (/ x (sqrt -1)))))) (* (sqrt eps) (sqrt -1)))
(- (* x (+ 1 (* x (- (* 1/8 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))))))) (* (sqrt eps) (sqrt -1)))
(* 1/2 (/ eps x))
(/ (- (* 1/8 (/ (pow eps 2) (pow x 2))) (* -1/2 eps)) x)
(/ (- (* 1/16 (/ (pow eps 3) (pow x 4))) (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2))))) x)
(/ (- (* 1/2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) (pow x 6))) (+ (* -1/2 eps) (+ (* -1/8 (/ (pow eps 2) (pow x 2))) (* -1/16 (/ (pow eps 3) (pow x 4)))))) x)
(* 2 x)
(* -1 (* x (- (* 1/2 (/ eps (pow x 2))) 2)))
(* -1 (* x (- (* 1/8 (/ (pow eps 2) (pow x 4))) (+ 2 (* -1/2 (/ eps (pow x 2)))))))
(* -1 (* x (- (* 1/16 (/ (pow eps 3) (pow x 6))) (+ 2 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4))))))))
(* 1/2 (/ eps x))
(* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))
(* eps (+ (* eps (+ (* 1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))
(* eps (+ (* eps (+ (* eps (+ (* 5/128 (/ eps (pow x 7))) (* 1/16 (/ 1 (pow x 5))))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))
(* -1 (* (sqrt eps) (sqrt -1)))
(* eps (- (/ x eps) (* (sqrt (/ 1 eps)) (sqrt -1))))
(* eps (- (+ (* -1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1))))
(* eps (- (+ (* 1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (/ x eps)) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* (sqrt eps) (sqrt -1))
(* -1 (* eps (- (* -1 (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* -1 (* eps (- (* -1 (/ (+ x (* 1/2 (* (sqrt (/ 1 eps)) (* (pow x 2) (sqrt -1))))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* -1 (* eps (- (* -1 (/ (+ x (* -1 (/ (- (* 1/8 (* (sqrt (/ 1 eps)) (* (pow x 4) (sqrt -1)))) (* 1/2 (* (sqrt eps) (* (pow x 2) (sqrt -1))))) eps))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* (sqrt eps) (sqrt -1))
(+ (* 1/2 (* (sqrt (/ 1 eps)) (/ (pow x 2) (sqrt -1)))) (* (sqrt eps) (sqrt -1)))
(+ (* (sqrt eps) (sqrt -1)) (* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))))))
(+ (* (sqrt eps) (sqrt -1)) (* (pow x 2) (+ (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))) (* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3)))) (* 1/16 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 2) (pow (sqrt -1) 5)))))))))
x
(* x (+ 1 (* -1/2 (/ eps (pow x 2)))))
(* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4))))))
(* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/8 (/ (pow eps 2) (pow x 4))) (* -1/16 (/ (pow eps 3) (pow x 6)))))))
(* -1 x)
(* -1 (* x (+ 1 (* -1/2 (/ eps (pow x 2))))))
(* -1 (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4)))))))
(* -1 (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/8 (/ (pow eps 2) (pow x 4))) (* -1/16 (/ (pow eps 3) (pow x 6))))))))
x
(+ x (* -1/2 (/ eps x)))
(+ x (* eps (- (* -1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))))
(+ x (* eps (- (* eps (- (* -1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))))
(* (sqrt eps) (sqrt -1))
(* eps (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))
(* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow eps 7))) (/ (pow x 6) (pow (sqrt -1) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))))
(* -1 (* (sqrt eps) (sqrt -1)))
(* -1 (* eps (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* -1 (* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (* (pow x 4) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))))
(* -1 (* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (* (pow x 4) (sqrt -1)))) (+ (* 1/16 (* (sqrt (/ 1 (pow eps 7))) (* (pow x 6) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))))
(* -1 (* (sqrt eps) (sqrt -1)))
(- x (* (sqrt eps) (sqrt -1)))
(- (* x (+ 1 (* -1/2 (* (sqrt (/ 1 eps)) (/ x (sqrt -1)))))) (* (sqrt eps) (sqrt -1)))
(- (* x (+ 1 (* x (- (* 1/8 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))))))) (* (sqrt eps) (sqrt -1)))
(* 1/2 (/ eps x))
(/ (- (* 1/8 (/ (pow eps 2) (pow x 2))) (* -1/2 eps)) x)
(/ (- (* 1/16 (/ (pow eps 3) (pow x 4))) (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2))))) x)
(/ (- (* 1/2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) (pow x 6))) (+ (* -1/2 eps) (+ (* -1/8 (/ (pow eps 2) (pow x 2))) (* -1/16 (/ (pow eps 3) (pow x 4)))))) x)
(* -1 (* x (- (pow (sqrt -1) 2) 1)))
(* -1 (* x (- (+ (* 1/2 (/ eps (pow x 2))) (pow (sqrt -1) 2)) 1)))
(* -1 (* x (- (+ (* 1/8 (/ (pow eps 2) (pow x 4))) (pow (sqrt -1) 2)) (+ 1 (* -1/2 (/ eps (pow x 2)))))))
(* -1 (* x (- (+ (* 1/16 (/ (pow eps 3) (pow x 6))) (pow (sqrt -1) 2)) (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4))))))))
(* 1/2 (/ eps x))
(* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))
(* eps (+ (* eps (+ (* 1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))
(* eps (+ (* eps (+ (* eps (+ (* 5/128 (/ eps (pow x 7))) (* 1/16 (/ 1 (pow x 5))))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))
(* -1 (* (sqrt eps) (sqrt -1)))
(* eps (- (/ x eps) (* (sqrt (/ 1 eps)) (sqrt -1))))
(* eps (- (+ (* -1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1))))
(* eps (- (+ (* 1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (/ x eps)) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* (sqrt eps) (sqrt -1))
(* -1 (* eps (- (* -1 (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* -1 (* eps (- (* -1 (/ (+ x (* 1/2 (* (sqrt (/ 1 eps)) (* (pow x 2) (sqrt -1))))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* -1 (* eps (- (* -1 (/ (+ x (* -1 (/ (- (* 1/8 (* (sqrt (/ 1 eps)) (* (pow x 4) (sqrt -1)))) (* 1/2 (* (sqrt eps) (* (pow x 2) (sqrt -1))))) eps))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt x)
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* (sqrt eps) (sqrt -1)))
(- (* -1/2 (* (sqrt (/ 1 eps)) (/ (pow x 2) (sqrt -1)))) (* (sqrt eps) (sqrt -1)))
(- (* (pow x 2) (- (* 1/8 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))))) (* (sqrt eps) (sqrt -1)))
(- (* (pow x 2) (- (* (pow x 2) (- (* -1/16 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 2) (pow (sqrt -1) 5)))) (* -1/8 (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3)))))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))))) (* (sqrt eps) (sqrt -1)))
(* -1 x)
(* x (- (* 1/2 (/ eps (pow x 2))) 1))
(* x (- (* 1/8 (/ (pow eps 2) (pow x 4))) (+ 1 (* -1/2 (/ eps (pow x 2))))))
(* x (- (* 1/16 (/ (pow eps 3) (pow x 6))) (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4)))))))
x
(* -1 (* x (- (* 1/2 (/ eps (pow x 2))) 1)))
(* -1 (* x (- (* 1/8 (/ (pow eps 2) (pow x 4))) (+ 1 (* -1/2 (/ eps (pow x 2)))))))
(* -1 (* x (- (* 1/16 (/ (pow eps 3) (pow x 6))) (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4))))))))
(* -1 x)
(- (* 1/2 (/ eps x)) x)
(- (* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))) x)
(- (* eps (+ (* eps (+ (* 1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))) x)
(* -1 (* (sqrt eps) (sqrt -1)))
(* eps (- (* -1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))
(* eps (- (* 1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* eps (- (* -1/16 (* (sqrt (/ 1 (pow eps 7))) (/ (pow x 6) (pow (sqrt -1) 5)))) (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))))
(* (sqrt eps) (sqrt -1))
(* -1 (* eps (- (* -1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* -1 (* eps (- (* 1/8 (* (sqrt (/ 1 (pow eps 5))) (* (pow x 4) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))))
(* -1 (* eps (- (* -1/16 (* (sqrt (/ 1 (pow eps 7))) (* (pow x 6) (sqrt -1)))) (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (* (pow x 4) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))))
(* -1 eps)
(- (pow x 2) eps)
(- (pow x 2) eps)
(- (pow x 2) eps)
(pow x 2)
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))
(pow x 2)
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))
(pow x 2)
(+ (* -1 eps) (pow x 2))
(+ (* -1 eps) (pow x 2))
(+ (* -1 eps) (pow x 2))
(* -1 eps)
(* eps (- (/ (pow x 2) eps) 1))
(* eps (- (/ (pow x 2) eps) 1))
(* eps (- (/ (pow x 2) eps) 1))
(* -1 eps)
(* -1 (* eps (+ 1 (* -1 (/ (pow x 2) eps)))))
(* -1 (* eps (+ 1 (* -1 (/ (pow x 2) eps)))))
(* -1 (* eps (+ 1 (* -1 (/ (pow x 2) eps)))))

Outputs
(* -1 (* (sqrt eps) (sqrt -1)))
(*.f64 (sqrt.f64 eps) (neg.f64 (sqrt.f64 #s(literal -1 binary64))))
(- x (* (sqrt eps) (sqrt -1)))
(fma.f64 (sqrt.f64 eps) (neg.f64 (sqrt.f64 #s(literal -1 binary64))) x)
(- (* x (+ 1 (* -1/2 (* (sqrt (/ 1 eps)) (/ x (sqrt -1)))))) (* (sqrt eps) (sqrt -1)))
(-.f64 (fma.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (/.f64 x (sqrt.f64 #s(literal -1 binary64)))) (.f64 #s(literal -1/2 binary64) x) x) (*.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64))))
(- (* x (+ 1 (* x (- (* 1/8 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))))))) (* (sqrt eps) (sqrt -1)))
(-.f64 (fma.f64 (.f64 x x) (fma.f64 #s(literal -1/2 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64))) (.f64 (.f64 #s(literal 1/8 binary64) (/.f64 (.f64 x x) (neg.f64 (sqrt.f64 #s(literal -1 binary64))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 eps (.f64 eps eps)))))) x) (*.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64))))
(* 1/2 (/ eps x))
(/.f64 (*.f64 eps #s(literal 1/2 binary64)) x)
(/ (- (* 1/8 (/ (pow eps 2) (pow x 2))) (* -1/2 eps)) x)
(/.f64 (fma.f64 #s(literal 1/8 binary64) (/.f64 (.f64 eps eps) (.f64 x x)) (*.f64 eps #s(literal 1/2 binary64))) x)
(/ (- (* 1/16 (/ (pow eps 3) (pow x 4))) (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2))))) x)
(/.f64 (fma.f64 #s(literal 1/16 binary64) (/.f64 (.f64 eps (.f64 eps eps)) (.f64 (.f64 x x) (.f64 x x))) (fma.f64 #s(literal 1/8 binary64) (/.f64 (.f64 eps eps) (.f64 x x)) (.f64 eps #s(literal 1/2 binary64)))) x)
(/ (- (* 1/2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) (pow x 6))) (+ (* -1/2 eps) (+ (* -1/8 (/ (pow eps 2) (pow x 2))) (* -1/16 (/ (pow eps 3) (pow x 4)))))) x)
(/.f64 (fma.f64 #s(literal 1/2 binary64) (/.f64 (.f64 (pow.f64 eps #s(literal 4 binary64)) #s(literal 5/64 binary64)) (pow.f64 x #s(literal 6 binary64))) (fma.f64 #s(literal 1/16 binary64) (/.f64 (.f64 eps (.f64 eps eps)) (.f64 (.f64 x x) (.f64 x x))) (fma.f64 #s(literal 1/8 binary64) (/.f64 (.f64 eps eps) (.f64 x x)) (*.f64 eps #s(literal 1/2 binary64))))) x)
(* 2 x)
(+.f64 x x)
(* -1 (* x (- (* 1/2 (/ eps (pow x 2))) 2)))
(fma.f64 x (fma.f64 eps (/.f64 #s(literal -1/2 binary64) (*.f64 x x)) #s(literal 1 binary64)) x)
(* -1 (* x (- (* 1/8 (/ (pow eps 2) (pow x 4))) (+ 2 (* -1/2 (/ eps (pow x 2)))))))
(.f64 x (neg.f64 (fma.f64 #s(literal 1/8 binary64) (/.f64 (.f64 eps eps) (.f64 (.f64 x x) (.f64 x x))) (fma.f64 eps (/.f64 #s(literal 1/2 binary64) (.f64 x x)) #s(literal -2 binary64)))))
(* -1 (* x (- (* 1/16 (/ (pow eps 3) (pow x 6))) (+ 2 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4))))))))
(.f64 (fma.f64 #s(literal 1/16 binary64) (/.f64 (.f64 eps (.f64 eps eps)) (pow.f64 x #s(literal 6 binary64))) (fma.f64 #s(literal 1/8 binary64) (/.f64 (.f64 eps eps) (.f64 (.f64 x x) (.f64 x x))) (fma.f64 eps (/.f64 #s(literal 1/2 binary64) (.f64 x x)) #s(literal -2 binary64)))) (neg.f64 x))
(* 1/2 (/ eps x))
(/.f64 (*.f64 eps #s(literal 1/2 binary64)) x)
(* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))
(/.f64 (fma.f64 #s(literal 1/8 binary64) (/.f64 (.f64 eps eps) (.f64 x x)) (*.f64 eps #s(literal 1/2 binary64))) x)
(* eps (+ (* eps (+ (* 1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))
(.f64 eps (fma.f64 eps (fma.f64 #s(literal 1/16 binary64) (/.f64 eps (pow.f64 x #s(literal 5 binary64))) (/.f64 #s(literal 1/8 binary64) (.f64 x (*.f64 x x)))) (/.f64 #s(literal 1/2 binary64) x)))
(* eps (+ (* eps (+ (* eps (+ (* 5/128 (/ eps (pow x 7))) (* 1/16 (/ 1 (pow x 5))))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))
(.f64 eps (fma.f64 eps (fma.f64 eps (fma.f64 #s(literal 5/128 binary64) (/.f64 eps (pow.f64 x #s(literal 7 binary64))) (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 5 binary64)))) (/.f64 #s(literal 1/8 binary64) (.f64 x (*.f64 x x)))) (/.f64 #s(literal 1/2 binary64) x)))
(* -1 (* (sqrt eps) (sqrt -1)))
(*.f64 (sqrt.f64 eps) (neg.f64 (sqrt.f64 #s(literal -1 binary64))))
(* eps (- (/ x eps) (* (sqrt (/ 1 eps)) (sqrt -1))))
(.f64 eps (-.f64 (/.f64 x eps) (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)))))
(* eps (- (+ (* -1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1))))
(.f64 eps (-.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 eps (.f64 eps eps)))) (.f64 (/.f64 (.f64 x x) (sqrt.f64 #s(literal -1 binary64))) #s(literal -1/2 binary64)) (/.f64 x eps)) (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)))))
(* eps (- (+ (* 1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (/ x eps)) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(.f64 eps (-.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 5 binary64)))) (.f64 (/.f64 (.f64 (.f64 x x) (.f64 x x)) (neg.f64 (sqrt.f64 #s(literal -1 binary64)))) #s(literal 1/8 binary64)) (/.f64 x eps)) (fma.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 eps (.f64 eps eps)))) (.f64 (/.f64 (.f64 x x) (sqrt.f64 #s(literal -1 binary64))) #s(literal 1/2 binary64))))))
(* (sqrt eps) (sqrt -1))
(*.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64)))
(* -1 (* eps (- (* -1 (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(.f64 eps (+.f64 (/.f64 x eps) (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)))))
(* -1 (* eps (- (* -1 (/ (+ x (* 1/2 (* (sqrt (/ 1 eps)) (* (pow x 2) (sqrt -1))))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(.f64 eps (+.f64 (/.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (.f64 (.f64 x (.f64 (sqrt.f64 #s(literal -1 binary64)) x)) #s(literal 1/2 binary64)) x) eps) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)))))
(* -1 (* eps (- (* -1 (/ (+ x (* -1 (/ (- (* 1/8 (* (sqrt (/ 1 eps)) (* (pow x 4) (sqrt -1)))) (* 1/2 (* (sqrt eps) (* (pow x 2) (sqrt -1))))) eps))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(.f64 eps (+.f64 (/.f64 (-.f64 x (/.f64 (fma.f64 #s(literal -1/2 binary64) (.f64 (sqrt.f64 eps) (.f64 x (.f64 (sqrt.f64 #s(literal -1 binary64)) x))) (.f64 #s(literal 1/8 binary64) (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)))))) eps)) eps) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)))))
(* (sqrt eps) (sqrt -1))
(*.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64)))
(+ (* 1/2 (* (sqrt (/ 1 eps)) (/ (pow x 2) (sqrt -1)))) (* (sqrt eps) (sqrt -1)))
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (.f64 (/.f64 (.f64 x x) (sqrt.f64 #s(literal -1 binary64))) #s(literal 1/2 binary64)) (*.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64))))
(+ (* (sqrt eps) (sqrt -1)) (* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))))))
(fma.f64 (.f64 x x) (fma.f64 (/.f64 (.f64 x x) (neg.f64 (sqrt.f64 #s(literal -1 binary64)))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 eps (.f64 eps eps)))) #s(literal -1/8 binary64)) (.f64 #s(literal 1/2 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64))))) (*.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64))))
(+ (* (sqrt eps) (sqrt -1)) (* (pow x 2) (+ (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))) (* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3)))) (* 1/16 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 2) (pow (sqrt -1) 5)))))))))
(fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 #s(literal 1/16 binary64) (/.f64 (.f64 (.f64 x x) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 5 binary64))))) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64))) (/.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 eps (.f64 eps eps)))) #s(literal -1/8 binary64)) (neg.f64 (sqrt.f64 #s(literal -1 binary64))))) (.f64 #s(literal 1/2 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64))))) (*.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64))))
x
(* x (+ 1 (* -1/2 (/ eps (pow x 2)))))
(fma.f64 (/.f64 eps (.f64 x x)) (.f64 #s(literal -1/2 binary64) x) x)
(* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4))))))
(fma.f64 x (fma.f64 #s(literal -1/8 binary64) (/.f64 (.f64 eps eps) (.f64 (.f64 x x) (.f64 x x))) (/.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 x x))) x)
(* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/8 (/ (pow eps 2) (pow x 4))) (* -1/16 (/ (pow eps 3) (pow x 6)))))))
(fma.f64 x (fma.f64 eps (/.f64 #s(literal -1/2 binary64) (.f64 x x)) (fma.f64 #s(literal -1/8 binary64) (/.f64 (.f64 eps eps) (.f64 (.f64 x x) (.f64 x x))) (/.f64 (.f64 (.f64 eps (.f64 eps eps)) #s(literal -1/16 binary64)) (pow.f64 x #s(literal 6 binary64))))) x)
(* -1 x)
(neg.f64 x)
(* -1 (* x (+ 1 (* -1/2 (/ eps (pow x 2))))))
(.f64 x (fma.f64 eps (/.f64 #s(literal 1/2 binary64) (.f64 x x)) #s(literal -1 binary64)))
(* -1 (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4)))))))
(.f64 x (fma.f64 #s(literal 1/8 binary64) (/.f64 (.f64 eps eps) (.f64 (.f64 x x) (.f64 x x))) (fma.f64 eps (/.f64 #s(literal 1/2 binary64) (.f64 x x)) #s(literal -1 binary64))))
(* -1 (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/8 (/ (pow eps 2) (pow x 4))) (* -1/16 (/ (pow eps 3) (pow x 6))))))))
(neg.f64 (fma.f64 x (fma.f64 eps (/.f64 #s(literal -1/2 binary64) (.f64 x x)) (fma.f64 #s(literal -1/8 binary64) (/.f64 (.f64 eps eps) (.f64 (.f64 x x) (.f64 x x))) (/.f64 (.f64 (.f64 eps (.f64 eps eps)) #s(literal -1/16 binary64)) (pow.f64 x #s(literal 6 binary64))))) x))
x
(+ x (* -1/2 (/ eps x)))
(fma.f64 eps (/.f64 #s(literal -1/2 binary64) x) x)
(+ x (* eps (- (* -1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))))
(fma.f64 eps (/.f64 (fma.f64 eps (/.f64 #s(literal -1/8 binary64) (*.f64 x x)) #s(literal -1/2 binary64)) x) x)
(+ x (* eps (- (* eps (- (* -1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))))
(fma.f64 eps (fma.f64 eps (fma.f64 #s(literal -1/16 binary64) (/.f64 eps (pow.f64 x #s(literal 5 binary64))) (/.f64 #s(literal -1/8 binary64) (.f64 x (.f64 x x)))) (/.f64 #s(literal -1/2 binary64) x)) x)
(* (sqrt eps) (sqrt -1))
(*.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64)))
(* eps (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))
(.f64 eps (fma.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 eps (.f64 eps eps)))) (.f64 (/.f64 (.f64 x x) (sqrt.f64 #s(literal -1 binary64))) #s(literal 1/2 binary64)))))
(* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(.f64 eps (fma.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 eps (.f64 eps eps)))) (.f64 (/.f64 (.f64 x x) (sqrt.f64 #s(literal -1 binary64))) #s(literal 1/2 binary64)) (.f64 (/.f64 (.f64 (.f64 x x) (.f64 x x)) (neg.f64 (sqrt.f64 #s(literal -1 binary64)))) (.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 5 binary64)))))))))
(* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow eps 7))) (/ (pow x 6) (pow (sqrt -1) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))))
(.f64 eps (fma.f64 #s(literal 1/16 binary64) (/.f64 (.f64 (pow.f64 x #s(literal 6 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 7 binary64))))) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64))) (fma.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 eps (.f64 eps eps)))) (.f64 (/.f64 (.f64 x x) (sqrt.f64 #s(literal -1 binary64))) #s(literal 1/2 binary64)) (.f64 (/.f64 (.f64 (.f64 x x) (.f64 x x)) (neg.f64 (sqrt.f64 #s(literal -1 binary64)))) (*.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 5 binary64))))))))))
(* -1 (* (sqrt eps) (sqrt -1)))
(*.f64 (sqrt.f64 eps) (neg.f64 (sqrt.f64 #s(literal -1 binary64))))
(* -1 (* eps (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(.f64 eps (-.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 eps (.f64 eps eps)))) (.f64 (.f64 x (.f64 (sqrt.f64 #s(literal -1 binary64)) x)) #s(literal -1/2 binary64))) (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)))))
(* -1 (* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (* (pow x 4) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))))
(.f64 eps (fma.f64 #s(literal 1/8 binary64) (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 5 binary64)))))) (-.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 eps (.f64 eps eps)))) (.f64 (.f64 x (.f64 (sqrt.f64 #s(literal -1 binary64)) x)) #s(literal -1/2 binary64))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))))))
(* -1 (* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (* (pow x 4) (sqrt -1)))) (+ (* 1/16 (* (sqrt (/ 1 (pow eps 7))) (* (pow x 6) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))))
(.f64 (fma.f64 #s(literal 1/16 binary64) (.f64 (sqrt.f64 #s(literal -1 binary64)) (.f64 (pow.f64 x #s(literal 6 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 7 binary64)))))) (fma.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) (.f64 (.f64 x x) (.f64 x x))) (.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 5 binary64))))) (fma.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 eps (.f64 eps eps)))) (.f64 (.f64 x (.f64 (sqrt.f64 #s(literal -1 binary64)) x)) #s(literal 1/2 binary64)))))) (neg.f64 eps))
(* -1 eps)
(neg.f64 eps)
(- (pow x 2) eps)
(-.f64 (*.f64 x x) eps)
(- (pow x 2) eps)
(-.f64 (*.f64 x x) eps)
(- (pow x 2) eps)
(-.f64 (*.f64 x x) eps)
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))
(.f64 (.f64 x x) (-.f64 #s(literal 1 binary64) (/.f64 eps (*.f64 x x))))
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))
(.f64 (.f64 x x) (-.f64 #s(literal 1 binary64) (/.f64 eps (*.f64 x x))))
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))
(.f64 (.f64 x x) (-.f64 #s(literal 1 binary64) (/.f64 eps (*.f64 x x))))
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))
(.f64 (.f64 x x) (-.f64 #s(literal 1 binary64) (/.f64 eps (*.f64 x x))))
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))
(.f64 (.f64 x x) (-.f64 #s(literal 1 binary64) (/.f64 eps (*.f64 x x))))
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))
(.f64 (.f64 x x) (-.f64 #s(literal 1 binary64) (/.f64 eps (*.f64 x x))))
(pow x 2)
(*.f64 x x)
(+ (* -1 eps) (pow x 2))
(-.f64 (*.f64 x x) eps)
(+ (* -1 eps) (pow x 2))
(-.f64 (*.f64 x x) eps)
(+ (* -1 eps) (pow x 2))
(-.f64 (*.f64 x x) eps)
(* -1 eps)
(neg.f64 eps)
(* eps (- (/ (pow x 2) eps) 1))
(*.f64 eps (fma.f64 x (/.f64 x eps) #s(literal -1 binary64)))
(* eps (- (/ (pow x 2) eps) 1))
(*.f64 eps (fma.f64 x (/.f64 x eps) #s(literal -1 binary64)))
(* eps (- (/ (pow x 2) eps) 1))
(*.f64 eps (fma.f64 x (/.f64 x eps) #s(literal -1 binary64)))
(* -1 eps)
(neg.f64 eps)
(* -1 (* eps (+ 1 (* -1 (/ (pow x 2) eps)))))
(*.f64 eps (fma.f64 x (/.f64 x eps) #s(literal -1 binary64)))
(* -1 (* eps (+ 1 (* -1 (/ (pow x 2) eps)))))
(*.f64 eps (fma.f64 x (/.f64 x eps) #s(literal -1 binary64)))
(* -1 (* eps (+ 1 (* -1 (/ (pow x 2) eps)))))
(*.f64 eps (fma.f64 x (/.f64 x eps) #s(literal -1 binary64)))
(* -1 eps)
(neg.f64 eps)
(* -1 eps)
(neg.f64 eps)
(* -1 eps)
(neg.f64 eps)
(* -1 eps)
(neg.f64 eps)
(* -1 eps)
(neg.f64 eps)
(* -1 eps)
(neg.f64 eps)
(* -1 eps)
(neg.f64 eps)
(* -1 eps)
(neg.f64 eps)
(* -1 eps)
(neg.f64 eps)
(* -1 eps)
(neg.f64 eps)
(* -1 eps)
(neg.f64 eps)
(* -1 eps)
(neg.f64 eps)
0
#s(literal 0 binary64)
0
#s(literal 0 binary64)
0
#s(literal 0 binary64)
0
#s(literal 0 binary64)
0
#s(literal 0 binary64)
0
#s(literal 0 binary64)
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#s(literal 0 binary64)
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#s(literal 0 binary64)
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#s(literal 0 binary64)
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#s(literal 0 binary64)
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(* 1/2 (/ eps x))
(/.f64 (*.f64 eps #s(literal 1/2 binary64)) x)
(* 1/2 (/ eps x))
(/.f64 (*.f64 eps #s(literal 1/2 binary64)) x)
(* 1/2 (/ eps x))
(/.f64 (*.f64 eps #s(literal 1/2 binary64)) x)
(* 1/2 (/ eps x))
(/.f64 (*.f64 eps #s(literal 1/2 binary64)) x)
(* 1/2 (/ eps x))
(/.f64 (*.f64 eps #s(literal 1/2 binary64)) x)
(* 1/2 (/ eps x))
(/.f64 (*.f64 eps #s(literal 1/2 binary64)) x)
(* 1/2 (/ eps x))
(/.f64 (*.f64 eps #s(literal 1/2 binary64)) x)
(* 1/2 (/ eps x))
(/.f64 (*.f64 eps #s(literal 1/2 binary64)) x)
(* 1/2 (/ eps x))
(/.f64 (*.f64 eps #s(literal 1/2 binary64)) x)
(* 1/2 (/ eps x))
(/.f64 (*.f64 eps #s(literal 1/2 binary64)) x)
(* 1/2 (/ eps x))
(/.f64 (*.f64 eps #s(literal 1/2 binary64)) x)
(* 1/2 (/ eps x))
(/.f64 (*.f64 eps #s(literal 1/2 binary64)) x)
(* 1/2 (/ eps x))
(/.f64 (*.f64 eps #s(literal 1/2 binary64)) x)
(* 1/2 (/ eps x))
(/.f64 (*.f64 eps #s(literal 1/2 binary64)) x)
(* 1/2 (/ eps x))
(/.f64 (*.f64 eps #s(literal 1/2 binary64)) x)
(* 1/2 (/ eps x))
(/.f64 (*.f64 eps #s(literal 1/2 binary64)) x)
(* 1/2 (/ eps x))
(/.f64 (*.f64 eps #s(literal 1/2 binary64)) x)
(* 1/2 (/ eps x))
(/.f64 (*.f64 eps #s(literal 1/2 binary64)) x)
(* 1/2 (/ eps x))
(/.f64 (*.f64 eps #s(literal 1/2 binary64)) x)
(* 1/2 (/ eps x))
(/.f64 (*.f64 eps #s(literal 1/2 binary64)) x)
(* 1/2 (/ eps x))
(/.f64 (*.f64 eps #s(literal 1/2 binary64)) x)
(* 1/2 (/ eps x))
(/.f64 (*.f64 eps #s(literal 1/2 binary64)) x)
(* 1/2 (/ eps x))
(/.f64 (*.f64 eps #s(literal 1/2 binary64)) x)
(* 1/2 (/ eps x))
(/.f64 (*.f64 eps #s(literal 1/2 binary64)) x)
(* 1/2 eps)
(*.f64 eps #s(literal 1/2 binary64))
(* 1/2 eps)
(*.f64 eps #s(literal 1/2 binary64))
(* 1/2 eps)
(*.f64 eps #s(literal 1/2 binary64))
(* 1/2 eps)
(*.f64 eps #s(literal 1/2 binary64))
(* 1/2 eps)
(*.f64 eps #s(literal 1/2 binary64))
(* 1/2 eps)
(*.f64 eps #s(literal 1/2 binary64))
(* 1/2 eps)
(*.f64 eps #s(literal 1/2 binary64))
(* 1/2 eps)
(*.f64 eps #s(literal 1/2 binary64))
(* 1/2 eps)
(*.f64 eps #s(literal 1/2 binary64))
(* 1/2 eps)
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(* 1/2 eps)
(*.f64 eps #s(literal 1/2 binary64))
(* 1/2 eps)
(*.f64 eps #s(literal 1/2 binary64))
(* -1 (* (sqrt eps) (sqrt -1)))
(*.f64 (sqrt.f64 eps) (neg.f64 (sqrt.f64 #s(literal -1 binary64))))
(- x (* (sqrt eps) (sqrt -1)))
(fma.f64 (sqrt.f64 eps) (neg.f64 (sqrt.f64 #s(literal -1 binary64))) x)
(- (* x (+ 1 (* -1/2 (* (sqrt (/ 1 eps)) (/ x (sqrt -1)))))) (* (sqrt eps) (sqrt -1)))
(-.f64 (fma.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (/.f64 x (sqrt.f64 #s(literal -1 binary64)))) (.f64 #s(literal -1/2 binary64) x) x) (*.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64))))
(- (* x (+ 1 (* x (- (* 1/8 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))))))) (* (sqrt eps) (sqrt -1)))
(-.f64 (fma.f64 (.f64 x x) (fma.f64 #s(literal -1/2 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64))) (.f64 (.f64 #s(literal 1/8 binary64) (/.f64 (.f64 x x) (neg.f64 (sqrt.f64 #s(literal -1 binary64))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 eps (.f64 eps eps)))))) x) (*.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64))))
(* 1/2 (/ eps x))
(/.f64 (*.f64 eps #s(literal 1/2 binary64)) x)
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(.f64 eps (fma.f64 eps (fma.f64 eps (fma.f64 #s(literal 5/128 binary64) (/.f64 eps (pow.f64 x #s(literal 7 binary64))) (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 5 binary64)))) (/.f64 #s(literal 1/8 binary64) (.f64 x (*.f64 x x)))) (/.f64 #s(literal 1/2 binary64) x)))
(* -1 (* (sqrt eps) (sqrt -1)))
(*.f64 (sqrt.f64 eps) (neg.f64 (sqrt.f64 #s(literal -1 binary64))))
(* eps (- (/ x eps) (* (sqrt (/ 1 eps)) (sqrt -1))))
(.f64 eps (-.f64 (/.f64 x eps) (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)))))
(* eps (- (+ (* -1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1))))
(.f64 eps (-.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 eps (.f64 eps eps)))) (.f64 (/.f64 (.f64 x x) (sqrt.f64 #s(literal -1 binary64))) #s(literal -1/2 binary64)) (/.f64 x eps)) (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)))))
(* eps (- (+ (* 1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (/ x eps)) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(.f64 eps (-.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 5 binary64)))) (.f64 (/.f64 (.f64 (.f64 x x) (.f64 x x)) (neg.f64 (sqrt.f64 #s(literal -1 binary64)))) #s(literal 1/8 binary64)) (/.f64 x eps)) (fma.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 eps (.f64 eps eps)))) (.f64 (/.f64 (.f64 x x) (sqrt.f64 #s(literal -1 binary64))) #s(literal 1/2 binary64))))))
(* (sqrt eps) (sqrt -1))
(*.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64)))
(* -1 (* eps (- (* -1 (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(.f64 eps (+.f64 (/.f64 x eps) (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)))))
(* -1 (* eps (- (* -1 (/ (+ x (* 1/2 (* (sqrt (/ 1 eps)) (* (pow x 2) (sqrt -1))))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(.f64 eps (+.f64 (/.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (.f64 (.f64 x (.f64 (sqrt.f64 #s(literal -1 binary64)) x)) #s(literal 1/2 binary64)) x) eps) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)))))
(* -1 (* eps (- (* -1 (/ (+ x (* -1 (/ (- (* 1/8 (* (sqrt (/ 1 eps)) (* (pow x 4) (sqrt -1)))) (* 1/2 (* (sqrt eps) (* (pow x 2) (sqrt -1))))) eps))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(.f64 eps (+.f64 (/.f64 (-.f64 x (/.f64 (fma.f64 #s(literal -1/2 binary64) (.f64 (sqrt.f64 eps) (.f64 x (.f64 (sqrt.f64 #s(literal -1 binary64)) x))) (.f64 #s(literal 1/8 binary64) (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)))))) eps)) eps) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)))))
(* (sqrt eps) (sqrt -1))
(*.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64)))
(+ (* 1/2 (* (sqrt (/ 1 eps)) (/ (pow x 2) (sqrt -1)))) (* (sqrt eps) (sqrt -1)))
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (.f64 (/.f64 (.f64 x x) (sqrt.f64 #s(literal -1 binary64))) #s(literal 1/2 binary64)) (*.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64))))
(+ (* (sqrt eps) (sqrt -1)) (* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))))))
(fma.f64 (.f64 x x) (fma.f64 (/.f64 (.f64 x x) (neg.f64 (sqrt.f64 #s(literal -1 binary64)))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 eps (.f64 eps eps)))) #s(literal -1/8 binary64)) (.f64 #s(literal 1/2 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64))))) (*.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64))))
(+ (* (sqrt eps) (sqrt -1)) (* (pow x 2) (+ (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))) (* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3)))) (* 1/16 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 2) (pow (sqrt -1) 5)))))))))
(fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 #s(literal 1/16 binary64) (/.f64 (.f64 (.f64 x x) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 5 binary64))))) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64))) (/.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 eps (.f64 eps eps)))) #s(literal -1/8 binary64)) (neg.f64 (sqrt.f64 #s(literal -1 binary64))))) (.f64 #s(literal 1/2 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64))))) (*.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64))))
x
(* x (+ 1 (* -1/2 (/ eps (pow x 2)))))
(fma.f64 (/.f64 eps (.f64 x x)) (.f64 #s(literal -1/2 binary64) x) x)
(* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4))))))
(fma.f64 x (fma.f64 #s(literal -1/8 binary64) (/.f64 (.f64 eps eps) (.f64 (.f64 x x) (.f64 x x))) (/.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 x x))) x)
(* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/8 (/ (pow eps 2) (pow x 4))) (* -1/16 (/ (pow eps 3) (pow x 6)))))))
(fma.f64 x (fma.f64 eps (/.f64 #s(literal -1/2 binary64) (.f64 x x)) (fma.f64 #s(literal -1/8 binary64) (/.f64 (.f64 eps eps) (.f64 (.f64 x x) (.f64 x x))) (/.f64 (.f64 (.f64 eps (.f64 eps eps)) #s(literal -1/16 binary64)) (pow.f64 x #s(literal 6 binary64))))) x)
(* -1 x)
(neg.f64 x)
(* -1 (* x (+ 1 (* -1/2 (/ eps (pow x 2))))))
(.f64 x (fma.f64 eps (/.f64 #s(literal 1/2 binary64) (.f64 x x)) #s(literal -1 binary64)))
(* -1 (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4)))))))
(.f64 x (fma.f64 #s(literal 1/8 binary64) (/.f64 (.f64 eps eps) (.f64 (.f64 x x) (.f64 x x))) (fma.f64 eps (/.f64 #s(literal 1/2 binary64) (.f64 x x)) #s(literal -1 binary64))))
(* -1 (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/8 (/ (pow eps 2) (pow x 4))) (* -1/16 (/ (pow eps 3) (pow x 6))))))))
(neg.f64 (fma.f64 x (fma.f64 eps (/.f64 #s(literal -1/2 binary64) (.f64 x x)) (fma.f64 #s(literal -1/8 binary64) (/.f64 (.f64 eps eps) (.f64 (.f64 x x) (.f64 x x))) (/.f64 (.f64 (.f64 eps (.f64 eps eps)) #s(literal -1/16 binary64)) (pow.f64 x #s(literal 6 binary64))))) x))
x
(+ x (* -1/2 (/ eps x)))
(fma.f64 eps (/.f64 #s(literal -1/2 binary64) x) x)
(+ x (* eps (- (* -1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))))
(fma.f64 eps (/.f64 (fma.f64 eps (/.f64 #s(literal -1/8 binary64) (*.f64 x x)) #s(literal -1/2 binary64)) x) x)
(+ x (* eps (- (* eps (- (* -1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))))
(fma.f64 eps (fma.f64 eps (fma.f64 #s(literal -1/16 binary64) (/.f64 eps (pow.f64 x #s(literal 5 binary64))) (/.f64 #s(literal -1/8 binary64) (.f64 x (.f64 x x)))) (/.f64 #s(literal -1/2 binary64) x)) x)
(* (sqrt eps) (sqrt -1))
(*.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64)))
(* eps (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))
(.f64 eps (fma.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 eps (.f64 eps eps)))) (.f64 (/.f64 (.f64 x x) (sqrt.f64 #s(literal -1 binary64))) #s(literal 1/2 binary64)))))
(* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(.f64 eps (fma.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 eps (.f64 eps eps)))) (.f64 (/.f64 (.f64 x x) (sqrt.f64 #s(literal -1 binary64))) #s(literal 1/2 binary64)) (.f64 (/.f64 (.f64 (.f64 x x) (.f64 x x)) (neg.f64 (sqrt.f64 #s(literal -1 binary64)))) (.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 5 binary64)))))))))
(* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow eps 7))) (/ (pow x 6) (pow (sqrt -1) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))))
(.f64 eps (fma.f64 #s(literal 1/16 binary64) (/.f64 (.f64 (pow.f64 x #s(literal 6 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 7 binary64))))) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64))) (fma.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 eps (.f64 eps eps)))) (.f64 (/.f64 (.f64 x x) (sqrt.f64 #s(literal -1 binary64))) #s(literal 1/2 binary64)) (.f64 (/.f64 (.f64 (.f64 x x) (.f64 x x)) (neg.f64 (sqrt.f64 #s(literal -1 binary64)))) (*.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 5 binary64))))))))))
(* -1 (* (sqrt eps) (sqrt -1)))
(*.f64 (sqrt.f64 eps) (neg.f64 (sqrt.f64 #s(literal -1 binary64))))
(* -1 (* eps (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(.f64 eps (-.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 eps (.f64 eps eps)))) (.f64 (.f64 x (.f64 (sqrt.f64 #s(literal -1 binary64)) x)) #s(literal -1/2 binary64))) (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)))))
(* -1 (* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (* (pow x 4) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))))
(.f64 eps (fma.f64 #s(literal 1/8 binary64) (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 5 binary64)))))) (-.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 eps (.f64 eps eps)))) (.f64 (.f64 x (.f64 (sqrt.f64 #s(literal -1 binary64)) x)) #s(literal -1/2 binary64))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))))))
(* -1 (* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (* (pow x 4) (sqrt -1)))) (+ (* 1/16 (* (sqrt (/ 1 (pow eps 7))) (* (pow x 6) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))))
(.f64 (fma.f64 #s(literal 1/16 binary64) (.f64 (sqrt.f64 #s(literal -1 binary64)) (.f64 (pow.f64 x #s(literal 6 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 7 binary64)))))) (fma.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) (.f64 (.f64 x x) (.f64 x x))) (.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 5 binary64))))) (fma.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 eps (.f64 eps eps)))) (.f64 (.f64 x (.f64 (sqrt.f64 #s(literal -1 binary64)) x)) #s(literal 1/2 binary64)))))) (neg.f64 eps))
(* -1 (* (sqrt eps) (sqrt -1)))
(*.f64 (sqrt.f64 eps) (neg.f64 (sqrt.f64 #s(literal -1 binary64))))
(- x (* (sqrt eps) (sqrt -1)))
(fma.f64 (sqrt.f64 eps) (neg.f64 (sqrt.f64 #s(literal -1 binary64))) x)
(- (* x (+ 1 (* -1/2 (* (sqrt (/ 1 eps)) (/ x (sqrt -1)))))) (* (sqrt eps) (sqrt -1)))
(-.f64 (fma.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (/.f64 x (sqrt.f64 #s(literal -1 binary64)))) (.f64 #s(literal -1/2 binary64) x) x) (*.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64))))
(- (* x (+ 1 (* x (- (* 1/8 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))))))) (* (sqrt eps) (sqrt -1)))
(-.f64 (fma.f64 (.f64 x x) (fma.f64 #s(literal -1/2 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64))) (.f64 (.f64 #s(literal 1/8 binary64) (/.f64 (.f64 x x) (neg.f64 (sqrt.f64 #s(literal -1 binary64))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 eps (.f64 eps eps)))))) x) (*.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64))))
(* 1/2 (/ eps x))
(/.f64 (*.f64 eps #s(literal 1/2 binary64)) x)
(/ (- (* 1/8 (/ (pow eps 2) (pow x 2))) (* -1/2 eps)) x)
(/.f64 (fma.f64 #s(literal 1/8 binary64) (/.f64 (.f64 eps eps) (.f64 x x)) (*.f64 eps #s(literal 1/2 binary64))) x)
(/ (- (* 1/16 (/ (pow eps 3) (pow x 4))) (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2))))) x)
(/.f64 (fma.f64 #s(literal 1/16 binary64) (/.f64 (.f64 eps (.f64 eps eps)) (.f64 (.f64 x x) (.f64 x x))) (fma.f64 #s(literal 1/8 binary64) (/.f64 (.f64 eps eps) (.f64 x x)) (.f64 eps #s(literal 1/2 binary64)))) x)
(/ (- (* 1/2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) (pow x 6))) (+ (* -1/2 eps) (+ (* -1/8 (/ (pow eps 2) (pow x 2))) (* -1/16 (/ (pow eps 3) (pow x 4)))))) x)
(/.f64 (fma.f64 #s(literal 1/2 binary64) (/.f64 (.f64 (pow.f64 eps #s(literal 4 binary64)) #s(literal 5/64 binary64)) (pow.f64 x #s(literal 6 binary64))) (fma.f64 #s(literal 1/16 binary64) (/.f64 (.f64 eps (.f64 eps eps)) (.f64 (.f64 x x) (.f64 x x))) (fma.f64 #s(literal 1/8 binary64) (/.f64 (.f64 eps eps) (.f64 x x)) (*.f64 eps #s(literal 1/2 binary64))))) x)
(* -1 (* x (- (pow (sqrt -1) 2) 1)))
(+.f64 x x)
(* -1 (* x (- (+ (* 1/2 (/ eps (pow x 2))) (pow (sqrt -1) 2)) 1)))
(fma.f64 x (fma.f64 eps (/.f64 #s(literal -1/2 binary64) (*.f64 x x)) #s(literal 1 binary64)) x)
(* -1 (* x (- (+ (* 1/8 (/ (pow eps 2) (pow x 4))) (pow (sqrt -1) 2)) (+ 1 (* -1/2 (/ eps (pow x 2)))))))
(.f64 x (neg.f64 (fma.f64 #s(literal 1/8 binary64) (/.f64 (.f64 eps eps) (.f64 (.f64 x x) (.f64 x x))) (fma.f64 eps (/.f64 #s(literal 1/2 binary64) (.f64 x x)) #s(literal -2 binary64)))))
(* -1 (* x (- (+ (* 1/16 (/ (pow eps 3) (pow x 6))) (pow (sqrt -1) 2)) (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4))))))))
(.f64 (fma.f64 #s(literal 1/16 binary64) (/.f64 (.f64 eps (.f64 eps eps)) (pow.f64 x #s(literal 6 binary64))) (fma.f64 #s(literal 1/8 binary64) (/.f64 (.f64 eps eps) (.f64 (.f64 x x) (.f64 x x))) (fma.f64 eps (/.f64 #s(literal 1/2 binary64) (.f64 x x)) #s(literal -2 binary64)))) (neg.f64 x))
(* 1/2 (/ eps x))
(/.f64 (*.f64 eps #s(literal 1/2 binary64)) x)
(* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))
(/.f64 (fma.f64 #s(literal 1/8 binary64) (/.f64 (.f64 eps eps) (.f64 x x)) (*.f64 eps #s(literal 1/2 binary64))) x)
(* eps (+ (* eps (+ (* 1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))
(.f64 eps (fma.f64 eps (fma.f64 #s(literal 1/16 binary64) (/.f64 eps (pow.f64 x #s(literal 5 binary64))) (/.f64 #s(literal 1/8 binary64) (.f64 x (*.f64 x x)))) (/.f64 #s(literal 1/2 binary64) x)))
(* eps (+ (* eps (+ (* eps (+ (* 5/128 (/ eps (pow x 7))) (* 1/16 (/ 1 (pow x 5))))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))
(.f64 eps (fma.f64 eps (fma.f64 eps (fma.f64 #s(literal 5/128 binary64) (/.f64 eps (pow.f64 x #s(literal 7 binary64))) (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 5 binary64)))) (/.f64 #s(literal 1/8 binary64) (.f64 x (*.f64 x x)))) (/.f64 #s(literal 1/2 binary64) x)))
(* -1 (* (sqrt eps) (sqrt -1)))
(*.f64 (sqrt.f64 eps) (neg.f64 (sqrt.f64 #s(literal -1 binary64))))
(* eps (- (/ x eps) (* (sqrt (/ 1 eps)) (sqrt -1))))
(.f64 eps (-.f64 (/.f64 x eps) (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)))))
(* eps (- (+ (* -1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1))))
(.f64 eps (-.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 eps (.f64 eps eps)))) (.f64 (/.f64 (.f64 x x) (sqrt.f64 #s(literal -1 binary64))) #s(literal -1/2 binary64)) (/.f64 x eps)) (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)))))
(* eps (- (+ (* 1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (/ x eps)) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(.f64 eps (-.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 5 binary64)))) (.f64 (/.f64 (.f64 (.f64 x x) (.f64 x x)) (neg.f64 (sqrt.f64 #s(literal -1 binary64)))) #s(literal 1/8 binary64)) (/.f64 x eps)) (fma.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 eps (.f64 eps eps)))) (.f64 (/.f64 (.f64 x x) (sqrt.f64 #s(literal -1 binary64))) #s(literal 1/2 binary64))))))
(* (sqrt eps) (sqrt -1))
(*.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64)))
(* -1 (* eps (- (* -1 (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(.f64 eps (+.f64 (/.f64 x eps) (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)))))
(* -1 (* eps (- (* -1 (/ (+ x (* 1/2 (* (sqrt (/ 1 eps)) (* (pow x 2) (sqrt -1))))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(.f64 eps (+.f64 (/.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (.f64 (.f64 x (.f64 (sqrt.f64 #s(literal -1 binary64)) x)) #s(literal 1/2 binary64)) x) eps) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)))))
(* -1 (* eps (- (* -1 (/ (+ x (* -1 (/ (- (* 1/8 (* (sqrt (/ 1 eps)) (* (pow x 4) (sqrt -1)))) (* 1/2 (* (sqrt eps) (* (pow x 2) (sqrt -1))))) eps))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(.f64 eps (+.f64 (/.f64 (-.f64 x (/.f64 (fma.f64 #s(literal -1/2 binary64) (.f64 (sqrt.f64 eps) (.f64 x (.f64 (sqrt.f64 #s(literal -1 binary64)) x))) (.f64 #s(literal 1/8 binary64) (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)))))) eps)) eps) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)))))
(sqrt x)
(sqrt.f64 x)
(sqrt x)
(sqrt.f64 x)
(sqrt x)
(sqrt.f64 x)
(sqrt x)
(sqrt.f64 x)
(sqrt x)
(sqrt.f64 x)
(sqrt x)
(sqrt.f64 x)
(sqrt x)
(sqrt.f64 x)
(sqrt x)
(sqrt.f64 x)
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(sqrt.f64 x)
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(sqrt.f64 x)
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(sqrt.f64 x)
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(sqrt.f64 x)
(* -1 (* (sqrt eps) (sqrt -1)))
(*.f64 (sqrt.f64 eps) (neg.f64 (sqrt.f64 #s(literal -1 binary64))))
(- (* -1/2 (* (sqrt (/ 1 eps)) (/ (pow x 2) (sqrt -1)))) (* (sqrt eps) (sqrt -1)))
(fma.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (/.f64 x (sqrt.f64 #s(literal -1 binary64)))) (.f64 #s(literal -1/2 binary64) x) (*.f64 (sqrt.f64 eps) (neg.f64 (sqrt.f64 #s(literal -1 binary64)))))
(- (* (pow x 2) (- (* 1/8 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))))) (* (sqrt eps) (sqrt -1)))
(fma.f64 (.f64 x x) (fma.f64 #s(literal -1/2 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64))) (.f64 (.f64 #s(literal 1/8 binary64) (/.f64 (.f64 x x) (neg.f64 (sqrt.f64 #s(literal -1 binary64))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 eps (.f64 eps eps)))))) (*.f64 (sqrt.f64 eps) (neg.f64 (sqrt.f64 #s(literal -1 binary64)))))
(- (* (pow x 2) (- (* (pow x 2) (- (* -1/16 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 2) (pow (sqrt -1) 5)))) (* -1/8 (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3)))))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))))) (* (sqrt eps) (sqrt -1)))
(fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 #s(literal 1/8 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 eps (.f64 eps eps)))) (neg.f64 (sqrt.f64 #s(literal -1 binary64)))) (/.f64 (.f64 #s(literal -1/16 binary64) (.f64 (.f64 x x) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 5 binary64)))))) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64)))) (.f64 #s(literal -1/2 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64))))) (*.f64 (sqrt.f64 eps) (neg.f64 (sqrt.f64 #s(literal -1 binary64)))))
(* -1 x)
(neg.f64 x)
(* x (- (* 1/2 (/ eps (pow x 2))) 1))
(.f64 x (fma.f64 eps (/.f64 #s(literal 1/2 binary64) (.f64 x x)) #s(literal -1 binary64)))
(* x (- (* 1/8 (/ (pow eps 2) (pow x 4))) (+ 1 (* -1/2 (/ eps (pow x 2))))))
(.f64 x (fma.f64 #s(literal 1/8 binary64) (/.f64 (.f64 eps eps) (.f64 (.f64 x x) (.f64 x x))) (fma.f64 eps (/.f64 #s(literal 1/2 binary64) (.f64 x x)) #s(literal -1 binary64))))
(* x (- (* 1/16 (/ (pow eps 3) (pow x 6))) (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4)))))))
(.f64 x (fma.f64 #s(literal 1/16 binary64) (/.f64 (.f64 eps (.f64 eps eps)) (pow.f64 x #s(literal 6 binary64))) (fma.f64 #s(literal 1/8 binary64) (/.f64 (.f64 eps eps) (.f64 (.f64 x x) (.f64 x x))) (fma.f64 eps (/.f64 #s(literal 1/2 binary64) (.f64 x x)) #s(literal -1 binary64)))))
x
(* -1 (* x (- (* 1/2 (/ eps (pow x 2))) 1)))
(fma.f64 (/.f64 eps (.f64 x x)) (.f64 #s(literal -1/2 binary64) x) x)
(* -1 (* x (- (* 1/8 (/ (pow eps 2) (pow x 4))) (+ 1 (* -1/2 (/ eps (pow x 2)))))))
(fma.f64 x (fma.f64 #s(literal -1/8 binary64) (/.f64 (.f64 eps eps) (.f64 (.f64 x x) (.f64 x x))) (/.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 x x))) x)
(* -1 (* x (- (* 1/16 (/ (pow eps 3) (pow x 6))) (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4))))))))
(.f64 (fma.f64 #s(literal 1/16 binary64) (/.f64 (.f64 eps (.f64 eps eps)) (pow.f64 x #s(literal 6 binary64))) (fma.f64 #s(literal 1/8 binary64) (/.f64 (.f64 eps eps) (.f64 (.f64 x x) (.f64 x x))) (fma.f64 eps (/.f64 #s(literal 1/2 binary64) (.f64 x x)) #s(literal -1 binary64)))) (neg.f64 x))
(* -1 x)
(neg.f64 x)
(- (* 1/2 (/ eps x)) x)
(-.f64 (/.f64 (*.f64 eps #s(literal 1/2 binary64)) x) x)
(- (* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))) x)
(fma.f64 eps (fma.f64 eps (/.f64 #s(literal 1/8 binary64) (.f64 x (.f64 x x))) (/.f64 #s(literal 1/2 binary64) x)) (neg.f64 x))
(- (* eps (+ (* eps (+ (* 1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))) x)
(fma.f64 eps (fma.f64 eps (fma.f64 #s(literal 1/16 binary64) (/.f64 eps (pow.f64 x #s(literal 5 binary64))) (/.f64 #s(literal 1/8 binary64) (.f64 x (.f64 x x)))) (/.f64 #s(literal 1/2 binary64) x)) (neg.f64 x))
(* -1 (* (sqrt eps) (sqrt -1)))
(*.f64 (sqrt.f64 eps) (neg.f64 (sqrt.f64 #s(literal -1 binary64))))
(* eps (- (* -1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))
(.f64 eps (fma.f64 #s(literal -1/2 binary64) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 eps (.f64 eps eps)))) (/.f64 (.f64 x x) (sqrt.f64 #s(literal -1 binary64)))) (neg.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))))))
(* eps (- (* 1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(neg.f64 (.f64 eps (fma.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 eps (.f64 eps eps)))) (.f64 (/.f64 (.f64 x x) (sqrt.f64 #s(literal -1 binary64))) #s(literal 1/2 binary64)) (.f64 (/.f64 (.f64 (.f64 x x) (.f64 x x)) (neg.f64 (sqrt.f64 #s(literal -1 binary64)))) (.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 5 binary64))))))))))
(* eps (- (* -1/16 (* (sqrt (/ 1 (pow eps 7))) (/ (pow x 6) (pow (sqrt -1) 5)))) (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))))
(.f64 eps (-.f64 (.f64 #s(literal -1/16 binary64) (/.f64 (.f64 (pow.f64 x #s(literal 6 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 7 binary64))))) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64)))) (fma.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 eps (.f64 eps eps)))) (.f64 (/.f64 (.f64 x x) (sqrt.f64 #s(literal -1 binary64))) #s(literal 1/2 binary64)) (.f64 (/.f64 (.f64 (.f64 x x) (.f64 x x)) (neg.f64 (sqrt.f64 #s(literal -1 binary64)))) (.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 5 binary64))))))))))
(* (sqrt eps) (sqrt -1))
(*.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64)))
(* -1 (* eps (- (* -1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(.f64 (neg.f64 eps) (-.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 eps (.f64 eps eps)))) (.f64 (.f64 x (.f64 (sqrt.f64 #s(literal -1 binary64)) x)) #s(literal -1/2 binary64))) (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)))))
(* -1 (* eps (- (* 1/8 (* (sqrt (/ 1 (pow eps 5))) (* (pow x 4) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))))
(.f64 (neg.f64 eps) (fma.f64 #s(literal 1/8 binary64) (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 5 binary64)))))) (-.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 eps (.f64 eps eps)))) (.f64 (.f64 x (.f64 (sqrt.f64 #s(literal -1 binary64)) x)) #s(literal -1/2 binary64))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))))))
(* -1 (* eps (- (* -1/16 (* (sqrt (/ 1 (pow eps 7))) (* (pow x 6) (sqrt -1)))) (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (* (pow x 4) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))))
(.f64 (neg.f64 eps) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 7 binary64)))) (.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) (pow.f64 x #s(literal 6 binary64))) #s(literal -1/16 binary64)) (fma.f64 #s(literal 1/8 binary64) (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 5 binary64)))))) (-.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 eps (.f64 eps eps)))) (.f64 (.f64 x (.f64 (sqrt.f64 #s(literal -1 binary64)) x)) #s(literal -1/2 binary64))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)))))))
(* -1 eps)
(neg.f64 eps)
(- (pow x 2) eps)
(-.f64 (*.f64 x x) eps)
(- (pow x 2) eps)
(-.f64 (*.f64 x x) eps)
(- (pow x 2) eps)
(-.f64 (*.f64 x x) eps)
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))
(.f64 (.f64 x x) (-.f64 #s(literal 1 binary64) (/.f64 eps (*.f64 x x))))
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))
(.f64 (.f64 x x) (-.f64 #s(literal 1 binary64) (/.f64 eps (*.f64 x x))))
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))
(.f64 (.f64 x x) (-.f64 #s(literal 1 binary64) (/.f64 eps (*.f64 x x))))
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))
(.f64 (.f64 x x) (-.f64 #s(literal 1 binary64) (/.f64 eps (*.f64 x x))))
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))
(.f64 (.f64 x x) (-.f64 #s(literal 1 binary64) (/.f64 eps (*.f64 x x))))
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))
(.f64 (.f64 x x) (-.f64 #s(literal 1 binary64) (/.f64 eps (*.f64 x x))))
(pow x 2)
(*.f64 x x)
(+ (* -1 eps) (pow x 2))
(-.f64 (*.f64 x x) eps)
(+ (* -1 eps) (pow x 2))
(-.f64 (*.f64 x x) eps)
(+ (* -1 eps) (pow x 2))
(-.f64 (*.f64 x x) eps)
(* -1 eps)
(neg.f64 eps)
(* eps (- (/ (pow x 2) eps) 1))
(*.f64 eps (fma.f64 x (/.f64 x eps) #s(literal -1 binary64)))
(* eps (- (/ (pow x 2) eps) 1))
(*.f64 eps (fma.f64 x (/.f64 x eps) #s(literal -1 binary64)))
(* eps (- (/ (pow x 2) eps) 1))
(*.f64 eps (fma.f64 x (/.f64 x eps) #s(literal -1 binary64)))
(* -1 eps)
(neg.f64 eps)
(* -1 (* eps (+ 1 (* -1 (/ (pow x 2) eps)))))
(*.f64 eps (fma.f64 x (/.f64 x eps) #s(literal -1 binary64)))
(* -1 (* eps (+ 1 (* -1 (/ (pow x 2) eps)))))
(*.f64 eps (fma.f64 x (/.f64 x eps) #s(literal -1 binary64)))
(* -1 (* eps (+ 1 (* -1 (/ (pow x 2) eps)))))
(*.f64 eps (fma.f64 x (/.f64 x eps) #s(literal -1 binary64)))

eval104.0ms (1%)

Memory: -20.8MiB live, 257.7MiB allocated
Compiler: Compiled 15 248 to 1 224 computations (92% saved)

prune66.0ms (0.7%)

Memory

-2.9MiB live, 199.0MiB allocated

Pruning

12 alts after pruning (9 fresh and 3 done)

	Pruned	Kept	Total
New	777	5	782
Fresh	5	4	9
Picked	2	3	5
Done	0	0	0
Total	784	12	796

Accuracy

100.0%

Counts

796 → 12

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	45.6%	(/.f64 (*.f64 eps #s(literal 1/2 binary64)) x)
▶	44.9%	(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 eps (/.f64 (fma.f64 eps (/.f64 #s(literal -1/8 binary64) (*.f64 x x)) #s(literal -1/2 binary64)) x) (+.f64 x x)) eps))
	46.1%	(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 eps (/.f64 #s(literal -1/2 binary64) x) (+.f64 x x)) eps))
✓	60.3%	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))))
▶	6.7%	(-.f64 x (fma.f64 eps (/.f64 #s(literal -1/2 binary64) x) x))
▶	60.0%	(-.f64 x (/.f64 (-.f64 (.f64 x x) eps) (sqrt.f64 (-.f64 (.f64 x x) eps))))
✓	60.4%	(-.f64 x (sqrt.f64 (fma.f64 x x (neg.f64 eps))))
▶	56.2%	(-.f64 x (sqrt.f64 (neg.f64 eps)))
	3.7%	(+.f64 x x)
	45.5%	(*.f64 (/.f64 #s(literal 1/2 binary64) x) eps)
	31.0%	(.f64 eps (fma.f64 eps (fma.f64 eps (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 5 binary64))) (/.f64 #s(literal 1/8 binary64) (.f64 x (*.f64 x x)))) (/.f64 #s(literal 1/2 binary64) x)))
▶	4.3%	#s(literal 0 binary64)

Compiler

Compiled 243 to 152 computations (37.4% saved)

simplify273.0ms (2.7%)

Memory

5.4MiB live, 254.8MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 14 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(/.f64 (fma.f64 eps (/.f64 #s(literal -1/8 binary64) (*.f64 x x)) #s(literal -1/2 binary64)) x)
✓	cost-diff	0	(fma.f64 eps (/.f64 (fma.f64 eps (/.f64 #s(literal -1/8 binary64) (*.f64 x x)) #s(literal -1/2 binary64)) x) (+.f64 x x))
✓	cost-diff	0	(/.f64 (fma.f64 eps (/.f64 (fma.f64 eps (/.f64 #s(literal -1/8 binary64) (*.f64 x x)) #s(literal -1/2 binary64)) x) (+.f64 x x)) eps)
✓	cost-diff	704	(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 eps (/.f64 (fma.f64 eps (/.f64 #s(literal -1/8 binary64) (*.f64 x x)) #s(literal -1/2 binary64)) x) (+.f64 x x)) eps))
✓	cost-diff	0	(/.f64 #s(literal -1/2 binary64) x)
✓	cost-diff	0	(fma.f64 eps (/.f64 #s(literal -1/2 binary64) x) x)
✓	cost-diff	256	(-.f64 x (fma.f64 eps (/.f64 #s(literal -1/2 binary64) x) x))
✓	cost-diff	0	(neg.f64 eps)
✓	cost-diff	0	(sqrt.f64 (neg.f64 eps))
✓	cost-diff	0	(-.f64 x (sqrt.f64 (neg.f64 eps)))
✓	cost-diff	0	(*.f64 x x)
✓	cost-diff	0	(-.f64 (*.f64 x x) eps)
✓	cost-diff	0	(/.f64 (-.f64 (.f64 x x) eps) (sqrt.f64 (-.f64 (.f64 x x) eps)))
✓	cost-diff	0	(-.f64 x (/.f64 (-.f64 (.f64 x x) eps) (sqrt.f64 (-.f64 (.f64 x x) eps))))

Rules

6 998×	`accelerator-lowering-fma.f32`
6 998×	`accelerator-lowering-fma.f64`
2 110×	`-lowering-.f32`
2 110×	`-lowering-.f64`
1 828×	`unsub-neg`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	170
1	63	170
2	129	164
3	259	164
4	670	164
5	1783	164
6	4733	164
7	6819	164
8	7720	164
0	8037	155

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

Inputs
(- x (/ (- (* x x) eps) (sqrt (- (* x x) eps))))
x
(/ (- (* x x) eps) (sqrt (- (* x x) eps)))
(- (* x x) eps)
(* x x)
eps
(sqrt (- (* x x) eps))
0
(- x (sqrt (neg eps)))
x
(sqrt (neg eps))
(neg eps)
eps
(- x (+ (* eps (/ -1/2 x)) x))
x
(+ (* eps (/ -1/2 x)) x)
eps
(/ -1/2 x)
-1/2
(/ 1 (/ (+ (* eps (/ (+ (* eps (/ -1/8 (* x x))) -1/2) x)) (+ x x)) eps))
1
(/ (+ (* eps (/ (+ (* eps (/ -1/8 (* x x))) -1/2) x)) (+ x x)) eps)
(+ (* eps (/ (+ (* eps (/ -1/8 (* x x))) -1/2) x)) (+ x x))
eps
(/ (+ (* eps (/ -1/8 (* x x))) -1/2) x)
(+ (* eps (/ -1/8 (* x x))) -1/2)
(/ -1/8 (* x x))
-1/8
(* x x)
x
-1/2
(+ x x)

Outputs
(- x (/ (- (* x x) eps) (sqrt (- (* x x) eps))))
(+.f64 x (/.f64 (-.f64 eps (.f64 x x)) (sqrt.f64 (-.f64 (.f64 x x) eps))))
x
(/ (- (* x x) eps) (sqrt (- (* x x) eps)))
(/.f64 (-.f64 (.f64 x x) eps) (sqrt.f64 (-.f64 (.f64 x x) eps)))
(- (* x x) eps)
(-.f64 (*.f64 x x) eps)
(* x x)
(*.f64 x x)
eps
(sqrt (- (* x x) eps))
(sqrt.f64 (-.f64 (*.f64 x x) eps))
0
#s(literal 0 binary64)
(- x (sqrt (neg eps)))
(-.f64 x (sqrt.f64 (neg.f64 eps)))
x
(sqrt (neg eps))
(sqrt.f64 (neg.f64 eps))
(neg eps)
(neg.f64 eps)
eps
(- x (+ (* eps (/ -1/2 x)) x))
(*.f64 (/.f64 eps x) #s(literal 1/2 binary64))
x
(+ (* eps (/ -1/2 x)) x)
(fma.f64 #s(literal -1/2 binary64) (/.f64 eps x) x)
eps
(/ -1/2 x)
(/.f64 #s(literal -1/2 binary64) x)
-1/2
#s(literal -1/2 binary64)
(/ 1 (/ (+ (* eps (/ (+ (* eps (/ -1/8 (* x x))) -1/2) x)) (+ x x)) eps))
(/.f64 eps (+.f64 x (fma.f64 (fma.f64 eps (/.f64 #s(literal -1/8 binary64) (*.f64 x x)) #s(literal -1/2 binary64)) (/.f64 eps x) x)))
1
#s(literal 1 binary64)
(/ (+ (* eps (/ (+ (* eps (/ -1/8 (* x x))) -1/2) x)) (+ x x)) eps)
(/.f64 (+.f64 x (fma.f64 (fma.f64 eps (/.f64 #s(literal -1/8 binary64) (*.f64 x x)) #s(literal -1/2 binary64)) (/.f64 eps x) x)) eps)
(+ (* eps (/ (+ (* eps (/ -1/8 (* x x))) -1/2) x)) (+ x x))
(+.f64 x (fma.f64 (fma.f64 eps (/.f64 #s(literal -1/8 binary64) (*.f64 x x)) #s(literal -1/2 binary64)) (/.f64 eps x) x))
eps
(/ (+ (* eps (/ -1/8 (* x x))) -1/2) x)
(/.f64 (fma.f64 eps (/.f64 #s(literal -1/8 binary64) (*.f64 x x)) #s(literal -1/2 binary64)) x)
(+ (* eps (/ -1/8 (* x x))) -1/2)
(fma.f64 eps (/.f64 #s(literal -1/8 binary64) (*.f64 x x)) #s(literal -1/2 binary64))
(/ -1/8 (* x x))
(/.f64 #s(literal -1/8 binary64) (*.f64 x x))
-1/8
#s(literal -1/8 binary64)
(* x x)
(*.f64 x x)
x
-1/2
#s(literal -1/2 binary64)
(+ x x)
(+.f64 x x)

localize100.0ms (1%)

Memory

23.9MiB live, 217.6MiB allocated

Localize:

Found 14 expressions of interest:

New	Metric	Score	Program
✓	accuracy	99.9%	(/.f64 #s(literal -1/8 binary64) (*.f64 x x))
✓	accuracy	98.6%	(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 eps (/.f64 (fma.f64 eps (/.f64 #s(literal -1/8 binary64) (*.f64 x x)) #s(literal -1/2 binary64)) x) (+.f64 x x)) eps))
✓	accuracy	84.9%	(fma.f64 eps (/.f64 (fma.f64 eps (/.f64 #s(literal -1/8 binary64) (*.f64 x x)) #s(literal -1/2 binary64)) x) (+.f64 x x))
✓	accuracy	80.6%	(fma.f64 eps (/.f64 #s(literal -1/8 binary64) (*.f64 x x)) #s(literal -1/2 binary64))
✓	accuracy	100.0%	(/.f64 #s(literal -1/2 binary64) x)
✓	accuracy	99.7%	(fma.f64 eps (/.f64 #s(literal -1/2 binary64) x) x)
✓	accuracy	82.3%	(-.f64 x (fma.f64 eps (/.f64 #s(literal -1/2 binary64) x) x))
✓	accuracy	100.0%	(sqrt.f64 (neg.f64 eps))
✓	accuracy	100.0%	(neg.f64 eps)
✓	accuracy	100.0%	(-.f64 x (sqrt.f64 (neg.f64 eps)))
✓	accuracy	100.0%	(*.f64 x x)
✓	accuracy	100.0%	(sqrt.f64 (-.f64 (*.f64 x x) eps))
✓	accuracy	99.5%	(/.f64 (-.f64 (.f64 x x) eps) (sqrt.f64 (-.f64 (.f64 x x) eps)))
✓	accuracy	82.3%	(-.f64 x (/.f64 (-.f64 (.f64 x x) eps) (sqrt.f64 (-.f64 (.f64 x x) eps))))

Samples

28.0ms	147×	0	valid
18.0ms	37×	1	valid
12.0ms	61×	0	invalid
8.0ms	11×	2	valid

Compiler

Compiled 162 to 29 computations (82.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 48.0ms

ival-div: 13.0ms (27.1% of total)

ival-mult: 12.0ms (25% of total)

ival-sub: 8.0ms (16.7% of total)

ival-sqrt: 5.0ms (10.4% of total)

ival-add: 5.0ms (10.4% of total)

adjust: 2.0ms (4.2% of total)

ival-neg: 1.0ms (2.1% of total)

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

exact: 0.0ms (0% of total)

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

series24.0ms (0.2%)

Memory

-18.9MiB live, 56.9MiB allocated

Counts

17 → 348

Calls

Call 1

Inputs
#<alt (- x (/ (- (* x x) eps) (sqrt (- (* x x) eps))))>
#<alt (/ (- (* x x) eps) (sqrt (- (* x x) eps)))>
#<alt (- (* x x) eps)>
#<alt (* x x)>
#<alt (- x (sqrt (neg eps)))>
#<alt (sqrt (neg eps))>
#<alt (neg eps)>
#<alt (- x (+ (* eps (/ -1/2 x)) x))>
#<alt (+ (* eps (/ -1/2 x)) x)>
#<alt (/ -1/2 x)>
#<alt (/ 1 (/ (+ (* eps (/ (+ (* eps (/ -1/8 (* x x))) -1/2) x)) (+ x x)) eps))>
#<alt (/ (+ (* eps (/ (+ (* eps (/ -1/8 (* x x))) -1/2) x)) (+ x x)) eps)>
#<alt (+ (* eps (/ (+ (* eps (/ -1/8 (* x x))) -1/2) x)) (+ x x))>
#<alt (/ (+ (* eps (/ -1/8 (* x x))) -1/2) x)>
#<alt (sqrt (- (* x x) eps))>
#<alt (+ (* eps (/ -1/8 (* x x))) -1/2)>
#<alt (/ -1/8 (* x x))>

Outputs
#<alt (* -1 (* (sqrt eps) (sqrt -1)))>
#<alt (- x (* (sqrt eps) (sqrt -1)))>
#<alt (- (* x (+ 1 (* -1/2 (* (sqrt (/ 1 eps)) (/ x (sqrt -1)))))) (* (sqrt eps) (sqrt -1)))>
#<alt (- (* x (+ 1 (* x (- (* 1/8 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))))))) (* (sqrt eps) (sqrt -1)))>
#<alt (* 1/2 (/ eps x))>
#<alt (/ (- (* 1/8 (/ (pow eps 2) (pow x 2))) (* -1/2 eps)) x)>
#<alt (/ (- (* 1/16 (/ (pow eps 3) (pow x 4))) (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2))))) x)>
#<alt (/ (- (* 1/2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) (pow x 6))) (+ (* -1/2 eps) (+ (* -1/8 (/ (pow eps 2) (pow x 2))) (* -1/16 (/ (pow eps 3) (pow x 4)))))) x)>
#<alt (* 2 x)>
#<alt (* -1 (* x (- (* 1/2 (/ eps (pow x 2))) 2)))>
#<alt (* -1 (* x (- (* 1/8 (/ (pow eps 2) (pow x 4))) (+ 2 (* -1/2 (/ eps (pow x 2)))))))>
#<alt (* -1 (* x (- (* 1/16 (/ (pow eps 3) (pow x 6))) (+ 2 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4))))))))>
#<alt (* 1/2 (/ eps x))>
#<alt (* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))>
#<alt (* eps (+ (* eps (+ (* 1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))>
#<alt (* eps (+ (* eps (+ (* eps (+ (* 5/128 (/ eps (pow x 7))) (* 1/16 (/ 1 (pow x 5))))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))>
#<alt (* -1 (* (sqrt eps) (sqrt -1)))>
#<alt (* eps (- (/ x eps) (* (sqrt (/ 1 eps)) (sqrt -1))))>
#<alt (* eps (- (+ (* -1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1))))>
#<alt (* eps (- (+ (* 1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (/ x eps)) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))>
#<alt (* (sqrt eps) (sqrt -1))>
#<alt (* -1 (* eps (- (* -1 (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))>
#<alt (* -1 (* eps (- (* -1 (/ (+ x (* 1/2 (* (sqrt (/ 1 eps)) (* (pow x 2) (sqrt -1))))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))>
#<alt (* -1 (* eps (- (* -1 (/ (+ x (* -1 (/ (- (* 1/8 (* (sqrt (/ 1 eps)) (* (pow x 4) (sqrt -1)))) (* 1/2 (* (sqrt eps) (* (pow x 2) (sqrt -1))))) eps))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))>
#<alt (* (sqrt eps) (sqrt -1))>
#<alt (+ (* 1/2 (* (sqrt (/ 1 eps)) (/ (pow x 2) (sqrt -1)))) (* (sqrt eps) (sqrt -1)))>
#<alt (+ (* (sqrt eps) (sqrt -1)) (* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))))))>
#<alt (+ (* (sqrt eps) (sqrt -1)) (* (pow x 2) (+ (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))) (* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3)))) (* 1/16 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 2) (pow (sqrt -1) 5)))))))))>
#<alt x>
#<alt (* x (+ 1 (* -1/2 (/ eps (pow x 2)))))>
#<alt (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4))))))>
#<alt (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/8 (/ (pow eps 2) (pow x 4))) (* -1/16 (/ (pow eps 3) (pow x 6)))))))>
#<alt (* -1 x)>
#<alt (* -1 (* x (+ 1 (* -1/2 (/ eps (pow x 2))))))>
#<alt (* -1 (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4)))))))>
#<alt (* -1 (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/8 (/ (pow eps 2) (pow x 4))) (* -1/16 (/ (pow eps 3) (pow x 6))))))))>
#<alt x>
#<alt (+ x (* -1/2 (/ eps x)))>
#<alt (+ x (* eps (- (* -1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))))>
#<alt (+ x (* eps (- (* eps (- (* -1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))))>
#<alt (* (sqrt eps) (sqrt -1))>
#<alt (* eps (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))>
#<alt (* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))>
#<alt (* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow eps 7))) (/ (pow x 6) (pow (sqrt -1) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))))>
#<alt (* -1 (* (sqrt eps) (sqrt -1)))>
#<alt (* -1 (* eps (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))>
#<alt (* -1 (* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (* (pow x 4) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))))>
#<alt (* -1 (* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (* (pow x 4) (sqrt -1)))) (+ (* 1/16 (* (sqrt (/ 1 (pow eps 7))) (* (pow x 6) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))))>
#<alt (* -1 eps)>
#<alt (- (pow x 2) eps)>
#<alt (- (pow x 2) eps)>
#<alt (- (pow x 2) eps)>
#<alt (pow x 2)>
#<alt (* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))>
#<alt (* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))>
#<alt (* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))>
#<alt (pow x 2)>
#<alt (* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))>
#<alt (* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))>
#<alt (* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))>
#<alt (pow x 2)>
#<alt (+ (* -1 eps) (pow x 2))>
#<alt (+ (* -1 eps) (pow x 2))>
#<alt (+ (* -1 eps) (pow x 2))>
#<alt (* -1 eps)>
#<alt (* eps (- (/ (pow x 2) eps) 1))>
#<alt (* eps (- (/ (pow x 2) eps) 1))>
#<alt (* eps (- (/ (pow x 2) eps) 1))>
#<alt (* -1 eps)>
#<alt (* -1 (* eps (+ 1 (* -1 (/ (pow x 2) eps)))))>
#<alt (* -1 (* eps (+ 1 (* -1 (/ (pow x 2) eps)))))>
#<alt (* -1 (* eps (+ 1 (* -1 (/ (pow x 2) eps)))))>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (* -1 (* (sqrt eps) (sqrt -1)))>
#<alt (- x (* (sqrt eps) (sqrt -1)))>
#<alt (- x (* (sqrt eps) (sqrt -1)))>
#<alt (- x (* (sqrt eps) (sqrt -1)))>
#<alt x>
#<alt (* x (+ 1 (* -1 (* (sqrt eps) (/ (sqrt -1) x)))))>
#<alt (* x (+ 1 (* -1 (* (sqrt eps) (/ (sqrt -1) x)))))>
#<alt (* x (+ 1 (* -1 (* (sqrt eps) (/ (sqrt -1) x)))))>
#<alt x>
#<alt (* -1 (* x (- (* (sqrt eps) (/ (sqrt -1) x)) 1)))>
#<alt (* -1 (* x (- (* (sqrt eps) (/ (sqrt -1) x)) 1)))>
#<alt (* -1 (* x (- (* (sqrt eps) (/ (sqrt -1) x)) 1)))>
#<alt (- x (* (sqrt eps) (sqrt -1)))>
#<alt (- x (* (sqrt eps) (sqrt -1)))>
#<alt (- x (* (sqrt eps) (sqrt -1)))>
#<alt (- x (* (sqrt eps) (sqrt -1)))>
#<alt (* -1 (* (sqrt eps) (sqrt -1)))>
#<alt (* eps (- (/ x eps) (* (sqrt (/ 1 eps)) (sqrt -1))))>
#<alt (* eps (- (/ x eps) (* (sqrt (/ 1 eps)) (sqrt -1))))>
#<alt (* eps (- (/ x eps) (* (sqrt (/ 1 eps)) (sqrt -1))))>
#<alt (* (sqrt eps) (sqrt -1))>
#<alt (* -1 (* eps (- (* -1 (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))>
#<alt (* -1 (* eps (- (* -1 (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))>
#<alt (* -1 (* eps (- (* -1 (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))>
#<alt (* (sqrt eps) (sqrt -1))>
#<alt (* (sqrt eps) (sqrt -1))>
#<alt (* (sqrt eps) (sqrt -1))>
#<alt (* (sqrt eps) (sqrt -1))>
#<alt (* (sqrt eps) (sqrt -1))>
#<alt (* (sqrt eps) (sqrt -1))>
#<alt (* (sqrt eps) (sqrt -1))>
#<alt (* (sqrt eps) (sqrt -1))>
#<alt (* -1 (* (sqrt eps) (sqrt -1)))>
#<alt (* -1 (* (sqrt eps) (sqrt -1)))>
#<alt (* -1 (* (sqrt eps) (sqrt -1)))>
#<alt (* -1 (* (sqrt eps) (sqrt -1)))>
#<alt (* -1 eps)>
#<alt (* -1 eps)>
#<alt (* -1 eps)>
#<alt (* -1 eps)>
#<alt (* -1 eps)>
#<alt (* -1 eps)>
#<alt (* -1 eps)>
#<alt (* -1 eps)>
#<alt (* -1 eps)>
#<alt (* -1 eps)>
#<alt (* -1 eps)>
#<alt (* -1 eps)>
#<alt (* 1/2 (/ eps x))>
#<alt (* 1/2 (/ eps x))>
#<alt (* 1/2 (/ eps x))>
#<alt (* 1/2 (/ eps x))>
#<alt (* 1/2 (/ eps x))>
#<alt (* 1/2 (/ eps x))>
#<alt (* 1/2 (/ eps x))>
#<alt (* 1/2 (/ eps x))>
#<alt (* 1/2 (/ eps x))>
#<alt (* 1/2 (/ eps x))>
#<alt (* 1/2 (/ eps x))>
#<alt (* 1/2 (/ eps x))>
#<alt (* 1/2 (/ eps x))>
#<alt (* 1/2 (/ eps x))>
#<alt (* 1/2 (/ eps x))>
#<alt (* 1/2 (/ eps x))>
#<alt (* 1/2 (/ eps x))>
#<alt (* 1/2 (/ eps x))>
#<alt (* 1/2 (/ eps x))>
#<alt (* 1/2 (/ eps x))>
#<alt (* 1/2 (/ eps x))>
#<alt (* 1/2 (/ eps x))>
#<alt (* 1/2 (/ eps x))>
#<alt (* 1/2 (/ eps x))>
#<alt x>
#<alt (+ x (* -1/2 (/ eps x)))>
#<alt (+ x (* -1/2 (/ eps x)))>
#<alt (+ x (* -1/2 (/ eps x)))>
#<alt (* -1/2 (/ eps x))>
#<alt (* eps (- (/ x eps) (* 1/2 (/ 1 x))))>
#<alt (* eps (- (/ x eps) (* 1/2 (/ 1 x))))>
#<alt (* eps (- (/ x eps) (* 1/2 (/ 1 x))))>
#<alt (* -1/2 (/ eps x))>
#<alt (* -1 (* eps (+ (* -1 (/ x eps)) (* 1/2 (/ 1 x)))))>
#<alt (* -1 (* eps (+ (* -1 (/ x eps)) (* 1/2 (/ 1 x)))))>
#<alt (* -1 (* eps (+ (* -1 (/ x eps)) (* 1/2 (/ 1 x)))))>
#<alt (* -1/2 (/ eps x))>
#<alt (/ (+ (* -1/2 eps) (pow x 2)) x)>
#<alt (/ (+ (* -1/2 eps) (pow x 2)) x)>
#<alt (/ (+ (* -1/2 eps) (pow x 2)) x)>
#<alt x>
#<alt (* x (+ 1 (* -1/2 (/ eps (pow x 2)))))>
#<alt (* x (+ 1 (* -1/2 (/ eps (pow x 2)))))>
#<alt (* x (+ 1 (* -1/2 (/ eps (pow x 2)))))>
#<alt x>
#<alt (* -1 (* x (- (* 1/2 (/ eps (pow x 2))) 1)))>
#<alt (* -1 (* x (- (* 1/2 (/ eps (pow x 2))) 1)))>
#<alt (* -1 (* x (- (* 1/2 (/ eps (pow x 2))) 1)))>
#<alt (/ -1/2 x)>
#<alt (/ -1/2 x)>
#<alt (/ -1/2 x)>
#<alt (/ -1/2 x)>
#<alt (/ -1/2 x)>
#<alt (/ -1/2 x)>
#<alt (/ -1/2 x)>
#<alt (/ -1/2 x)>
#<alt (/ -1/2 x)>
#<alt (/ -1/2 x)>
#<alt (/ -1/2 x)>
#<alt (/ -1/2 x)>
#<alt (* 1/2 (/ eps x))>
#<alt (* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))>
#<alt (* eps (+ (* eps (+ (* 1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))>
#<alt (* eps (+ (* eps (+ (* eps (+ (* 3/128 (/ eps (pow x 7))) (* 1/16 (/ 1 (pow x 5))))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))>
#<alt (* -8 (/ (pow x 3) eps))>
#<alt (/ (+ (* -8 (pow x 3)) (* 32 (/ (pow x 5) eps))) eps)>
#<alt (/ (- (+ (* -256 (/ (pow x 7) (pow eps 2))) (* -8 (pow x 3))) (* -32 (/ (pow x 5) eps))) eps)>
#<alt (/ (- (+ (* -8 (pow x 3)) (* -1 (/ (+ (* -1024 (pow x 9)) (* -512 (pow x 9))) (pow eps 3)))) (+ (* -32 (/ (pow x 5) eps)) (* 256 (/ (pow x 7) (pow eps 2))))) eps)>
#<alt (* -8 (/ (pow x 3) eps))>
#<alt (* -1 (/ (+ (* -32 (/ (pow x 5) eps)) (* 8 (pow x 3))) eps))>
#<alt (* -1 (/ (+ (* -1 (/ (- (* -256 (/ (pow x 7) eps)) (* -32 (pow x 5))) eps)) (* 8 (pow x 3))) eps))>
#<alt (* -1 (/ (+ (* -1 (/ (- (* -1 (/ (- (+ (* -1024 (/ (pow x 9) eps)) (* -512 (/ (pow x 9) eps))) (* -256 (pow x 7))) eps)) (* -32 (pow x 5))) eps)) (* 8 (pow x 3))) eps))>
#<alt (* -8 (/ (pow x 3) eps))>
#<alt (* (pow x 3) (- (* 32 (/ (pow x 2) (pow eps 2))) (* 8 (/ 1 eps))))>
#<alt (* (pow x 3) (- (* (pow x 2) (+ (* -256 (/ (pow x 2) (pow eps 3))) (* 32 (/ 1 (pow eps 2))))) (* 8 (/ 1 eps))))>
#<alt (* (pow x 3) (- (* (pow x 2) (+ (* (pow x 2) (- (* 1536 (/ (pow x 2) (pow eps 4))) (* 256 (/ 1 (pow eps 3))))) (* 32 (/ 1 (pow eps 2))))) (* 8 (/ 1 eps))))>
#<alt (* 1/2 (/ eps x))>
#<alt (/ (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps)) x)>
#<alt (/ (- (+ (* 1/16 (/ (pow eps 3) (pow x 4))) (* 1/2 eps)) (* -1/8 (/ (pow eps 2) (pow x 2)))) x)>
#<alt (/ (- (+ (* -1 (/ (+ (* -1/64 (pow eps 4)) (* -1/128 (pow eps 4))) (pow x 6))) (* 1/2 eps)) (+ (* -1/8 (/ (pow eps 2) (pow x 2))) (* -1/16 (/ (pow eps 3) (pow x 4))))) x)>
#<alt (* 1/2 (/ eps x))>
#<alt (* -1 (/ (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2)))) x))>
#<alt (* -1 (/ (- (+ (* -1/2 eps) (* -1/16 (/ (pow eps 3) (pow x 4)))) (* 1/8 (/ (pow eps 2) (pow x 2)))) x))>
#<alt (* -1 (/ (- (+ (* -1 (/ (+ (* 1/128 (pow eps 4)) (* 1/64 (pow eps 4))) (pow x 6))) (* -1/2 eps)) (+ (* 1/16 (/ (pow eps 3) (pow x 4))) (* 1/8 (/ (pow eps 2) (pow x 2))))) x))>
#<alt (* 2 (/ x eps))>
#<alt (/ (+ (* -1/2 (/ eps x)) (* 2 x)) eps)>
#<alt (/ (+ (* 2 x) (* eps (- (* -1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))) eps)>
#<alt (/ (+ (* 2 x) (* eps (- (* -1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))) eps)>
#<alt (* -1/8 (/ eps (pow x 3)))>
#<alt (* -1 (* eps (+ (* 1/8 (/ 1 (pow x 3))) (* 1/2 (/ 1 (* eps x))))))>
#<alt (* eps (- (* 2 (/ x (pow eps 2))) (+ (* 1/8 (/ 1 (pow x 3))) (/ 1/2 (* eps x)))))>
#<alt (* eps (- (* 2 (/ x (pow eps 2))) (+ (* 1/8 (/ 1 (pow x 3))) (/ 1/2 (* eps x)))))>
#<alt (* -1/8 (/ eps (pow x 3)))>
#<alt (* -1 (* eps (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3))))))>
#<alt (* -1 (* eps (+ (* -1 (/ (- (* 2 (/ x eps)) (* 1/2 (/ 1 x))) eps)) (* 1/8 (/ 1 (pow x 3))))))>
#<alt (* -1 (* eps (+ (* -1 (/ (- (* 2 (/ x eps)) (* 1/2 (/ 1 x))) eps)) (* 1/8 (/ 1 (pow x 3))))))>
#<alt (* -1/8 (/ eps (pow x 3)))>
#<alt (/ (+ (* -1/2 (pow x 2)) (* -1/8 eps)) (pow x 3))>
#<alt (/ (+ (* -1/8 eps) (* (pow x 2) (- (* 2 (/ (pow x 2) eps)) 1/2))) (pow x 3))>
#<alt (/ (+ (* -1/8 eps) (* (pow x 2) (- (* 2 (/ (pow x 2) eps)) 1/2))) (pow x 3))>
#<alt (* 2 (/ x eps))>
#<alt (* x (- (* 2 (/ 1 eps)) (* 1/2 (/ 1 (pow x 2)))))>
#<alt (* x (- (+ (* -1/8 (/ eps (pow x 4))) (* 2 (/ 1 eps))) (* 1/2 (/ 1 (pow x 2)))))>
#<alt (* x (- (+ (* -1/8 (/ eps (pow x 4))) (* 2 (/ 1 eps))) (* 1/2 (/ 1 (pow x 2)))))>
#<alt (* 2 (/ x eps))>
#<alt (* -1 (* x (- (* 1/2 (/ 1 (pow x 2))) (* 2 (/ 1 eps)))))>
#<alt (* -1 (* x (- (+ (* 1/8 (/ eps (pow x 4))) (* 1/2 (/ 1 (pow x 2)))) (* 2 (/ 1 eps)))))>
#<alt (* -1 (* x (- (+ (* 1/8 (/ eps (pow x 4))) (* 1/2 (/ 1 (pow x 2)))) (* 2 (/ 1 eps)))))>
#<alt (* 2 x)>
#<alt (+ (* -1/2 (/ eps x)) (* 2 x))>
#<alt (+ (* 2 x) (* eps (- (* -1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))))>
#<alt (+ (* 2 x) (* eps (- (* -1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))))>
#<alt (* -1/8 (/ (pow eps 2) (pow x 3)))>
#<alt (* -1 (* (pow eps 2) (+ (* 1/8 (/ 1 (pow x 3))) (* 1/2 (/ 1 (* eps x))))))>
#<alt (* (pow eps 2) (- (* 2 (/ x (pow eps 2))) (+ (* 1/8 (/ 1 (pow x 3))) (/ 1/2 (* eps x)))))>
#<alt (* (pow eps 2) (- (* 2 (/ x (pow eps 2))) (+ (* 1/8 (/ 1 (pow x 3))) (/ 1/2 (* eps x)))))>
#<alt (* -1/8 (/ (pow eps 2) (pow x 3)))>
#<alt (* -1 (* (pow eps 2) (+ (* 1/8 (/ 1 (pow x 3))) (* 1/2 (/ 1 (* eps x))))))>
#<alt (* (pow eps 2) (- (* -1 (/ (+ (* -2 (/ x eps)) (* 1/2 (/ 1 x))) eps)) (* 1/8 (/ 1 (pow x 3)))))>
#<alt (* (pow eps 2) (- (* -1 (/ (+ (* -2 (/ x eps)) (* 1/2 (/ 1 x))) eps)) (* 1/8 (/ 1 (pow x 3)))))>
#<alt (* -1/8 (/ (pow eps 2) (pow x 3)))>
#<alt (/ (+ (* -1/2 (* eps (pow x 2))) (* -1/8 (pow eps 2))) (pow x 3))>
#<alt (/ (+ (* -1/8 (pow eps 2)) (* (pow x 2) (+ (* -1/2 eps) (* 2 (pow x 2))))) (pow x 3))>
#<alt (/ (+ (* -1/8 (pow eps 2)) (* (pow x 2) (+ (* -1/2 eps) (* 2 (pow x 2))))) (pow x 3))>
#<alt (* 2 x)>
#<alt (* x (+ 2 (* -1/2 (/ eps (pow x 2)))))>
#<alt (* x (+ 2 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4))))))>
#<alt (* x (+ 2 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4))))))>
#<alt (* 2 x)>
#<alt (* -1 (* x (- (* 1/2 (/ eps (pow x 2))) 2)))>
#<alt (* -1 (* x (- (+ (* 1/8 (/ (pow eps 2) (pow x 4))) (* 1/2 (/ eps (pow x 2)))) 2)))>
#<alt (* -1 (* x (- (+ (* 1/8 (/ (pow eps 2) (pow x 4))) (* 1/2 (/ eps (pow x 2)))) 2)))>
#<alt (/ -1/2 x)>
#<alt (- (* -1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))>
#<alt (- (* -1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))>
#<alt (- (* -1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))>
#<alt (* -1/8 (/ eps (pow x 3)))>
#<alt (* -1 (* eps (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3))))))>
#<alt (* -1 (* eps (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3))))))>
#<alt (* -1 (* eps (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3))))))>
#<alt (* -1/8 (/ eps (pow x 3)))>
#<alt (* -1 (* eps (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3))))))>
#<alt (* -1 (* eps (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3))))))>
#<alt (* -1 (* eps (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3))))))>
#<alt (* -1/8 (/ eps (pow x 3)))>
#<alt (/ (+ (* -1/2 (pow x 2)) (* -1/8 eps)) (pow x 3))>
#<alt (/ (+ (* -1/2 (pow x 2)) (* -1/8 eps)) (pow x 3))>
#<alt (/ (+ (* -1/2 (pow x 2)) (* -1/8 eps)) (pow x 3))>
#<alt (/ -1/2 x)>
#<alt (/ (- (* -1/8 (/ eps (pow x 2))) 1/2) x)>
#<alt (/ (- (* -1/8 (/ eps (pow x 2))) 1/2) x)>
#<alt (/ (- (* -1/8 (/ eps (pow x 2))) 1/2) x)>
#<alt (/ -1/2 x)>
#<alt (* -1 (/ (+ 1/2 (* 1/8 (/ eps (pow x 2)))) x))>
#<alt (* -1 (/ (+ 1/2 (* 1/8 (/ eps (pow x 2)))) x))>
#<alt (* -1 (/ (+ 1/2 (* 1/8 (/ eps (pow x 2)))) x))>
#<alt (* (sqrt eps) (sqrt -1))>
#<alt (+ (* 1/2 (* (sqrt (/ 1 eps)) (/ (pow x 2) (sqrt -1)))) (* (sqrt eps) (sqrt -1)))>
#<alt (+ (* (sqrt eps) (sqrt -1)) (* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))))))>
#<alt (+ (* (sqrt eps) (sqrt -1)) (* (pow x 2) (+ (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))) (* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3)))) (* 1/16 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 2) (pow (sqrt -1) 5)))))))))>
#<alt x>
#<alt (* x (+ 1 (* -1/2 (/ eps (pow x 2)))))>
#<alt (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4))))))>
#<alt (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/8 (/ (pow eps 2) (pow x 4))) (* -1/16 (/ (pow eps 3) (pow x 6)))))))>
#<alt (* -1 x)>
#<alt (* -1 (* x (+ 1 (* -1/2 (/ eps (pow x 2))))))>
#<alt (* -1 (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4)))))))>
#<alt (* -1 (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/8 (/ (pow eps 2) (pow x 4))) (* -1/16 (/ (pow eps 3) (pow x 6))))))))>
#<alt x>
#<alt (+ x (* -1/2 (/ eps x)))>
#<alt (+ x (* eps (- (* -1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))))>
#<alt (+ x (* eps (- (* eps (- (* -1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))))>
#<alt (* (sqrt eps) (sqrt -1))>
#<alt (* eps (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))>
#<alt (* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))>
#<alt (* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow eps 7))) (/ (pow x 6) (pow (sqrt -1) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))))>
#<alt (* -1 (* (sqrt eps) (sqrt -1)))>
#<alt (* -1 (* eps (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))>
#<alt (* -1 (* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (* (pow x 4) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))))>
#<alt (* -1 (* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (* (pow x 4) (sqrt -1)))) (+ (* 1/16 (* (sqrt (/ 1 (pow eps 7))) (* (pow x 6) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))))>
#<alt -1/2>
#<alt (- (* -1/8 (/ eps (pow x 2))) 1/2)>
#<alt (- (* -1/8 (/ eps (pow x 2))) 1/2)>
#<alt (- (* -1/8 (/ eps (pow x 2))) 1/2)>
#<alt (* -1/8 (/ eps (pow x 2)))>
#<alt (* -1 (* eps (+ (* 1/8 (/ 1 (pow x 2))) (* 1/2 (/ 1 eps)))))>
#<alt (* -1 (* eps (+ (* 1/8 (/ 1 (pow x 2))) (* 1/2 (/ 1 eps)))))>
#<alt (* -1 (* eps (+ (* 1/8 (/ 1 (pow x 2))) (* 1/2 (/ 1 eps)))))>
#<alt (* -1/8 (/ eps (pow x 2)))>
#<alt (* -1 (* eps (+ (* 1/2 (/ 1 eps)) (* 1/8 (/ 1 (pow x 2))))))>
#<alt (* -1 (* eps (+ (* 1/2 (/ 1 eps)) (* 1/8 (/ 1 (pow x 2))))))>
#<alt (* -1 (* eps (+ (* 1/2 (/ 1 eps)) (* 1/8 (/ 1 (pow x 2))))))>
#<alt (* -1/8 (/ eps (pow x 2)))>
#<alt (/ (+ (* -1/2 (pow x 2)) (* -1/8 eps)) (pow x 2))>
#<alt (/ (+ (* -1/2 (pow x 2)) (* -1/8 eps)) (pow x 2))>
#<alt (/ (+ (* -1/2 (pow x 2)) (* -1/8 eps)) (pow x 2))>
#<alt -1/2>
#<alt (- (* -1/8 (/ eps (pow x 2))) 1/2)>
#<alt (- (* -1/8 (/ eps (pow x 2))) 1/2)>
#<alt (- (* -1/8 (/ eps (pow x 2))) 1/2)>
#<alt -1/2>
#<alt (- (* -1/8 (/ eps (pow x 2))) 1/2)>
#<alt (- (* -1/8 (/ eps (pow x 2))) 1/2)>
#<alt (- (* -1/8 (/ eps (pow x 2))) 1/2)>
#<alt (/ -1/8 (pow x 2))>
#<alt (/ -1/8 (pow x 2))>
#<alt (/ -1/8 (pow x 2))>
#<alt (/ -1/8 (pow x 2))>
#<alt (/ -1/8 (pow x 2))>
#<alt (/ -1/8 (pow x 2))>
#<alt (/ -1/8 (pow x 2))>
#<alt (/ -1/8 (pow x 2))>
#<alt (/ -1/8 (pow x 2))>
#<alt (/ -1/8 (pow x 2))>
#<alt (/ -1/8 (pow x 2))>
#<alt (/ -1/8 (pow x 2))>

Calls

87 calls:

Time	Variable		Point	Expression
3.0ms	eps	@	inf	(/ 1 (/ (+ (* eps (/ (+ (* eps (/ -1/8 (* x x))) -1/2) x)) (+ x x)) eps))
2.0ms	eps	@	-inf	(/ (+ (* eps (/ -1/8 (* x x))) -1/2) x)
2.0ms	eps	@	-inf	(- x (/ (- (* x x) eps) (sqrt (- (* x x) eps))))
1.0ms	eps	@	0	(/ 1 (/ (+ (* eps (/ (+ (* eps (/ -1/8 (* x x))) -1/2) x)) (+ x x)) eps))
1.0ms	x	@	0	(/ 1 (/ (+ (* eps (/ (+ (* eps (/ -1/8 (* x x))) -1/2) x)) (+ x x)) eps))

rewrite412.0ms (4.1%)

Memory

-16.4MiB live, 625.7MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

4 770×	`/-lowering-/.f32`
4 770×	`/-lowering-/.f64`
3 850×	`-lowering-.f32`
3 850×	`-lowering-.f64`
3 144×	`accelerator-lowering-fma.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	26	157
1	192	153
2	1767	135
0	8484	123

Stop Event

1×	iter limit
1×	node limit

Counts

17 → 876

Calls

Call 1

Inputs
(- x (/ (- (* x x) eps) (sqrt (- (* x x) eps))))
(/ (- (* x x) eps) (sqrt (- (* x x) eps)))
(- (* x x) eps)
(* x x)
(- x (sqrt (neg eps)))
(sqrt (neg eps))
(neg eps)
(- x (+ (* eps (/ -1/2 x)) x))
(+ (* eps (/ -1/2 x)) x)
(/ -1/2 x)
(/ 1 (/ (+ (* eps (/ (+ (* eps (/ -1/8 (* x x))) -1/2) x)) (+ x x)) eps))
(/ (+ (* eps (/ (+ (* eps (/ -1/8 (* x x))) -1/2) x)) (+ x x)) eps)
(+ (* eps (/ (+ (* eps (/ -1/8 (* x x))) -1/2) x)) (+ x x))
(/ (+ (* eps (/ -1/8 (* x x))) -1/2) x)
(sqrt (- (* x x) eps))
(+ (* eps (/ -1/8 (* x x))) -1/2)
(/ -1/8 (* x x))

Outputs
(+.f64 x (neg.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps))))
(+.f64 (neg.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps))) x)
(+.f64 (-.f64 x (/.f64 (.f64 x x) (sqrt.f64 (-.f64 (.f64 x x) eps)))) (/.f64 eps (sqrt.f64 (-.f64 (*.f64 x x) eps))))
(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
(-.f64 (/.f64 (.f64 x (.f64 x x)) (fma.f64 x x (fma.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps)) (-.f64 (.f64 x x) eps)))) (/.f64 (.f64 (-.f64 (.f64 x x) eps) (sqrt.f64 (-.f64 (.f64 x x) eps))) (fma.f64 x x (fma.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps)) (-.f64 (*.f64 x x) eps)))))
(-.f64 (/.f64 (.f64 x x) (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps)))) (/.f64 (-.f64 (.f64 x x) eps) (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps)))))
(-.f64 (/.f64 (.f64 x x) (-.f64 x (neg.f64 (sqrt.f64 (-.f64 (.f64 x x) eps))))) (/.f64 (-.f64 (.f64 x x) eps) (-.f64 x (neg.f64 (sqrt.f64 (-.f64 (.f64 x x) eps))))))
(fma.f64 (-.f64 (.f64 x x) eps) (neg.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 (.f64 x x) eps)))) x)
(fma.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)
(fma.f64 (neg.f64 (-.f64 (.f64 x x) eps)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 (.f64 x x) eps))) x)
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 x x (fma.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps)) (-.f64 (.f64 x x) eps))) (-.f64 (.f64 x (.f64 x x)) (.f64 (-.f64 (.f64 x x) eps) (sqrt.f64 (-.f64 (*.f64 x x) eps))))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) (-.f64 (.f64 x x) (-.f64 (*.f64 x x) eps))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (fma.f64 x x (fma.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps)) (-.f64 (.f64 x x) eps))) (-.f64 (.f64 x (.f64 x x)) (.f64 (-.f64 (.f64 x x) eps) (sqrt.f64 (-.f64 (*.f64 x x) eps)))))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) (-.f64 (.f64 x x) (-.f64 (*.f64 x x) eps)))))
(/.f64 (-.f64 (.f64 x (.f64 x x)) (.f64 (-.f64 (.f64 x x) eps) (sqrt.f64 (-.f64 (.f64 x x) eps)))) (fma.f64 x x (fma.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps)) (-.f64 (*.f64 x x) eps))))
(/.f64 (-.f64 (.f64 x (.f64 x x)) (.f64 (-.f64 (.f64 x x) eps) (sqrt.f64 (-.f64 (.f64 x x) eps)))) (fma.f64 x x (-.f64 (-.f64 (.f64 x x) eps) (.f64 x (neg.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)))))))
(/.f64 (-.f64 (.f64 x x) (-.f64 (.f64 x x) eps)) (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))
(/.f64 (-.f64 (.f64 x x) (-.f64 (.f64 x x) eps)) (-.f64 x (neg.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)))))
(/.f64 (neg.f64 (-.f64 (.f64 x (.f64 x x)) (.f64 (-.f64 (.f64 x x) eps) (sqrt.f64 (-.f64 (.f64 x x) eps))))) (neg.f64 (fma.f64 x x (fma.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps)) (-.f64 (*.f64 x x) eps)))))
(/.f64 (neg.f64 (-.f64 (.f64 x (.f64 x x)) (.f64 (-.f64 (.f64 x x) eps) (sqrt.f64 (-.f64 (.f64 x x) eps))))) (neg.f64 (fma.f64 x x (-.f64 (-.f64 (.f64 x x) eps) (.f64 x (neg.f64 (sqrt.f64 (-.f64 (.f64 x x) eps))))))))
(/.f64 (neg.f64 (-.f64 (.f64 x x) (-.f64 (.f64 x x) eps))) (neg.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))))
(/.f64 (neg.f64 (-.f64 (.f64 x x) (-.f64 (.f64 x x) eps))) (neg.f64 (-.f64 x (neg.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps))))))
(/.f64 (-.f64 (.f64 (.f64 x (.f64 x x)) (fma.f64 x x (fma.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps)) (-.f64 (.f64 x x) eps)))) (.f64 (fma.f64 x x (fma.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps)) (-.f64 (.f64 x x) eps))) (.f64 (-.f64 (.f64 x x) eps) (sqrt.f64 (-.f64 (.f64 x x) eps))))) (.f64 (fma.f64 x x (fma.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps)) (-.f64 (.f64 x x) eps))) (fma.f64 x x (fma.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps)) (-.f64 (.f64 x x) eps)))))
(/.f64 (-.f64 (.f64 (.f64 x x) (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps)))) (.f64 (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) (-.f64 (.f64 x x) eps))) (.f64 (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))))
(/.f64 (neg.f64 (neg.f64 (-.f64 (.f64 x (.f64 x x)) (.f64 (-.f64 (.f64 x x) eps) (sqrt.f64 (-.f64 (.f64 x x) eps)))))) (neg.f64 (neg.f64 (fma.f64 x x (fma.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps)) (-.f64 (*.f64 x x) eps))))))
(/.f64 (neg.f64 (neg.f64 (-.f64 (.f64 x x) (-.f64 (.f64 x x) eps)))) (neg.f64 (neg.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))))
(pow.f64 (/.f64 (fma.f64 x x (fma.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps)) (-.f64 (.f64 x x) eps))) (-.f64 (.f64 x (.f64 x x)) (.f64 (-.f64 (.f64 x x) eps) (sqrt.f64 (-.f64 (*.f64 x x) eps))))) #s(literal -1 binary64))
(pow.f64 (/.f64 (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) (-.f64 (.f64 x x) (-.f64 (*.f64 x x) eps))) #s(literal -1 binary64))
(.f64 (-.f64 (.f64 x (.f64 x x)) (.f64 (-.f64 (.f64 x x) eps) (sqrt.f64 (-.f64 (.f64 x x) eps)))) (/.f64 #s(literal 1 binary64) (fma.f64 x x (fma.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps)) (-.f64 (.f64 x x) eps)))))
(.f64 (-.f64 (.f64 x x) (-.f64 (.f64 x x) eps)) (/.f64 #s(literal 1 binary64) (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps)))))
(+.f64 (/.f64 (.f64 x x) (sqrt.f64 (-.f64 (.f64 x x) eps))) (neg.f64 (/.f64 eps (sqrt.f64 (-.f64 (*.f64 x x) eps)))))
(exp.f64 (.f64 (log.f64 (-.f64 (.f64 x x) eps)) #s(literal 1/2 binary64)))
(exp.f64 (.f64 (log.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 (.f64 x x) eps)))) #s(literal -1 binary64)))
(hypot.f64 x (sqrt.f64 (neg.f64 eps)))
(hypot.f64 x (neg.f64 (sqrt.f64 (neg.f64 eps))))
(hypot.f64 (sqrt.f64 (neg.f64 eps)) x)
(hypot.f64 (sqrt.f64 (neg.f64 eps)) (exp.f64 (log.f64 x)))
(hypot.f64 (neg.f64 (sqrt.f64 (neg.f64 eps))) x)
(hypot.f64 (neg.f64 (sqrt.f64 (neg.f64 eps))) (exp.f64 (log.f64 x)))
(hypot.f64 (exp.f64 (log.f64 x)) (sqrt.f64 (neg.f64 eps)))
(hypot.f64 (exp.f64 (log.f64 x)) (neg.f64 (sqrt.f64 (neg.f64 eps))))
(-.f64 (/.f64 (.f64 x x) (sqrt.f64 (-.f64 (.f64 x x) eps))) (/.f64 eps (sqrt.f64 (-.f64 (*.f64 x x) eps))))
(-.f64 (/.f64 #s(literal 0 binary64) (neg.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)))) (neg.f64 (sqrt.f64 (-.f64 (.f64 x x) eps))))
(-.f64 (/.f64 (fma.f64 x x #s(literal 0 binary64)) (sqrt.f64 (-.f64 (.f64 x x) eps))) (/.f64 eps (sqrt.f64 (-.f64 (.f64 x x) eps))))
(-.f64 (/.f64 (/.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) (fma.f64 (.f64 x x) (.f64 x x) (.f64 eps (fma.f64 x x eps)))) (sqrt.f64 (-.f64 (.f64 x x) eps))) (/.f64 (/.f64 (.f64 eps (.f64 eps eps)) (fma.f64 (.f64 x x) (.f64 x x) (.f64 eps (fma.f64 x x eps)))) (sqrt.f64 (-.f64 (*.f64 x x) eps))))
(-.f64 (/.f64 (/.f64 (.f64 x (.f64 x (.f64 x x))) (fma.f64 x x eps)) (sqrt.f64 (-.f64 (.f64 x x) eps))) (/.f64 (/.f64 (.f64 eps eps) (fma.f64 x x eps)) (sqrt.f64 (-.f64 (.f64 x x) eps))))
(-.f64 (/.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) (.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) (fma.f64 (.f64 x x) (.f64 x x) (.f64 eps (fma.f64 x x eps))))) (/.f64 (.f64 eps (.f64 eps eps)) (.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) (fma.f64 (.f64 x x) (.f64 x x) (*.f64 eps (fma.f64 x x eps))))))
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(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (/.f64 (.f64 (.f64 eps #s(literal -1/8 binary64)) (.f64 eps #s(literal -1/8 binary64))) (.f64 x (.f64 x (.f64 x x)))) (-.f64 #s(literal 1/4 binary64) (.f64 eps (.f64 (/.f64 #s(literal -1/8 binary64) (.f64 x x)) #s(literal -1/2 binary64))))) (fma.f64 (.f64 eps (.f64 eps eps)) (/.f64 #s(literal -1/512 binary64) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))))) #s(literal -1/8 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 eps (/.f64 #s(literal -1/8 binary64) (.f64 x x)) #s(literal 1/2 binary64)) (+.f64 (/.f64 (.f64 (.f64 eps #s(literal -1/8 binary64)) (.f64 eps #s(literal -1/8 binary64))) (.f64 x (.f64 x (*.f64 x x)))) #s(literal -1/4 binary64))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (+.f64 (/.f64 (.f64 (.f64 eps #s(literal -1/8 binary64)) (.f64 eps #s(literal -1/8 binary64))) (.f64 x (.f64 x (.f64 x x)))) (-.f64 #s(literal 1/4 binary64) (.f64 eps (.f64 (/.f64 #s(literal -1/8 binary64) (.f64 x x)) #s(literal -1/2 binary64))))) (fma.f64 (.f64 eps (.f64 eps eps)) (/.f64 #s(literal -1/512 binary64) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))))) #s(literal -1/8 binary64)))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (fma.f64 eps (/.f64 #s(literal -1/8 binary64) (.f64 x x)) #s(literal 1/2 binary64)) (+.f64 (/.f64 (.f64 (.f64 eps #s(literal -1/8 binary64)) (.f64 eps #s(literal -1/8 binary64))) (.f64 x (.f64 x (*.f64 x x)))) #s(literal -1/4 binary64)))))
(/.f64 (fma.f64 (.f64 eps (.f64 eps eps)) (/.f64 #s(literal -1/512 binary64) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))))) #s(literal -1/8 binary64)) (+.f64 (/.f64 (.f64 (.f64 eps #s(literal -1/8 binary64)) (.f64 eps #s(literal -1/8 binary64))) (.f64 x (.f64 x (.f64 x x)))) (-.f64 #s(literal 1/4 binary64) (.f64 eps (.f64 (/.f64 #s(literal -1/8 binary64) (.f64 x x)) #s(literal -1/2 binary64))))))
(/.f64 (fma.f64 (.f64 eps (.f64 eps eps)) (/.f64 #s(literal -1/512 binary64) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))))) #s(literal -1/8 binary64)) (+.f64 #s(literal 1/4 binary64) (/.f64 (-.f64 (.f64 (/.f64 eps (.f64 (.f64 x x) #s(literal -8 binary64))) (.f64 eps #s(literal -1/8 binary64))) (.f64 (.f64 eps #s(literal -1/8 binary64)) #s(literal -1/2 binary64))) (.f64 x x))))
(/.f64 (+.f64 (/.f64 (.f64 (.f64 eps #s(literal -1/8 binary64)) (.f64 eps #s(literal -1/8 binary64))) (.f64 x (.f64 x (.f64 x x)))) #s(literal -1/4 binary64)) (fma.f64 eps (/.f64 #s(literal -1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64)))
(/.f64 (neg.f64 (fma.f64 (.f64 eps (.f64 eps eps)) (/.f64 #s(literal -1/512 binary64) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))))) #s(literal -1/8 binary64))) (neg.f64 (+.f64 (/.f64 (.f64 (.f64 eps #s(literal -1/8 binary64)) (.f64 eps #s(literal -1/8 binary64))) (.f64 x (.f64 x (.f64 x x)))) (-.f64 #s(literal 1/4 binary64) (.f64 eps (.f64 (/.f64 #s(literal -1/8 binary64) (.f64 x x)) #s(literal -1/2 binary64)))))))
(/.f64 (neg.f64 (fma.f64 (.f64 eps (.f64 eps eps)) (/.f64 #s(literal -1/512 binary64) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))))) #s(literal -1/8 binary64))) (neg.f64 (+.f64 #s(literal 1/4 binary64) (/.f64 (-.f64 (.f64 (/.f64 eps (.f64 (.f64 x x) #s(literal -8 binary64))) (.f64 eps #s(literal -1/8 binary64))) (.f64 (.f64 eps #s(literal -1/8 binary64)) #s(literal -1/2 binary64))) (.f64 x x)))))
(/.f64 (neg.f64 (+.f64 (/.f64 (.f64 (.f64 eps #s(literal -1/8 binary64)) (.f64 eps #s(literal -1/8 binary64))) (.f64 x (.f64 x (.f64 x x)))) #s(literal -1/4 binary64))) (neg.f64 (fma.f64 eps (/.f64 #s(literal -1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64))))
(/.f64 (-.f64 #s(literal 1/4 binary64) (/.f64 (.f64 (.f64 eps #s(literal -1/8 binary64)) (.f64 eps #s(literal -1/8 binary64))) (.f64 x (.f64 x (.f64 x x))))) (-.f64 #s(literal -1/2 binary64) (/.f64 eps (.f64 (.f64 x x) #s(literal -8 binary64)))))
(/.f64 (-.f64 (.f64 (/.f64 (.f64 (.f64 eps #s(literal -1/8 binary64)) (.f64 eps #s(literal -1/8 binary64))) (.f64 x (.f64 x (.f64 x x)))) (fma.f64 eps (/.f64 #s(literal -1/8 binary64) (.f64 x x)) #s(literal 1/2 binary64))) (.f64 (fma.f64 eps (/.f64 #s(literal -1/8 binary64) (.f64 x x)) #s(literal 1/2 binary64)) #s(literal 1/4 binary64))) (.f64 (fma.f64 eps (/.f64 #s(literal -1/8 binary64) (.f64 x x)) #s(literal 1/2 binary64)) (fma.f64 eps (/.f64 #s(literal -1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64))))
(/.f64 (neg.f64 (neg.f64 (fma.f64 (.f64 eps (.f64 eps eps)) (/.f64 #s(literal -1/512 binary64) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))))) #s(literal -1/8 binary64)))) (neg.f64 (neg.f64 (+.f64 (/.f64 (.f64 (.f64 eps #s(literal -1/8 binary64)) (.f64 eps #s(literal -1/8 binary64))) (.f64 x (.f64 x (.f64 x x)))) (-.f64 #s(literal 1/4 binary64) (.f64 eps (.f64 (/.f64 #s(literal -1/8 binary64) (.f64 x x)) #s(literal -1/2 binary64))))))))
(/.f64 (neg.f64 (neg.f64 (+.f64 (/.f64 (.f64 (.f64 eps #s(literal -1/8 binary64)) (.f64 eps #s(literal -1/8 binary64))) (.f64 x (.f64 x (.f64 x x)))) #s(literal -1/4 binary64)))) (neg.f64 (neg.f64 (fma.f64 eps (/.f64 #s(literal -1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64)))))
(/.f64 (neg.f64 (-.f64 #s(literal 1/4 binary64) (/.f64 (.f64 (.f64 eps #s(literal -1/8 binary64)) (.f64 eps #s(literal -1/8 binary64))) (.f64 x (.f64 x (.f64 x x)))))) (neg.f64 (-.f64 #s(literal -1/2 binary64) (/.f64 eps (.f64 (.f64 x x) #s(literal -8 binary64))))))
(pow.f64 (/.f64 (+.f64 (/.f64 (.f64 (.f64 eps #s(literal -1/8 binary64)) (.f64 eps #s(literal -1/8 binary64))) (.f64 x (.f64 x (.f64 x x)))) (-.f64 #s(literal 1/4 binary64) (.f64 eps (.f64 (/.f64 #s(literal -1/8 binary64) (.f64 x x)) #s(literal -1/2 binary64))))) (fma.f64 (.f64 eps (.f64 eps eps)) (/.f64 #s(literal -1/512 binary64) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))))) #s(literal -1/8 binary64))) #s(literal -1 binary64))
(pow.f64 (/.f64 (fma.f64 eps (/.f64 #s(literal -1/8 binary64) (.f64 x x)) #s(literal 1/2 binary64)) (+.f64 (/.f64 (.f64 (.f64 eps #s(literal -1/8 binary64)) (.f64 eps #s(literal -1/8 binary64))) (.f64 x (.f64 x (*.f64 x x)))) #s(literal -1/4 binary64))) #s(literal -1 binary64))
(.f64 (fma.f64 (.f64 eps (.f64 eps eps)) (/.f64 #s(literal -1/512 binary64) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))))) #s(literal -1/8 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 (/.f64 (.f64 (.f64 eps #s(literal -1/8 binary64)) (.f64 eps #s(literal -1/8 binary64))) (.f64 x (.f64 x (.f64 x x)))) (-.f64 #s(literal 1/4 binary64) (.f64 eps (.f64 (/.f64 #s(literal -1/8 binary64) (*.f64 x x)) #s(literal -1/2 binary64)))))))
(.f64 (+.f64 (/.f64 (.f64 (.f64 eps #s(literal -1/8 binary64)) (.f64 eps #s(literal -1/8 binary64))) (.f64 x (.f64 x (.f64 x x)))) #s(literal -1/4 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 eps (/.f64 #s(literal -1/8 binary64) (.f64 x x)) #s(literal 1/2 binary64))))
(exp.f64 (.f64 (log.f64 (.f64 (*.f64 x x) #s(literal -8 binary64))) #s(literal -1 binary64)))
(neg.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 x x)))
(/.f64 #s(literal 1 binary64) (.f64 (.f64 x x) #s(literal -8 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (.f64 (.f64 x x) #s(literal -8 binary64)) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 x (/.f64 #s(literal -1/8 binary64) x)))
(/.f64 #s(literal 1 binary64) (neg.f64 (neg.f64 (.f64 (.f64 x x) #s(literal -8 binary64)))))
(/.f64 #s(literal -1/8 binary64) (*.f64 x x))
(/.f64 #s(literal -1/8 binary64) (neg.f64 (*.f64 x (neg.f64 x))))
(/.f64 #s(literal -1 binary64) (neg.f64 (.f64 (.f64 x x) #s(literal -8 binary64))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (.f64 (.f64 x x) #s(literal -8 binary64)) #s(literal 1 binary64))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 x (/.f64 #s(literal -1/8 binary64) x))))
(/.f64 #s(literal 1/8 binary64) (*.f64 x (neg.f64 x)))
(/.f64 #s(literal 1/8 binary64) (neg.f64 (neg.f64 (*.f64 x (neg.f64 x)))))
(/.f64 (/.f64 #s(literal -1/8 binary64) x) x)
(/.f64 (neg.f64 (/.f64 #s(literal -1/8 binary64) x)) (neg.f64 x))
(/.f64 (neg.f64 (neg.f64 (/.f64 #s(literal -1/8 binary64) x))) (neg.f64 (neg.f64 x)))
(pow.f64 (.f64 (.f64 x x) #s(literal -8 binary64)) #s(literal -1 binary64))
(pow.f64 (/.f64 (.f64 (.f64 x x) #s(literal -8 binary64)) #s(literal 1 binary64)) #s(literal -1 binary64))
(pow.f64 (/.f64 x (/.f64 #s(literal -1/8 binary64) x)) #s(literal -1 binary64))
(.f64 #s(literal 1 binary64) (/.f64 #s(literal -1/8 binary64) (.f64 x x)))
(.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1 binary64) (.f64 x x)))
(.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1 binary64) (.f64 x (neg.f64 x))))
(*.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal -1/8 binary64) x))
(.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) #s(literal -1/8 binary64))
(*.f64 (/.f64 #s(literal -1/8 binary64) x) (/.f64 #s(literal 1 binary64) x))

simplify2.5s (25.4%)

Memory

13.0MiB live, 882.0MiB allocated

Algorithm

1×	egg-herbie

Rules

15 218×	`accelerator-lowering-fma.f32`
15 218×	`accelerator-lowering-fma.f64`
6 774×	`-lowering-.f32`
6 774×	`-lowering-.f64`
3 594×	`+-lowering-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	497	4226
1	1476	4172
2	4605	4071
0	8785	3836

Stop Event

1×	iter limit
1×	node limit

Counts

348 → 348

Calls

Call 1

Inputs
(* -1 (* (sqrt eps) (sqrt -1)))
(- x (* (sqrt eps) (sqrt -1)))
(- (* x (+ 1 (* -1/2 (* (sqrt (/ 1 eps)) (/ x (sqrt -1)))))) (* (sqrt eps) (sqrt -1)))
(- (* x (+ 1 (* x (- (* 1/8 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))))))) (* (sqrt eps) (sqrt -1)))
(* 1/2 (/ eps x))
(/ (- (* 1/8 (/ (pow eps 2) (pow x 2))) (* -1/2 eps)) x)
(/ (- (* 1/16 (/ (pow eps 3) (pow x 4))) (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2))))) x)
(/ (- (* 1/2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) (pow x 6))) (+ (* -1/2 eps) (+ (* -1/8 (/ (pow eps 2) (pow x 2))) (* -1/16 (/ (pow eps 3) (pow x 4)))))) x)
(* 2 x)
(* -1 (* x (- (* 1/2 (/ eps (pow x 2))) 2)))
(* -1 (* x (- (* 1/8 (/ (pow eps 2) (pow x 4))) (+ 2 (* -1/2 (/ eps (pow x 2)))))))
(* -1 (* x (- (* 1/16 (/ (pow eps 3) (pow x 6))) (+ 2 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4))))))))
(* 1/2 (/ eps x))
(* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))
(* eps (+ (* eps (+ (* 1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))
(* eps (+ (* eps (+ (* eps (+ (* 5/128 (/ eps (pow x 7))) (* 1/16 (/ 1 (pow x 5))))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))
(* -1 (* (sqrt eps) (sqrt -1)))
(* eps (- (/ x eps) (* (sqrt (/ 1 eps)) (sqrt -1))))
(* eps (- (+ (* -1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1))))
(* eps (- (+ (* 1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (/ x eps)) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* (sqrt eps) (sqrt -1))
(* -1 (* eps (- (* -1 (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* -1 (* eps (- (* -1 (/ (+ x (* 1/2 (* (sqrt (/ 1 eps)) (* (pow x 2) (sqrt -1))))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* -1 (* eps (- (* -1 (/ (+ x (* -1 (/ (- (* 1/8 (* (sqrt (/ 1 eps)) (* (pow x 4) (sqrt -1)))) (* 1/2 (* (sqrt eps) (* (pow x 2) (sqrt -1))))) eps))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* (sqrt eps) (sqrt -1))
(+ (* 1/2 (* (sqrt (/ 1 eps)) (/ (pow x 2) (sqrt -1)))) (* (sqrt eps) (sqrt -1)))
(+ (* (sqrt eps) (sqrt -1)) (* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))))))
(+ (* (sqrt eps) (sqrt -1)) (* (pow x 2) (+ (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))) (* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3)))) (* 1/16 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 2) (pow (sqrt -1) 5)))))))))
x
(* x (+ 1 (* -1/2 (/ eps (pow x 2)))))
(* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4))))))
(* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/8 (/ (pow eps 2) (pow x 4))) (* -1/16 (/ (pow eps 3) (pow x 6)))))))
(* -1 x)
(* -1 (* x (+ 1 (* -1/2 (/ eps (pow x 2))))))
(* -1 (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4)))))))
(* -1 (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/8 (/ (pow eps 2) (pow x 4))) (* -1/16 (/ (pow eps 3) (pow x 6))))))))
x
(+ x (* -1/2 (/ eps x)))
(+ x (* eps (- (* -1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))))
(+ x (* eps (- (* eps (- (* -1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))))
(* (sqrt eps) (sqrt -1))
(* eps (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))
(* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow eps 7))) (/ (pow x 6) (pow (sqrt -1) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))))
(* -1 (* (sqrt eps) (sqrt -1)))
(* -1 (* eps (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* -1 (* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (* (pow x 4) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))))
(* -1 (* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (* (pow x 4) (sqrt -1)))) (+ (* 1/16 (* (sqrt (/ 1 (pow eps 7))) (* (pow x 6) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))))
(* -1 eps)
(- (pow x 2) eps)
(- (pow x 2) eps)
(- (pow x 2) eps)
(pow x 2)
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))
(pow x 2)
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))
(pow x 2)
(+ (* -1 eps) (pow x 2))
(+ (* -1 eps) (pow x 2))
(+ (* -1 eps) (pow x 2))
(* -1 eps)
(* eps (- (/ (pow x 2) eps) 1))
(* eps (- (/ (pow x 2) eps) 1))
(* eps (- (/ (pow x 2) eps) 1))
(* -1 eps)
(* -1 (* eps (+ 1 (* -1 (/ (pow x 2) eps)))))
(* -1 (* eps (+ 1 (* -1 (/ (pow x 2) eps)))))
(* -1 (* eps (+ 1 (* -1 (/ (pow x 2) eps)))))
(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)
(* -1 (* (sqrt eps) (sqrt -1)))
(- x (* (sqrt eps) (sqrt -1)))
(- x (* (sqrt eps) (sqrt -1)))
(- x (* (sqrt eps) (sqrt -1)))
x
(* x (+ 1 (* -1 (* (sqrt eps) (/ (sqrt -1) x)))))
(* x (+ 1 (* -1 (* (sqrt eps) (/ (sqrt -1) x)))))
(* x (+ 1 (* -1 (* (sqrt eps) (/ (sqrt -1) x)))))
x
(* -1 (* x (- (* (sqrt eps) (/ (sqrt -1) x)) 1)))
(* -1 (* x (- (* (sqrt eps) (/ (sqrt -1) x)) 1)))
(* -1 (* x (- (* (sqrt eps) (/ (sqrt -1) x)) 1)))
(- x (* (sqrt eps) (sqrt -1)))
(- x (* (sqrt eps) (sqrt -1)))
(- x (* (sqrt eps) (sqrt -1)))
(- x (* (sqrt eps) (sqrt -1)))
(* -1 (* (sqrt eps) (sqrt -1)))
(* eps (- (/ x eps) (* (sqrt (/ 1 eps)) (sqrt -1))))
(* eps (- (/ x eps) (* (sqrt (/ 1 eps)) (sqrt -1))))
(* eps (- (/ x eps) (* (sqrt (/ 1 eps)) (sqrt -1))))
(* (sqrt eps) (sqrt -1))
(* -1 (* eps (- (* -1 (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* -1 (* eps (- (* -1 (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* -1 (* eps (- (* -1 (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* (sqrt eps) (sqrt -1))
(* (sqrt eps) (sqrt -1))
(* (sqrt eps) (sqrt -1))
(* (sqrt eps) (sqrt -1))
(* (sqrt eps) (sqrt -1))
(* (sqrt eps) (sqrt -1))
(* (sqrt eps) (sqrt -1))
(* (sqrt eps) (sqrt -1))
(* -1 (* (sqrt eps) (sqrt -1)))
(* -1 (* (sqrt eps) (sqrt -1)))
(* -1 (* (sqrt eps) (sqrt -1)))
(* -1 (* (sqrt eps) (sqrt -1)))
(* -1 eps)
(* -1 eps)
(* -1 eps)
(* -1 eps)
(* -1 eps)
(* -1 eps)
(* -1 eps)
(* -1 eps)
(* -1 eps)
(* -1 eps)
(* -1 eps)
(* -1 eps)
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
x
(+ x (* -1/2 (/ eps x)))
(+ x (* -1/2 (/ eps x)))
(+ x (* -1/2 (/ eps x)))
(* -1/2 (/ eps x))
(* eps (- (/ x eps) (* 1/2 (/ 1 x))))
(* eps (- (/ x eps) (* 1/2 (/ 1 x))))
(* eps (- (/ x eps) (* 1/2 (/ 1 x))))
(* -1/2 (/ eps x))
(* -1 (* eps (+ (* -1 (/ x eps)) (* 1/2 (/ 1 x)))))
(* -1 (* eps (+ (* -1 (/ x eps)) (* 1/2 (/ 1 x)))))
(* -1 (* eps (+ (* -1 (/ x eps)) (* 1/2 (/ 1 x)))))
(* -1/2 (/ eps x))
(/ (+ (* -1/2 eps) (pow x 2)) x)
(/ (+ (* -1/2 eps) (pow x 2)) x)
(/ (+ (* -1/2 eps) (pow x 2)) x)
x
(* x (+ 1 (* -1/2 (/ eps (pow x 2)))))
(* x (+ 1 (* -1/2 (/ eps (pow x 2)))))
(* x (+ 1 (* -1/2 (/ eps (pow x 2)))))
x
(* -1 (* x (- (* 1/2 (/ eps (pow x 2))) 1)))
(* -1 (* x (- (* 1/2 (/ eps (pow x 2))) 1)))
(* -1 (* x (- (* 1/2 (/ eps (pow x 2))) 1)))
(/ -1/2 x)
(/ -1/2 x)
(/ -1/2 x)
(/ -1/2 x)
(/ -1/2 x)
(/ -1/2 x)
(/ -1/2 x)
(/ -1/2 x)
(/ -1/2 x)
(/ -1/2 x)
(/ -1/2 x)
(/ -1/2 x)
(* 1/2 (/ eps x))
(* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))
(* eps (+ (* eps (+ (* 1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))
(* eps (+ (* eps (+ (* eps (+ (* 3/128 (/ eps (pow x 7))) (* 1/16 (/ 1 (pow x 5))))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))
(* -8 (/ (pow x 3) eps))
(/ (+ (* -8 (pow x 3)) (* 32 (/ (pow x 5) eps))) eps)
(/ (- (+ (* -256 (/ (pow x 7) (pow eps 2))) (* -8 (pow x 3))) (* -32 (/ (pow x 5) eps))) eps)
(/ (- (+ (* -8 (pow x 3)) (* -1 (/ (+ (* -1024 (pow x 9)) (* -512 (pow x 9))) (pow eps 3)))) (+ (* -32 (/ (pow x 5) eps)) (* 256 (/ (pow x 7) (pow eps 2))))) eps)
(* -8 (/ (pow x 3) eps))
(* -1 (/ (+ (* -32 (/ (pow x 5) eps)) (* 8 (pow x 3))) eps))
(* -1 (/ (+ (* -1 (/ (- (* -256 (/ (pow x 7) eps)) (* -32 (pow x 5))) eps)) (* 8 (pow x 3))) eps))
(* -1 (/ (+ (* -1 (/ (- (* -1 (/ (- (+ (* -1024 (/ (pow x 9) eps)) (* -512 (/ (pow x 9) eps))) (* -256 (pow x 7))) eps)) (* -32 (pow x 5))) eps)) (* 8 (pow x 3))) eps))
(* -8 (/ (pow x 3) eps))
(* (pow x 3) (- (* 32 (/ (pow x 2) (pow eps 2))) (* 8 (/ 1 eps))))
(* (pow x 3) (- (* (pow x 2) (+ (* -256 (/ (pow x 2) (pow eps 3))) (* 32 (/ 1 (pow eps 2))))) (* 8 (/ 1 eps))))
(* (pow x 3) (- (* (pow x 2) (+ (* (pow x 2) (- (* 1536 (/ (pow x 2) (pow eps 4))) (* 256 (/ 1 (pow eps 3))))) (* 32 (/ 1 (pow eps 2))))) (* 8 (/ 1 eps))))
(* 1/2 (/ eps x))
(/ (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps)) x)
(/ (- (+ (* 1/16 (/ (pow eps 3) (pow x 4))) (* 1/2 eps)) (* -1/8 (/ (pow eps 2) (pow x 2)))) x)
(/ (- (+ (* -1 (/ (+ (* -1/64 (pow eps 4)) (* -1/128 (pow eps 4))) (pow x 6))) (* 1/2 eps)) (+ (* -1/8 (/ (pow eps 2) (pow x 2))) (* -1/16 (/ (pow eps 3) (pow x 4))))) x)
(* 1/2 (/ eps x))
(* -1 (/ (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2)))) x))
(* -1 (/ (- (+ (* -1/2 eps) (* -1/16 (/ (pow eps 3) (pow x 4)))) (* 1/8 (/ (pow eps 2) (pow x 2)))) x))
(* -1 (/ (- (+ (* -1 (/ (+ (* 1/128 (pow eps 4)) (* 1/64 (pow eps 4))) (pow x 6))) (* -1/2 eps)) (+ (* 1/16 (/ (pow eps 3) (pow x 4))) (* 1/8 (/ (pow eps 2) (pow x 2))))) x))
(* 2 (/ x eps))
(/ (+ (* -1/2 (/ eps x)) (* 2 x)) eps)
(/ (+ (* 2 x) (* eps (- (* -1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))) eps)
(/ (+ (* 2 x) (* eps (- (* -1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))) eps)
(* -1/8 (/ eps (pow x 3)))
(* -1 (* eps (+ (* 1/8 (/ 1 (pow x 3))) (* 1/2 (/ 1 (* eps x))))))
(* eps (- (* 2 (/ x (pow eps 2))) (+ (* 1/8 (/ 1 (pow x 3))) (/ 1/2 (* eps x)))))
(* eps (- (* 2 (/ x (pow eps 2))) (+ (* 1/8 (/ 1 (pow x 3))) (/ 1/2 (* eps x)))))
(* -1/8 (/ eps (pow x 3)))
(* -1 (* eps (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3))))))
(* -1 (* eps (+ (* -1 (/ (- (* 2 (/ x eps)) (* 1/2 (/ 1 x))) eps)) (* 1/8 (/ 1 (pow x 3))))))
(* -1 (* eps (+ (* -1 (/ (- (* 2 (/ x eps)) (* 1/2 (/ 1 x))) eps)) (* 1/8 (/ 1 (pow x 3))))))
(* -1/8 (/ eps (pow x 3)))
(/ (+ (* -1/2 (pow x 2)) (* -1/8 eps)) (pow x 3))
(/ (+ (* -1/8 eps) (* (pow x 2) (- (* 2 (/ (pow x 2) eps)) 1/2))) (pow x 3))
(/ (+ (* -1/8 eps) (* (pow x 2) (- (* 2 (/ (pow x 2) eps)) 1/2))) (pow x 3))
(* 2 (/ x eps))
(* x (- (* 2 (/ 1 eps)) (* 1/2 (/ 1 (pow x 2)))))
(* x (- (+ (* -1/8 (/ eps (pow x 4))) (* 2 (/ 1 eps))) (* 1/2 (/ 1 (pow x 2)))))
(* x (- (+ (* -1/8 (/ eps (pow x 4))) (* 2 (/ 1 eps))) (* 1/2 (/ 1 (pow x 2)))))
(* 2 (/ x eps))
(* -1 (* x (- (* 1/2 (/ 1 (pow x 2))) (* 2 (/ 1 eps)))))
(* -1 (* x (- (+ (* 1/8 (/ eps (pow x 4))) (* 1/2 (/ 1 (pow x 2)))) (* 2 (/ 1 eps)))))
(* -1 (* x (- (+ (* 1/8 (/ eps (pow x 4))) (* 1/2 (/ 1 (pow x 2)))) (* 2 (/ 1 eps)))))
(* 2 x)
(+ (* -1/2 (/ eps x)) (* 2 x))
(+ (* 2 x) (* eps (- (* -1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))))
(+ (* 2 x) (* eps (- (* -1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))))
(* -1/8 (/ (pow eps 2) (pow x 3)))
(* -1 (* (pow eps 2) (+ (* 1/8 (/ 1 (pow x 3))) (* 1/2 (/ 1 (* eps x))))))
(* (pow eps 2) (- (* 2 (/ x (pow eps 2))) (+ (* 1/8 (/ 1 (pow x 3))) (/ 1/2 (* eps x)))))
(* (pow eps 2) (- (* 2 (/ x (pow eps 2))) (+ (* 1/8 (/ 1 (pow x 3))) (/ 1/2 (* eps x)))))
(* -1/8 (/ (pow eps 2) (pow x 3)))
(* -1 (* (pow eps 2) (+ (* 1/8 (/ 1 (pow x 3))) (* 1/2 (/ 1 (* eps x))))))
(* (pow eps 2) (- (* -1 (/ (+ (* -2 (/ x eps)) (* 1/2 (/ 1 x))) eps)) (* 1/8 (/ 1 (pow x 3)))))
(* (pow eps 2) (- (* -1 (/ (+ (* -2 (/ x eps)) (* 1/2 (/ 1 x))) eps)) (* 1/8 (/ 1 (pow x 3)))))
(* -1/8 (/ (pow eps 2) (pow x 3)))
(/ (+ (* -1/2 (* eps (pow x 2))) (* -1/8 (pow eps 2))) (pow x 3))
(/ (+ (* -1/8 (pow eps 2)) (* (pow x 2) (+ (* -1/2 eps) (* 2 (pow x 2))))) (pow x 3))
(/ (+ (* -1/8 (pow eps 2)) (* (pow x 2) (+ (* -1/2 eps) (* 2 (pow x 2))))) (pow x 3))
(* 2 x)
(* x (+ 2 (* -1/2 (/ eps (pow x 2)))))
(* x (+ 2 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4))))))
(* x (+ 2 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4))))))
(* 2 x)
(* -1 (* x (- (* 1/2 (/ eps (pow x 2))) 2)))
(* -1 (* x (- (+ (* 1/8 (/ (pow eps 2) (pow x 4))) (* 1/2 (/ eps (pow x 2)))) 2)))
(* -1 (* x (- (+ (* 1/8 (/ (pow eps 2) (pow x 4))) (* 1/2 (/ eps (pow x 2)))) 2)))
(/ -1/2 x)
(- (* -1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))
(- (* -1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))
(- (* -1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))
(* -1/8 (/ eps (pow x 3)))
(* -1 (* eps (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3))))))
(* -1 (* eps (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3))))))
(* -1 (* eps (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3))))))
(* -1/8 (/ eps (pow x 3)))
(* -1 (* eps (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3))))))
(* -1 (* eps (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3))))))
(* -1 (* eps (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3))))))
(* -1/8 (/ eps (pow x 3)))
(/ (+ (* -1/2 (pow x 2)) (* -1/8 eps)) (pow x 3))
(/ (+ (* -1/2 (pow x 2)) (* -1/8 eps)) (pow x 3))
(/ (+ (* -1/2 (pow x 2)) (* -1/8 eps)) (pow x 3))
(/ -1/2 x)
(/ (- (* -1/8 (/ eps (pow x 2))) 1/2) x)
(/ (- (* -1/8 (/ eps (pow x 2))) 1/2) x)
(/ (- (* -1/8 (/ eps (pow x 2))) 1/2) x)
(/ -1/2 x)
(* -1 (/ (+ 1/2 (* 1/8 (/ eps (pow x 2)))) x))
(* -1 (/ (+ 1/2 (* 1/8 (/ eps (pow x 2)))) x))
(* -1 (/ (+ 1/2 (* 1/8 (/ eps (pow x 2)))) x))
(* (sqrt eps) (sqrt -1))
(+ (* 1/2 (* (sqrt (/ 1 eps)) (/ (pow x 2) (sqrt -1)))) (* (sqrt eps) (sqrt -1)))
(+ (* (sqrt eps) (sqrt -1)) (* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))))))
(+ (* (sqrt eps) (sqrt -1)) (* (pow x 2) (+ (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))) (* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3)))) (* 1/16 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 2) (pow (sqrt -1) 5)))))))))
x
(* x (+ 1 (* -1/2 (/ eps (pow x 2)))))
(* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4))))))
(* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/8 (/ (pow eps 2) (pow x 4))) (* -1/16 (/ (pow eps 3) (pow x 6)))))))
(* -1 x)
(* -1 (* x (+ 1 (* -1/2 (/ eps (pow x 2))))))
(* -1 (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4)))))))
(* -1 (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/8 (/ (pow eps 2) (pow x 4))) (* -1/16 (/ (pow eps 3) (pow x 6))))))))
x
(+ x (* -1/2 (/ eps x)))
(+ x (* eps (- (* -1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))))
(+ x (* eps (- (* eps (- (* -1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))))
(* (sqrt eps) (sqrt -1))
(* eps (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))
(* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow eps 7))) (/ (pow x 6) (pow (sqrt -1) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))))
(* -1 (* (sqrt eps) (sqrt -1)))
(* -1 (* eps (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* -1 (* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (* (pow x 4) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))))
(* -1 (* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (* (pow x 4) (sqrt -1)))) (+ (* 1/16 (* (sqrt (/ 1 (pow eps 7))) (* (pow x 6) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))))
-1/2
(- (* -1/8 (/ eps (pow x 2))) 1/2)
(- (* -1/8 (/ eps (pow x 2))) 1/2)
(- (* -1/8 (/ eps (pow x 2))) 1/2)
(* -1/8 (/ eps (pow x 2)))
(* -1 (* eps (+ (* 1/8 (/ 1 (pow x 2))) (* 1/2 (/ 1 eps)))))
(* -1 (* eps (+ (* 1/8 (/ 1 (pow x 2))) (* 1/2 (/ 1 eps)))))
(* -1 (* eps (+ (* 1/8 (/ 1 (pow x 2))) (* 1/2 (/ 1 eps)))))
(* -1/8 (/ eps (pow x 2)))
(* -1 (* eps (+ (* 1/2 (/ 1 eps)) (* 1/8 (/ 1 (pow x 2))))))
(* -1 (* eps (+ (* 1/2 (/ 1 eps)) (* 1/8 (/ 1 (pow x 2))))))
(* -1 (* eps (+ (* 1/2 (/ 1 eps)) (* 1/8 (/ 1 (pow x 2))))))
(* -1/8 (/ eps (pow x 2)))
(/ (+ (* -1/2 (pow x 2)) (* -1/8 eps)) (pow x 2))
(/ (+ (* -1/2 (pow x 2)) (* -1/8 eps)) (pow x 2))
(/ (+ (* -1/2 (pow x 2)) (* -1/8 eps)) (pow x 2))
-1/2
(- (* -1/8 (/ eps (pow x 2))) 1/2)
(- (* -1/8 (/ eps (pow x 2))) 1/2)
(- (* -1/8 (/ eps (pow x 2))) 1/2)
-1/2
(- (* -1/8 (/ eps (pow x 2))) 1/2)
(- (* -1/8 (/ eps (pow x 2))) 1/2)
(- (* -1/8 (/ eps (pow x 2))) 1/2)
(/ -1/8 (pow x 2))
(/ -1/8 (pow x 2))
(/ -1/8 (pow x 2))
(/ -1/8 (pow x 2))
(/ -1/8 (pow x 2))
(/ -1/8 (pow x 2))
(/ -1/8 (pow x 2))
(/ -1/8 (pow x 2))
(/ -1/8 (pow x 2))
(/ -1/8 (pow x 2))
(/ -1/8 (pow x 2))
(/ -1/8 (pow x 2))

Outputs
(* -1 (* (sqrt eps) (sqrt -1)))
(*.f64 (sqrt.f64 eps) (neg.f64 (sqrt.f64 #s(literal -1 binary64))))
(- x (* (sqrt eps) (sqrt -1)))
(fma.f64 (sqrt.f64 eps) (neg.f64 (sqrt.f64 #s(literal -1 binary64))) x)
(- (* x (+ 1 (* -1/2 (* (sqrt (/ 1 eps)) (/ x (sqrt -1)))))) (* (sqrt eps) (sqrt -1)))
(-.f64 (fma.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (/.f64 x (sqrt.f64 #s(literal -1 binary64)))) (.f64 #s(literal -1/2 binary64) x) x) (*.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64))))
(- (* x (+ 1 (* x (- (* 1/8 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))))))) (* (sqrt eps) (sqrt -1)))
(-.f64 (fma.f64 (.f64 x x) (fma.f64 #s(literal -1/8 binary64) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 eps (.f64 eps eps)))) (.f64 x (/.f64 x (sqrt.f64 #s(literal -1 binary64))))) (.f64 #s(literal -1/2 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64))))) x) (*.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64))))
(* 1/2 (/ eps x))
(*.f64 #s(literal 1/2 binary64) (/.f64 eps x))
(/ (- (* 1/8 (/ (pow eps 2) (pow x 2))) (* -1/2 eps)) x)
(/.f64 (fma.f64 #s(literal 1/8 binary64) (/.f64 (.f64 eps eps) (.f64 x x)) (*.f64 eps #s(literal 1/2 binary64))) x)
(/ (- (* 1/16 (/ (pow eps 3) (pow x 4))) (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2))))) x)
(/.f64 (fma.f64 #s(literal 1/8 binary64) (/.f64 (.f64 eps eps) (.f64 x x)) (fma.f64 #s(literal 1/16 binary64) (/.f64 (.f64 eps (.f64 eps eps)) (.f64 (.f64 x x) (.f64 x x))) (.f64 eps #s(literal 1/2 binary64)))) x)
(/ (- (* 1/2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) (pow x 6))) (+ (* -1/2 eps) (+ (* -1/8 (/ (pow eps 2) (pow x 2))) (* -1/16 (/ (pow eps 3) (pow x 4)))))) x)
(/.f64 (fma.f64 #s(literal 1/2 binary64) (/.f64 (.f64 (pow.f64 eps #s(literal 4 binary64)) #s(literal 5/64 binary64)) (pow.f64 x #s(literal 6 binary64))) (fma.f64 #s(literal 1/8 binary64) (/.f64 (.f64 eps eps) (.f64 x x)) (fma.f64 #s(literal 1/16 binary64) (/.f64 (.f64 eps (.f64 eps eps)) (.f64 (.f64 x x) (.f64 x x))) (*.f64 eps #s(literal 1/2 binary64))))) x)
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* -1 (* x (- (* 1/2 (/ eps (pow x 2))) 2)))
(.f64 x (fma.f64 eps (/.f64 #s(literal -1/2 binary64) (.f64 x x)) #s(literal 2 binary64)))
(* -1 (* x (- (* 1/8 (/ (pow eps 2) (pow x 4))) (+ 2 (* -1/2 (/ eps (pow x 2)))))))
(.f64 (fma.f64 eps (/.f64 #s(literal 1/2 binary64) (.f64 x x)) (fma.f64 #s(literal 1/8 binary64) (/.f64 (.f64 eps eps) (.f64 (.f64 x x) (.f64 x x))) #s(literal -2 binary64))) (neg.f64 x))
(* -1 (* x (- (* 1/16 (/ (pow eps 3) (pow x 6))) (+ 2 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4))))))))
(.f64 (fma.f64 #s(literal 1/16 binary64) (/.f64 (.f64 eps (.f64 eps eps)) (pow.f64 x #s(literal 6 binary64))) (fma.f64 eps (/.f64 #s(literal 1/2 binary64) (.f64 x x)) (fma.f64 #s(literal 1/8 binary64) (/.f64 (.f64 eps eps) (.f64 (.f64 x x) (.f64 x x))) #s(literal -2 binary64)))) (neg.f64 x))
(* 1/2 (/ eps x))
(*.f64 #s(literal 1/2 binary64) (/.f64 eps x))
(* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))
(/.f64 (fma.f64 #s(literal 1/8 binary64) (/.f64 (.f64 eps eps) (.f64 x x)) (*.f64 eps #s(literal 1/2 binary64))) x)
(* eps (+ (* eps (+ (* 1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))
(.f64 eps (fma.f64 eps (fma.f64 eps (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 5 binary64))) (/.f64 #s(literal 1/8 binary64) (.f64 x (*.f64 x x)))) (/.f64 #s(literal 1/2 binary64) x)))
(* eps (+ (* eps (+ (* eps (+ (* 5/128 (/ eps (pow x 7))) (* 1/16 (/ 1 (pow x 5))))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))
(.f64 eps (fma.f64 eps (fma.f64 eps (fma.f64 #s(literal 5/128 binary64) (/.f64 eps (pow.f64 x #s(literal 7 binary64))) (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 5 binary64)))) (/.f64 #s(literal 1/8 binary64) (.f64 x (*.f64 x x)))) (/.f64 #s(literal 1/2 binary64) x)))
(* -1 (* (sqrt eps) (sqrt -1)))
(*.f64 (sqrt.f64 eps) (neg.f64 (sqrt.f64 #s(literal -1 binary64))))
(* eps (- (/ x eps) (* (sqrt (/ 1 eps)) (sqrt -1))))
(*.f64 eps (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (neg.f64 (sqrt.f64 #s(literal -1 binary64))) (/.f64 x eps)))
(* eps (- (+ (* -1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1))))
(.f64 eps (fma.f64 #s(literal -1/2 binary64) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 eps (.f64 eps eps)))) (*.f64 x (/.f64 x (sqrt.f64 #s(literal -1 binary64))))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (neg.f64 (sqrt.f64 #s(literal -1 binary64))) (/.f64 x eps))))
(* eps (- (+ (* 1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (/ x eps)) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(.f64 eps (-.f64 (fma.f64 #s(literal -1/8 binary64) (/.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 5 binary64))))) (sqrt.f64 #s(literal -1 binary64))) (/.f64 x eps)) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 eps (.f64 eps eps)))) (.f64 (.f64 x (/.f64 x (sqrt.f64 #s(literal -1 binary64)))) #s(literal 1/2 binary64)) (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))))))
(* (sqrt eps) (sqrt -1))
(*.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64)))
(* -1 (* eps (- (* -1 (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(.f64 eps (+.f64 (/.f64 x eps) (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)))))
(* -1 (* eps (- (* -1 (/ (+ x (* 1/2 (* (sqrt (/ 1 eps)) (* (pow x 2) (sqrt -1))))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(.f64 eps (+.f64 (/.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (.f64 (.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) x) x) #s(literal 1/2 binary64)) x) eps) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)))))
(* -1 (* eps (- (* -1 (/ (+ x (* -1 (/ (- (* 1/8 (* (sqrt (/ 1 eps)) (* (pow x 4) (sqrt -1)))) (* 1/2 (* (sqrt eps) (* (pow x 2) (sqrt -1))))) eps))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(.f64 eps (+.f64 (/.f64 (-.f64 x (/.f64 (fma.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (.f64 (.f64 x x) (.f64 x x))) (.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 1/8 binary64)) (.f64 (.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) x) x) (.f64 (sqrt.f64 eps) #s(literal -1/2 binary64)))) eps)) eps) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)))))
(* (sqrt eps) (sqrt -1))
(*.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64)))
(+ (* 1/2 (* (sqrt (/ 1 eps)) (/ (pow x 2) (sqrt -1)))) (* (sqrt eps) (sqrt -1)))
(fma.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (.f64 (*.f64 x (/.f64 x (sqrt.f64 #s(literal -1 binary64)))) #s(literal 1/2 binary64))))
(+ (* (sqrt eps) (sqrt -1)) (* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))))))
(fma.f64 x (.f64 x (fma.f64 #s(literal 1/8 binary64) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 eps (.f64 eps eps)))) (.f64 x (/.f64 x (sqrt.f64 #s(literal -1 binary64))))) (.f64 #s(literal 1/2 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64)))))) (*.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64))))
(+ (* (sqrt eps) (sqrt -1)) (* (pow x 2) (+ (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))) (* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3)))) (* 1/16 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 2) (pow (sqrt -1) 5)))))))))
(fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 #s(literal 1/16 binary64) (/.f64 (.f64 (.f64 x x) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 5 binary64))))) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64))) (.f64 #s(literal 1/8 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 eps (.f64 eps eps)))) (sqrt.f64 #s(literal -1 binary64))))) (.f64 #s(literal 1/2 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64))))) (*.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64))))
x
(* x (+ 1 (* -1/2 (/ eps (pow x 2)))))
(fma.f64 (/.f64 eps (.f64 x x)) (.f64 #s(literal -1/2 binary64) x) x)
(* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4))))))
(fma.f64 x (fma.f64 eps (/.f64 #s(literal -1/2 binary64) (.f64 x x)) (/.f64 (.f64 eps (.f64 eps #s(literal -1/8 binary64))) (.f64 (.f64 x x) (.f64 x x)))) x)
(* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/8 (/ (pow eps 2) (pow x 4))) (* -1/16 (/ (pow eps 3) (pow x 6)))))))
(fma.f64 x (fma.f64 eps (/.f64 #s(literal -1/2 binary64) (.f64 x x)) (fma.f64 (.f64 eps eps) (/.f64 #s(literal -1/8 binary64) (.f64 (.f64 x x) (.f64 x x))) (/.f64 (.f64 (.f64 eps (.f64 eps eps)) #s(literal -1/16 binary64)) (pow.f64 x #s(literal 6 binary64))))) x)
(* -1 x)
(neg.f64 x)
(* -1 (* x (+ 1 (* -1/2 (/ eps (pow x 2))))))
(.f64 x (fma.f64 eps (/.f64 #s(literal 1/2 binary64) (.f64 x x)) #s(literal -1 binary64)))
(* -1 (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4)))))))
(.f64 x (fma.f64 #s(literal 1/8 binary64) (/.f64 (.f64 eps eps) (.f64 (.f64 x x) (.f64 x x))) (fma.f64 eps (/.f64 #s(literal 1/2 binary64) (.f64 x x)) #s(literal -1 binary64))))
(* -1 (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/8 (/ (pow eps 2) (pow x 4))) (* -1/16 (/ (pow eps 3) (pow x 6))))))))
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x
(+ x (* -1/2 (/ eps x)))
(fma.f64 eps (/.f64 #s(literal -1/2 binary64) x) x)
(+ x (* eps (- (* -1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))))
(fma.f64 eps (/.f64 (fma.f64 eps (/.f64 #s(literal -1/8 binary64) (*.f64 x x)) #s(literal -1/2 binary64)) x) x)
(+ x (* eps (- (* eps (- (* -1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))))
(fma.f64 eps (fma.f64 eps (fma.f64 #s(literal -1/16 binary64) (/.f64 eps (pow.f64 x #s(literal 5 binary64))) (/.f64 #s(literal -1/8 binary64) (.f64 x (.f64 x x)))) (/.f64 #s(literal -1/2 binary64) x)) x)
(* (sqrt eps) (sqrt -1))
(*.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64)))
(* eps (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))
(.f64 eps (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 eps (.f64 eps eps)))) (.f64 (.f64 x (/.f64 x (sqrt.f64 #s(literal -1 binary64)))) #s(literal 1/2 binary64)) (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)))))
(* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(.f64 eps (fma.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (fma.f64 #s(literal 1/8 binary64) (/.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 5 binary64))))) (sqrt.f64 #s(literal -1 binary64))) (/.f64 (.f64 #s(literal 1/2 binary64) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 eps (.f64 eps eps)))) (.f64 x x))) (sqrt.f64 #s(literal -1 binary64))))))
(* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow eps 7))) (/ (pow x 6) (pow (sqrt -1) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))))
(.f64 eps (fma.f64 #s(literal 1/8 binary64) (/.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 5 binary64))))) (sqrt.f64 #s(literal -1 binary64))) (fma.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 eps (.f64 eps eps)))) (.f64 (.f64 x (/.f64 x (sqrt.f64 #s(literal -1 binary64)))) #s(literal 1/2 binary64)) (.f64 (/.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64))) (*.f64 #s(literal 1/16 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 7 binary64))))))))))
(* -1 (* (sqrt eps) (sqrt -1)))
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(* -1 (* eps (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(neg.f64 (.f64 eps (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 eps (.f64 eps eps)))) (.f64 (.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) x) x) #s(literal 1/2 binary64)) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))))))
(* -1 (* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (* (pow x 4) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))))
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(* -1 (* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (* (pow x 4) (sqrt -1)))) (+ (* 1/16 (* (sqrt (/ 1 (pow eps 7))) (* (pow x 6) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))))
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(neg.f64 eps)
(- (pow x 2) eps)
(-.f64 (*.f64 x x) eps)
(- (pow x 2) eps)
(-.f64 (*.f64 x x) eps)
(- (pow x 2) eps)
(-.f64 (*.f64 x x) eps)
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))
(.f64 x (fma.f64 x (/.f64 eps (neg.f64 (.f64 x x))) x))
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))
(.f64 x (fma.f64 x (/.f64 eps (neg.f64 (.f64 x x))) x))
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))
(.f64 x (fma.f64 x (/.f64 eps (neg.f64 (.f64 x x))) x))
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))
(.f64 x (fma.f64 x (/.f64 eps (neg.f64 (.f64 x x))) x))
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))
(.f64 x (fma.f64 x (/.f64 eps (neg.f64 (.f64 x x))) x))
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))
(.f64 x (fma.f64 x (/.f64 eps (neg.f64 (.f64 x x))) x))
(pow x 2)
(*.f64 x x)
(+ (* -1 eps) (pow x 2))
(-.f64 (*.f64 x x) eps)
(+ (* -1 eps) (pow x 2))
(-.f64 (*.f64 x x) eps)
(+ (* -1 eps) (pow x 2))
(-.f64 (*.f64 x x) eps)
(* -1 eps)
(neg.f64 eps)
(* eps (- (/ (pow x 2) eps) 1))
(*.f64 eps (fma.f64 x (/.f64 x eps) #s(literal -1 binary64)))
(* eps (- (/ (pow x 2) eps) 1))
(*.f64 eps (fma.f64 x (/.f64 x eps) #s(literal -1 binary64)))
(* eps (- (/ (pow x 2) eps) 1))
(*.f64 eps (fma.f64 x (/.f64 x eps) #s(literal -1 binary64)))
(* -1 eps)
(neg.f64 eps)
(* -1 (* eps (+ 1 (* -1 (/ (pow x 2) eps)))))
(*.f64 eps (fma.f64 x (/.f64 x eps) #s(literal -1 binary64)))
(* -1 (* eps (+ 1 (* -1 (/ (pow x 2) eps)))))
(*.f64 eps (fma.f64 x (/.f64 x eps) #s(literal -1 binary64)))
(* -1 (* eps (+ 1 (* -1 (/ (pow x 2) eps)))))
(*.f64 eps (fma.f64 x (/.f64 x eps) #s(literal -1 binary64)))
(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)
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(pow x 2)
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(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(* -1 (* (sqrt eps) (sqrt -1)))
(*.f64 (sqrt.f64 eps) (neg.f64 (sqrt.f64 #s(literal -1 binary64))))
(- x (* (sqrt eps) (sqrt -1)))
(fma.f64 (sqrt.f64 eps) (neg.f64 (sqrt.f64 #s(literal -1 binary64))) x)
(- x (* (sqrt eps) (sqrt -1)))
(fma.f64 (sqrt.f64 eps) (neg.f64 (sqrt.f64 #s(literal -1 binary64))) x)
(- x (* (sqrt eps) (sqrt -1)))
(fma.f64 (sqrt.f64 eps) (neg.f64 (sqrt.f64 #s(literal -1 binary64))) x)
x
(* x (+ 1 (* -1 (* (sqrt eps) (/ (sqrt -1) x)))))
(fma.f64 (neg.f64 x) (*.f64 (sqrt.f64 eps) (/.f64 (sqrt.f64 #s(literal -1 binary64)) x)) x)
(* x (+ 1 (* -1 (* (sqrt eps) (/ (sqrt -1) x)))))
(fma.f64 (neg.f64 x) (*.f64 (sqrt.f64 eps) (/.f64 (sqrt.f64 #s(literal -1 binary64)) x)) x)
(* x (+ 1 (* -1 (* (sqrt eps) (/ (sqrt -1) x)))))
(fma.f64 (neg.f64 x) (*.f64 (sqrt.f64 eps) (/.f64 (sqrt.f64 #s(literal -1 binary64)) x)) x)
x
(* -1 (* x (- (* (sqrt eps) (/ (sqrt -1) x)) 1)))
(fma.f64 (neg.f64 x) (*.f64 (sqrt.f64 eps) (/.f64 (sqrt.f64 #s(literal -1 binary64)) x)) x)
(* -1 (* x (- (* (sqrt eps) (/ (sqrt -1) x)) 1)))
(fma.f64 (neg.f64 x) (*.f64 (sqrt.f64 eps) (/.f64 (sqrt.f64 #s(literal -1 binary64)) x)) x)
(* -1 (* x (- (* (sqrt eps) (/ (sqrt -1) x)) 1)))
(fma.f64 (neg.f64 x) (*.f64 (sqrt.f64 eps) (/.f64 (sqrt.f64 #s(literal -1 binary64)) x)) x)
(- x (* (sqrt eps) (sqrt -1)))
(fma.f64 (sqrt.f64 eps) (neg.f64 (sqrt.f64 #s(literal -1 binary64))) x)
(- x (* (sqrt eps) (sqrt -1)))
(fma.f64 (sqrt.f64 eps) (neg.f64 (sqrt.f64 #s(literal -1 binary64))) x)
(- x (* (sqrt eps) (sqrt -1)))
(fma.f64 (sqrt.f64 eps) (neg.f64 (sqrt.f64 #s(literal -1 binary64))) x)
(- x (* (sqrt eps) (sqrt -1)))
(fma.f64 (sqrt.f64 eps) (neg.f64 (sqrt.f64 #s(literal -1 binary64))) x)
(* -1 (* (sqrt eps) (sqrt -1)))
(*.f64 (sqrt.f64 eps) (neg.f64 (sqrt.f64 #s(literal -1 binary64))))
(* eps (- (/ x eps) (* (sqrt (/ 1 eps)) (sqrt -1))))
(*.f64 eps (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (neg.f64 (sqrt.f64 #s(literal -1 binary64))) (/.f64 x eps)))
(* eps (- (/ x eps) (* (sqrt (/ 1 eps)) (sqrt -1))))
(*.f64 eps (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (neg.f64 (sqrt.f64 #s(literal -1 binary64))) (/.f64 x eps)))
(* eps (- (/ x eps) (* (sqrt (/ 1 eps)) (sqrt -1))))
(*.f64 eps (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (neg.f64 (sqrt.f64 #s(literal -1 binary64))) (/.f64 x eps)))
(* (sqrt eps) (sqrt -1))
(*.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64)))
(* -1 (* eps (- (* -1 (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(.f64 eps (+.f64 (/.f64 x eps) (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)))))
(* -1 (* eps (- (* -1 (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(.f64 eps (+.f64 (/.f64 x eps) (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)))))
(* -1 (* eps (- (* -1 (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(.f64 eps (+.f64 (/.f64 x eps) (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)))))
(* (sqrt eps) (sqrt -1))
(*.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64)))
(* (sqrt eps) (sqrt -1))
(*.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64)))
(* (sqrt eps) (sqrt -1))
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x
(+ x (* -1/2 (/ eps x)))
(fma.f64 eps (/.f64 #s(literal -1/2 binary64) x) x)
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(.f64 (fma.f64 eps (/.f64 #s(literal 1/2 binary64) (.f64 x x)) (fma.f64 #s(literal 1/8 binary64) (/.f64 (.f64 eps eps) (.f64 (.f64 x x) (.f64 x x))) #s(literal -2 binary64))) (neg.f64 x))
(* -1 (* x (- (+ (* 1/8 (/ (pow eps 2) (pow x 4))) (* 1/2 (/ eps (pow x 2)))) 2)))
(.f64 (fma.f64 eps (/.f64 #s(literal 1/2 binary64) (.f64 x x)) (fma.f64 #s(literal 1/8 binary64) (/.f64 (.f64 eps eps) (.f64 (.f64 x x) (.f64 x x))) #s(literal -2 binary64))) (neg.f64 x))
(/ -1/2 x)
(/.f64 #s(literal -1/2 binary64) x)
(- (* -1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))
(/.f64 (fma.f64 eps (/.f64 #s(literal -1/8 binary64) (*.f64 x x)) #s(literal -1/2 binary64)) x)
(- (* -1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))
(/.f64 (fma.f64 eps (/.f64 #s(literal -1/8 binary64) (*.f64 x x)) #s(literal -1/2 binary64)) x)
(- (* -1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))
(/.f64 (fma.f64 eps (/.f64 #s(literal -1/8 binary64) (*.f64 x x)) #s(literal -1/2 binary64)) x)
(* -1/8 (/ eps (pow x 3)))
(/.f64 (.f64 eps #s(literal -1/8 binary64)) (.f64 x (*.f64 x x)))
(* -1 (* eps (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3))))))
(/.f64 (fma.f64 eps (/.f64 #s(literal -1/8 binary64) (*.f64 x x)) #s(literal -1/2 binary64)) x)
(* -1 (* eps (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3))))))
(/.f64 (fma.f64 eps (/.f64 #s(literal -1/8 binary64) (*.f64 x x)) #s(literal -1/2 binary64)) x)
(* -1 (* eps (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3))))))
(/.f64 (fma.f64 eps (/.f64 #s(literal -1/8 binary64) (*.f64 x x)) #s(literal -1/2 binary64)) x)
(* -1/8 (/ eps (pow x 3)))
(/.f64 (.f64 eps #s(literal -1/8 binary64)) (.f64 x (*.f64 x x)))
(* -1 (* eps (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3))))))
(/.f64 (fma.f64 eps (/.f64 #s(literal -1/8 binary64) (*.f64 x x)) #s(literal -1/2 binary64)) x)
(* -1 (* eps (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3))))))
(/.f64 (fma.f64 eps (/.f64 #s(literal -1/8 binary64) (*.f64 x x)) #s(literal -1/2 binary64)) x)
(* -1 (* eps (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3))))))
(/.f64 (fma.f64 eps (/.f64 #s(literal -1/8 binary64) (*.f64 x x)) #s(literal -1/2 binary64)) x)
(* -1/8 (/ eps (pow x 3)))
(/.f64 (.f64 eps #s(literal -1/8 binary64)) (.f64 x (*.f64 x x)))
(/ (+ (* -1/2 (pow x 2)) (* -1/8 eps)) (pow x 3))
(/.f64 (fma.f64 eps #s(literal -1/8 binary64) (.f64 x (.f64 x #s(literal -1/2 binary64)))) (.f64 x (.f64 x x)))
(/ (+ (* -1/2 (pow x 2)) (* -1/8 eps)) (pow x 3))
(/.f64 (fma.f64 eps #s(literal -1/8 binary64) (.f64 x (.f64 x #s(literal -1/2 binary64)))) (.f64 x (.f64 x x)))
(/ (+ (* -1/2 (pow x 2)) (* -1/8 eps)) (pow x 3))
(/.f64 (fma.f64 eps #s(literal -1/8 binary64) (.f64 x (.f64 x #s(literal -1/2 binary64)))) (.f64 x (.f64 x x)))
(/ -1/2 x)
(/.f64 #s(literal -1/2 binary64) x)
(/ (- (* -1/8 (/ eps (pow x 2))) 1/2) x)
(/.f64 (fma.f64 eps (/.f64 #s(literal -1/8 binary64) (*.f64 x x)) #s(literal -1/2 binary64)) x)
(/ (- (* -1/8 (/ eps (pow x 2))) 1/2) x)
(/.f64 (fma.f64 eps (/.f64 #s(literal -1/8 binary64) (*.f64 x x)) #s(literal -1/2 binary64)) x)
(/ (- (* -1/8 (/ eps (pow x 2))) 1/2) x)
(/.f64 (fma.f64 eps (/.f64 #s(literal -1/8 binary64) (*.f64 x x)) #s(literal -1/2 binary64)) x)
(/ -1/2 x)
(/.f64 #s(literal -1/2 binary64) x)
(* -1 (/ (+ 1/2 (* 1/8 (/ eps (pow x 2)))) x))
(/.f64 (fma.f64 eps (/.f64 #s(literal -1/8 binary64) (*.f64 x x)) #s(literal -1/2 binary64)) x)
(* -1 (/ (+ 1/2 (* 1/8 (/ eps (pow x 2)))) x))
(/.f64 (fma.f64 eps (/.f64 #s(literal -1/8 binary64) (*.f64 x x)) #s(literal -1/2 binary64)) x)
(* -1 (/ (+ 1/2 (* 1/8 (/ eps (pow x 2)))) x))
(/.f64 (fma.f64 eps (/.f64 #s(literal -1/8 binary64) (*.f64 x x)) #s(literal -1/2 binary64)) x)
(* (sqrt eps) (sqrt -1))
(*.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64)))
(+ (* 1/2 (* (sqrt (/ 1 eps)) (/ (pow x 2) (sqrt -1)))) (* (sqrt eps) (sqrt -1)))
(fma.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (.f64 (*.f64 x (/.f64 x (sqrt.f64 #s(literal -1 binary64)))) #s(literal 1/2 binary64))))
(+ (* (sqrt eps) (sqrt -1)) (* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))))))
(fma.f64 x (.f64 x (fma.f64 #s(literal 1/8 binary64) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 eps (.f64 eps eps)))) (.f64 x (/.f64 x (sqrt.f64 #s(literal -1 binary64))))) (.f64 #s(literal 1/2 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64)))))) (*.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64))))
(+ (* (sqrt eps) (sqrt -1)) (* (pow x 2) (+ (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))) (* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3)))) (* 1/16 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 2) (pow (sqrt -1) 5)))))))))
(fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 #s(literal 1/16 binary64) (/.f64 (.f64 (.f64 x x) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 5 binary64))))) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64))) (.f64 #s(literal 1/8 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 eps (.f64 eps eps)))) (sqrt.f64 #s(literal -1 binary64))))) (.f64 #s(literal 1/2 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64))))) (*.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64))))
x
(* x (+ 1 (* -1/2 (/ eps (pow x 2)))))
(fma.f64 (/.f64 eps (.f64 x x)) (.f64 #s(literal -1/2 binary64) x) x)
(* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4))))))
(fma.f64 x (fma.f64 eps (/.f64 #s(literal -1/2 binary64) (.f64 x x)) (/.f64 (.f64 eps (.f64 eps #s(literal -1/8 binary64))) (.f64 (.f64 x x) (.f64 x x)))) x)
(* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/8 (/ (pow eps 2) (pow x 4))) (* -1/16 (/ (pow eps 3) (pow x 6)))))))
(fma.f64 x (fma.f64 eps (/.f64 #s(literal -1/2 binary64) (.f64 x x)) (fma.f64 (.f64 eps eps) (/.f64 #s(literal -1/8 binary64) (.f64 (.f64 x x) (.f64 x x))) (/.f64 (.f64 (.f64 eps (.f64 eps eps)) #s(literal -1/16 binary64)) (pow.f64 x #s(literal 6 binary64))))) x)
(* -1 x)
(neg.f64 x)
(* -1 (* x (+ 1 (* -1/2 (/ eps (pow x 2))))))
(.f64 x (fma.f64 eps (/.f64 #s(literal 1/2 binary64) (.f64 x x)) #s(literal -1 binary64)))
(* -1 (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4)))))))
(.f64 x (fma.f64 #s(literal 1/8 binary64) (/.f64 (.f64 eps eps) (.f64 (.f64 x x) (.f64 x x))) (fma.f64 eps (/.f64 #s(literal 1/2 binary64) (.f64 x x)) #s(literal -1 binary64))))
(* -1 (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/8 (/ (pow eps 2) (pow x 4))) (* -1/16 (/ (pow eps 3) (pow x 6))))))))
(neg.f64 (fma.f64 x (fma.f64 eps (/.f64 #s(literal -1/2 binary64) (.f64 x x)) (fma.f64 (.f64 eps eps) (/.f64 #s(literal -1/8 binary64) (.f64 (.f64 x x) (.f64 x x))) (/.f64 (.f64 (.f64 eps (.f64 eps eps)) #s(literal -1/16 binary64)) (pow.f64 x #s(literal 6 binary64))))) x))
x
(+ x (* -1/2 (/ eps x)))
(fma.f64 eps (/.f64 #s(literal -1/2 binary64) x) x)
(+ x (* eps (- (* -1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))))
(fma.f64 eps (/.f64 (fma.f64 eps (/.f64 #s(literal -1/8 binary64) (*.f64 x x)) #s(literal -1/2 binary64)) x) x)
(+ x (* eps (- (* eps (- (* -1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))))
(fma.f64 eps (fma.f64 eps (fma.f64 #s(literal -1/16 binary64) (/.f64 eps (pow.f64 x #s(literal 5 binary64))) (/.f64 #s(literal -1/8 binary64) (.f64 x (.f64 x x)))) (/.f64 #s(literal -1/2 binary64) x)) x)
(* (sqrt eps) (sqrt -1))
(*.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64)))
(* eps (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))
(.f64 eps (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 eps (.f64 eps eps)))) (.f64 (.f64 x (/.f64 x (sqrt.f64 #s(literal -1 binary64)))) #s(literal 1/2 binary64)) (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)))))
(* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(.f64 eps (fma.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (fma.f64 #s(literal 1/8 binary64) (/.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 5 binary64))))) (sqrt.f64 #s(literal -1 binary64))) (/.f64 (.f64 #s(literal 1/2 binary64) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 eps (.f64 eps eps)))) (.f64 x x))) (sqrt.f64 #s(literal -1 binary64))))))
(* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow eps 7))) (/ (pow x 6) (pow (sqrt -1) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))))
(.f64 eps (fma.f64 #s(literal 1/8 binary64) (/.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 5 binary64))))) (sqrt.f64 #s(literal -1 binary64))) (fma.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 eps (.f64 eps eps)))) (.f64 (.f64 x (/.f64 x (sqrt.f64 #s(literal -1 binary64)))) #s(literal 1/2 binary64)) (.f64 (/.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64))) (*.f64 #s(literal 1/16 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 7 binary64))))))))))
(* -1 (* (sqrt eps) (sqrt -1)))
(*.f64 (sqrt.f64 eps) (neg.f64 (sqrt.f64 #s(literal -1 binary64))))
(* -1 (* eps (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(neg.f64 (.f64 eps (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 eps (.f64 eps eps)))) (.f64 (.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) x) x) #s(literal 1/2 binary64)) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))))))
(* -1 (* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (* (pow x 4) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))))
(neg.f64 (.f64 eps (fma.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 5 binary64))))) (.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal -1/8 binary64)) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 eps (.f64 eps eps)))) (.f64 (.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) x) x) #s(literal 1/2 binary64)) (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)))))))
(* -1 (* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (* (pow x 4) (sqrt -1)))) (+ (* 1/16 (* (sqrt (/ 1 (pow eps 7))) (* (pow x 6) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))))
(neg.f64 (.f64 eps (fma.f64 #s(literal 1/16 binary64) (.f64 (pow.f64 x #s(literal 6 binary64)) (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 7 binary64)))))) (fma.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 5 binary64))))) (.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal -1/8 binary64)) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 eps (.f64 eps eps)))) (.f64 (.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) x) x) #s(literal 1/2 binary64)) (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))))))))
-1/2
#s(literal -1/2 binary64)
(- (* -1/8 (/ eps (pow x 2))) 1/2)
(fma.f64 eps (/.f64 #s(literal -1/8 binary64) (*.f64 x x)) #s(literal -1/2 binary64))
(- (* -1/8 (/ eps (pow x 2))) 1/2)
(fma.f64 eps (/.f64 #s(literal -1/8 binary64) (*.f64 x x)) #s(literal -1/2 binary64))
(- (* -1/8 (/ eps (pow x 2))) 1/2)
(fma.f64 eps (/.f64 #s(literal -1/8 binary64) (*.f64 x x)) #s(literal -1/2 binary64))
(* -1/8 (/ eps (pow x 2)))
(/.f64 (.f64 eps #s(literal -1/8 binary64)) (.f64 x x))
(* -1 (* eps (+ (* 1/8 (/ 1 (pow x 2))) (* 1/2 (/ 1 eps)))))
(fma.f64 eps (/.f64 #s(literal -1/8 binary64) (*.f64 x x)) #s(literal -1/2 binary64))
(* -1 (* eps (+ (* 1/8 (/ 1 (pow x 2))) (* 1/2 (/ 1 eps)))))
(fma.f64 eps (/.f64 #s(literal -1/8 binary64) (*.f64 x x)) #s(literal -1/2 binary64))
(* -1 (* eps (+ (* 1/8 (/ 1 (pow x 2))) (* 1/2 (/ 1 eps)))))
(fma.f64 eps (/.f64 #s(literal -1/8 binary64) (*.f64 x x)) #s(literal -1/2 binary64))
(* -1/8 (/ eps (pow x 2)))
(/.f64 (.f64 eps #s(literal -1/8 binary64)) (.f64 x x))
(* -1 (* eps (+ (* 1/2 (/ 1 eps)) (* 1/8 (/ 1 (pow x 2))))))
(fma.f64 eps (/.f64 #s(literal -1/8 binary64) (*.f64 x x)) #s(literal -1/2 binary64))
(* -1 (* eps (+ (* 1/2 (/ 1 eps)) (* 1/8 (/ 1 (pow x 2))))))
(fma.f64 eps (/.f64 #s(literal -1/8 binary64) (*.f64 x x)) #s(literal -1/2 binary64))
(* -1 (* eps (+ (* 1/2 (/ 1 eps)) (* 1/8 (/ 1 (pow x 2))))))
(fma.f64 eps (/.f64 #s(literal -1/8 binary64) (*.f64 x x)) #s(literal -1/2 binary64))
(* -1/8 (/ eps (pow x 2)))
(/.f64 (.f64 eps #s(literal -1/8 binary64)) (.f64 x x))
(/ (+ (* -1/2 (pow x 2)) (* -1/8 eps)) (pow x 2))
(/.f64 (fma.f64 eps #s(literal -1/8 binary64) (.f64 x (.f64 x #s(literal -1/2 binary64)))) (*.f64 x x))
(/ (+ (* -1/2 (pow x 2)) (* -1/8 eps)) (pow x 2))
(/.f64 (fma.f64 eps #s(literal -1/8 binary64) (.f64 x (.f64 x #s(literal -1/2 binary64)))) (*.f64 x x))
(/ (+ (* -1/2 (pow x 2)) (* -1/8 eps)) (pow x 2))
(/.f64 (fma.f64 eps #s(literal -1/8 binary64) (.f64 x (.f64 x #s(literal -1/2 binary64)))) (*.f64 x x))
-1/2
#s(literal -1/2 binary64)
(- (* -1/8 (/ eps (pow x 2))) 1/2)
(fma.f64 eps (/.f64 #s(literal -1/8 binary64) (*.f64 x x)) #s(literal -1/2 binary64))
(- (* -1/8 (/ eps (pow x 2))) 1/2)
(fma.f64 eps (/.f64 #s(literal -1/8 binary64) (*.f64 x x)) #s(literal -1/2 binary64))
(- (* -1/8 (/ eps (pow x 2))) 1/2)
(fma.f64 eps (/.f64 #s(literal -1/8 binary64) (*.f64 x x)) #s(literal -1/2 binary64))
-1/2
#s(literal -1/2 binary64)
(- (* -1/8 (/ eps (pow x 2))) 1/2)
(fma.f64 eps (/.f64 #s(literal -1/8 binary64) (*.f64 x x)) #s(literal -1/2 binary64))
(- (* -1/8 (/ eps (pow x 2))) 1/2)
(fma.f64 eps (/.f64 #s(literal -1/8 binary64) (*.f64 x x)) #s(literal -1/2 binary64))
(- (* -1/8 (/ eps (pow x 2))) 1/2)
(fma.f64 eps (/.f64 #s(literal -1/8 binary64) (*.f64 x x)) #s(literal -1/2 binary64))
(/ -1/8 (pow x 2))
(/.f64 #s(literal -1/8 binary64) (*.f64 x x))
(/ -1/8 (pow x 2))
(/.f64 #s(literal -1/8 binary64) (*.f64 x x))
(/ -1/8 (pow x 2))
(/.f64 #s(literal -1/8 binary64) (*.f64 x x))
(/ -1/8 (pow x 2))
(/.f64 #s(literal -1/8 binary64) (*.f64 x x))
(/ -1/8 (pow x 2))
(/.f64 #s(literal -1/8 binary64) (*.f64 x x))
(/ -1/8 (pow x 2))
(/.f64 #s(literal -1/8 binary64) (*.f64 x x))
(/ -1/8 (pow x 2))
(/.f64 #s(literal -1/8 binary64) (*.f64 x x))
(/ -1/8 (pow x 2))
(/.f64 #s(literal -1/8 binary64) (*.f64 x x))
(/ -1/8 (pow x 2))
(/.f64 #s(literal -1/8 binary64) (*.f64 x x))
(/ -1/8 (pow x 2))
(/.f64 #s(literal -1/8 binary64) (*.f64 x x))
(/ -1/8 (pow x 2))
(/.f64 #s(literal -1/8 binary64) (*.f64 x x))
(/ -1/8 (pow x 2))
(/.f64 #s(literal -1/8 binary64) (*.f64 x x))

eval212.0ms (2.1%)

Memory: 42.1MiB live, 516.5MiB allocated
Compiler: Compiled 38 890 to 4 064 computations (89.6% saved)

prune155.0ms (1.5%)

Memory

-34.2MiB live, 374.3MiB allocated

Pruning

12 alts after pruning (6 fresh and 6 done)

	Pruned	Kept	Total
New	1 357	4	1 361
Fresh	2	2	4
Picked	2	3	5
Done	0	3	3
Total	1 361	12	1 373

Accuracy

100.0%

Counts

1 373 → 12

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	55.8%	(/.f64 (fma.f64 x x eps) (+.f64 x (sqrt.f64 (neg.f64 eps))))
✓	45.6%	(/.f64 (*.f64 eps #s(literal 1/2 binary64)) x)
▶	45.0%	(/.f64 eps (+.f64 x (fma.f64 eps (/.f64 (fma.f64 eps (/.f64 #s(literal -1/8 binary64) (*.f64 x x)) #s(literal -1/2 binary64)) x) x)))
▶	46.1%	(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 eps (/.f64 #s(literal -1/2 binary64) x) (+.f64 x x)) eps))
✓	60.3%	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))))
✓	6.7%	(-.f64 x (fma.f64 eps (/.f64 #s(literal -1/2 binary64) x) x))
✓	60.4%	(-.f64 x (sqrt.f64 (fma.f64 x x (neg.f64 eps))))
✓	56.2%	(-.f64 x (sqrt.f64 (neg.f64 eps)))
	44.9%	(.f64 (/.f64 #s(literal 1 binary64) (+.f64 x (fma.f64 eps (/.f64 (fma.f64 eps (/.f64 #s(literal -1/8 binary64) (.f64 x x)) #s(literal -1/2 binary64)) x) x))) eps)
▶	45.5%	(*.f64 (/.f64 #s(literal 1/2 binary64) x) eps)
▶	3.7%	x
✓	4.3%	#s(literal 0 binary64)

Compiler

Compiled 203 to 128 computations (36.9% saved)

simplify325.0ms (3.2%)

Memory

28.0MiB live, 300.3MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 14 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(/.f64 (fma.f64 eps (/.f64 #s(literal -1/8 binary64) (*.f64 x x)) #s(literal -1/2 binary64)) x)
✓	cost-diff	0	(fma.f64 eps (/.f64 (fma.f64 eps (/.f64 #s(literal -1/8 binary64) (*.f64 x x)) #s(literal -1/2 binary64)) x) x)
✓	cost-diff	0	(+.f64 x (fma.f64 eps (/.f64 (fma.f64 eps (/.f64 #s(literal -1/8 binary64) (*.f64 x x)) #s(literal -1/2 binary64)) x) x))
✓	cost-diff	0	(/.f64 eps (+.f64 x (fma.f64 eps (/.f64 (fma.f64 eps (/.f64 #s(literal -1/8 binary64) (*.f64 x x)) #s(literal -1/2 binary64)) x) x)))
✓	cost-diff	0	(/.f64 #s(literal -1/2 binary64) x)
✓	cost-diff	0	(fma.f64 eps (/.f64 #s(literal -1/2 binary64) x) (+.f64 x x))
✓	cost-diff	0	(/.f64 (fma.f64 eps (/.f64 #s(literal -1/2 binary64) x) (+.f64 x x)) eps)
✓	cost-diff	704	(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 eps (/.f64 #s(literal -1/2 binary64) x) (+.f64 x x)) eps))
✓	cost-diff	0	(/.f64 #s(literal 1/2 binary64) x)
✓	cost-diff	0	(*.f64 (/.f64 #s(literal 1/2 binary64) x) eps)
✓	cost-diff	0	(sqrt.f64 (neg.f64 eps))
✓	cost-diff	0	(+.f64 x (sqrt.f64 (neg.f64 eps)))
✓	cost-diff	0	(fma.f64 x x eps)
✓	cost-diff	0	(/.f64 (fma.f64 x x eps) (+.f64 x (sqrt.f64 (neg.f64 eps))))

Rules

5 512×	`accelerator-lowering-fma.f32`
5 512×	`accelerator-lowering-fma.f64`
2 624×	`-lowering-.f32`
2 624×	`-lowering-.f64`
1 306×	`unsub-neg`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	28	166
1	60	166
2	96	164
3	130	164
4	253	164
5	346	164
6	623	164
7	946	164
8	1118	164
9	1314	164
10	2878	164
11	4527	164
12	5466	164
13	6104	164
14	6544	164
15	6801	164
16	7008	164
17	7660	164
18	7958	164
19	7966	164
20	7968	164
21	7968	164
22	7972	164
23	7972	164
0	8166	151

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

Inputs
(/ (+ (* x x) eps) (+ x (sqrt (neg eps))))
(+ (* x x) eps)
x
eps
(+ x (sqrt (neg eps)))
(sqrt (neg eps))
(neg eps)
x
(* (/ 1/2 x) eps)
(/ 1/2 x)
1/2
x
eps
(/ 1 (/ (+ (* eps (/ -1/2 x)) (+ x x)) eps))
1
(/ (+ (* eps (/ -1/2 x)) (+ x x)) eps)
(+ (* eps (/ -1/2 x)) (+ x x))
eps
(/ -1/2 x)
-1/2
x
(+ x x)
(/ eps (+ x (+ (* eps (/ (+ (* eps (/ -1/8 (* x x))) -1/2) x)) x)))
eps
(+ x (+ (* eps (/ (+ (* eps (/ -1/8 (* x x))) -1/2) x)) x))
x
(+ (* eps (/ (+ (* eps (/ -1/8 (* x x))) -1/2) x)) x)
(/ (+ (* eps (/ -1/8 (* x x))) -1/2) x)
(+ (* eps (/ -1/8 (* x x))) -1/2)
(/ -1/8 (* x x))
-1/8
(* x x)
-1/2

Outputs
(/ (+ (* x x) eps) (+ x (sqrt (neg eps))))
(/.f64 (fma.f64 x x eps) (+.f64 x (sqrt.f64 (neg.f64 eps))))
(+ (* x x) eps)
(fma.f64 x x eps)
x
eps
(+ x (sqrt (neg eps)))
(+.f64 x (sqrt.f64 (neg.f64 eps)))
(sqrt (neg eps))
(sqrt.f64 (neg.f64 eps))
(neg eps)
(neg.f64 eps)
x
(* (/ 1/2 x) eps)
(/.f64 (*.f64 eps #s(literal 1/2 binary64)) x)
(/ 1/2 x)
(/.f64 #s(literal 1/2 binary64) x)
1/2
#s(literal 1/2 binary64)
x
eps
(/ 1 (/ (+ (* eps (/ -1/2 x)) (+ x x)) eps))
(/.f64 eps (+.f64 x (fma.f64 eps (/.f64 #s(literal -1/2 binary64) x) x)))
1
#s(literal 1 binary64)
(/ (+ (* eps (/ -1/2 x)) (+ x x)) eps)
(/.f64 (+.f64 x (fma.f64 eps (/.f64 #s(literal -1/2 binary64) x) x)) eps)
(+ (* eps (/ -1/2 x)) (+ x x))
(+.f64 x (fma.f64 eps (/.f64 #s(literal -1/2 binary64) x) x))
eps
(/ -1/2 x)
(/.f64 #s(literal -1/2 binary64) x)
-1/2
#s(literal -1/2 binary64)
x
(+ x x)
(+.f64 x x)
(/ eps (+ x (+ (* eps (/ (+ (* eps (/ -1/8 (* x x))) -1/2) x)) x)))
(/.f64 eps (+.f64 x (fma.f64 (fma.f64 eps (/.f64 #s(literal -1/8 binary64) (*.f64 x x)) #s(literal -1/2 binary64)) (/.f64 eps x) x)))
eps
(+ x (+ (* eps (/ (+ (* eps (/ -1/8 (* x x))) -1/2) x)) x))
(+.f64 x (fma.f64 (fma.f64 eps (/.f64 #s(literal -1/8 binary64) (*.f64 x x)) #s(literal -1/2 binary64)) (/.f64 eps x) x))
x
(+ (* eps (/ (+ (* eps (/ -1/8 (* x x))) -1/2) x)) x)
(fma.f64 (fma.f64 eps (/.f64 #s(literal -1/8 binary64) (*.f64 x x)) #s(literal -1/2 binary64)) (/.f64 eps x) x)
(/ (+ (* eps (/ -1/8 (* x x))) -1/2) x)
(/.f64 (fma.f64 eps (/.f64 #s(literal -1/8 binary64) (*.f64 x x)) #s(literal -1/2 binary64)) x)
(+ (* eps (/ -1/8 (* x x))) -1/2)
(fma.f64 eps (/.f64 #s(literal -1/8 binary64) (*.f64 x x)) #s(literal -1/2 binary64))
(/ -1/8 (* x x))
(/.f64 #s(literal -1/8 binary64) (*.f64 x x))
-1/8
#s(literal -1/8 binary64)
(* x x)
(*.f64 x x)
-1/2
#s(literal -1/2 binary64)

localize126.0ms (1.3%)

Memory

-38.7MiB live, 210.5MiB allocated

Localize:

Found 14 expressions of interest:

New	Metric	Score	Program
✓	accuracy	99.9%	(/.f64 eps (+.f64 x (fma.f64 eps (/.f64 (fma.f64 eps (/.f64 #s(literal -1/8 binary64) (*.f64 x x)) #s(literal -1/2 binary64)) x) x)))
✓	accuracy	99.9%	(/.f64 #s(literal -1/8 binary64) (*.f64 x x))
✓	accuracy	84.9%	(fma.f64 eps (/.f64 (fma.f64 eps (/.f64 #s(literal -1/8 binary64) (*.f64 x x)) #s(literal -1/2 binary64)) x) x)
✓	accuracy	80.6%	(fma.f64 eps (/.f64 #s(literal -1/8 binary64) (*.f64 x x)) #s(literal -1/2 binary64))
✓	accuracy	100.0%	(+.f64 x x)
✓	accuracy	99.8%	(/.f64 (fma.f64 eps (/.f64 #s(literal -1/2 binary64) x) (+.f64 x x)) eps)
✓	accuracy	99.7%	(fma.f64 eps (/.f64 #s(literal -1/2 binary64) x) (+.f64 x x))
✓	accuracy	99.7%	(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 eps (/.f64 #s(literal -1/2 binary64) x) (+.f64 x x)) eps))
✓	accuracy	100.0%	(/.f64 #s(literal 1/2 binary64) x)
✓	accuracy	99.7%	(*.f64 (/.f64 #s(literal 1/2 binary64) x) eps)
✓	accuracy	100.0%	(sqrt.f64 (neg.f64 eps))
✓	accuracy	100.0%	(neg.f64 eps)
✓	accuracy	100.0%	(+.f64 x (sqrt.f64 (neg.f64 eps)))
✓	accuracy	99.5%	(/.f64 (fma.f64 x x eps) (+.f64 x (sqrt.f64 (neg.f64 eps))))

Samples

38.0ms	195×	0	valid
15.0ms	61×	0	invalid

Compiler

Compiled 155 to 30 computations (80.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 38.0ms

ival-div: 13.0ms (34.4% of total)

ival-add: 13.0ms (34.4% of total)

ival-mult: 8.0ms (21.2% of total)

ival-sqrt: 2.0ms (5.3% of total)

ival-neg: 1.0ms (2.6% of total)

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

exact: 0.0ms (0% of total)

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

series14.0ms (0.1%)

Memory

28.9MiB live, 28.9MiB allocated

Counts

18 → 360

Calls

Call 1

Inputs
#<alt (/ (+ (* x x) eps) (+ x (sqrt (neg eps))))>
#<alt (+ (* x x) eps)>
#<alt (+ x (sqrt (neg eps)))>
#<alt (sqrt (neg eps))>
#<alt (* (/ 1/2 x) eps)>
#<alt (/ 1/2 x)>
#<alt (/ 1 (/ (+ (* eps (/ -1/2 x)) (+ x x)) eps))>
#<alt (/ (+ (* eps (/ -1/2 x)) (+ x x)) eps)>
#<alt (+ (* eps (/ -1/2 x)) (+ x x))>
#<alt (/ -1/2 x)>
#<alt (/ eps (+ x (+ (* eps (/ (+ (* eps (/ -1/8 (* x x))) -1/2) x)) x)))>
#<alt (+ x (+ (* eps (/ (+ (* eps (/ -1/8 (* x x))) -1/2) x)) x))>
#<alt (+ (* eps (/ (+ (* eps (/ -1/8 (* x x))) -1/2) x)) x)>
#<alt (/ (+ (* eps (/ -1/8 (* x x))) -1/2) x)>
#<alt (neg eps)>
#<alt (+ x x)>
#<alt (+ (* eps (/ -1/8 (* x x))) -1/2)>
#<alt (/ -1/8 (* x x))>

Outputs
#<alt (* (sqrt eps) (/ 1 (sqrt -1)))>
#<alt (+ (* -1 (/ x (pow (sqrt -1) 2))) (* (sqrt eps) (/ 1 (sqrt -1))))>
#<alt (+ (* x (- (* x (- (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1))) (* -1 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))))) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt eps) (/ 1 (sqrt -1))))>
#<alt (+ (* x (- (* x (- (+ (* -1 (* (sqrt (/ 1 eps)) (/ (* x (- (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1))) (* -1 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))))) (sqrt -1)))) (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))) (* -1 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))))) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt eps) (/ 1 (sqrt -1))))>
#<alt x>
#<alt (* x (+ 1 (* -1 (* (sqrt eps) (/ (sqrt -1) x)))))>
#<alt (* x (- (+ 1 (/ eps (pow x 2))) (+ (* -1 (/ (* eps (pow (sqrt -1) 2)) (pow x 2))) (* (sqrt eps) (/ (sqrt -1) x)))))>
#<alt (* x (- (+ 1 (+ (* -1 (* (sqrt eps) (/ (* (sqrt -1) (- eps (* -1 (* eps (pow (sqrt -1) 2))))) (pow x 3)))) (/ eps (pow x 2)))) (+ (* -1 (/ (* eps (pow (sqrt -1) 2)) (pow x 2))) (* (sqrt eps) (/ (sqrt -1) x)))))>
#<alt x>
#<alt (* -1 (* x (- (* (sqrt eps) (/ (sqrt -1) x)) 1)))>
#<alt (* -1 (* x (- (* -1 (/ (- (* -1 (/ (- (* -1 eps) (* eps (pow (sqrt -1) 2))) x)) (* (sqrt eps) (sqrt -1))) x)) 1)))>
#<alt (* -1 (* x (- (* -1 (/ (- (* -1 (/ (- (+ (* -1 eps) (* -1 (* (sqrt eps) (/ (* (sqrt -1) (- (* -1 eps) (* eps (pow (sqrt -1) 2)))) x)))) (* eps (pow (sqrt -1) 2))) x)) (* (sqrt eps) (sqrt -1))) x)) 1)))>
#<alt (/ (pow x 2) (+ x (* (sqrt eps) (sqrt -1))))>
#<alt (+ (/ eps (+ x (* (sqrt eps) (sqrt -1)))) (/ (pow x 2) (+ x (* (sqrt eps) (sqrt -1)))))>
#<alt (+ (/ eps (+ x (* (sqrt eps) (sqrt -1)))) (/ (pow x 2) (+ x (* (sqrt eps) (sqrt -1)))))>
#<alt (+ (/ eps (+ x (* (sqrt eps) (sqrt -1)))) (/ (pow x 2) (+ x (* (sqrt eps) (sqrt -1)))))>
#<alt (* (sqrt eps) (/ 1 (sqrt -1)))>
#<alt (- (+ (* (sqrt eps) (/ 1 (sqrt -1))) (* (sqrt (/ 1 eps)) (/ (pow x 2) (sqrt -1)))) (/ x (pow (sqrt -1) 2)))>
#<alt (- (+ (* -1 (* (sqrt (/ 1 (pow eps 3))) (/ (* x (- (* (sqrt eps) (/ (pow x 2) (sqrt -1))) (/ (* eps x) (pow (sqrt -1) 2)))) (sqrt -1)))) (+ (* (sqrt eps) (/ 1 (sqrt -1))) (* (sqrt (/ 1 eps)) (/ (pow x 2) (sqrt -1))))) (/ x (pow (sqrt -1) 2)))>
#<alt (- (+ (* (sqrt eps) (/ 1 (sqrt -1))) (+ (* (sqrt (/ 1 eps)) (/ (pow x 2) (sqrt -1))) (/ (* (pow x 2) (- (* (sqrt eps) (/ (pow x 2) (sqrt -1))) (/ (* eps x) (pow (sqrt -1) 2)))) (* (pow eps 2) (pow (sqrt -1) 2))))) (+ (* (sqrt (/ 1 (pow eps 3))) (/ (* x (- (* (sqrt eps) (/ (pow x 2) (sqrt -1))) (/ (* eps x) (pow (sqrt -1) 2)))) (sqrt -1))) (/ x (pow (sqrt -1) 2))))>
#<alt (* -1 (* (sqrt eps) (sqrt -1)))>
#<alt (+ (* -1 (* (sqrt eps) (sqrt -1))) (* -1 (/ (- (* (sqrt eps) (* (pow x 2) (sqrt -1))) (* eps x)) eps)))>
#<alt (+ (* -1 (* (sqrt eps) (sqrt -1))) (* -1 (/ (- (+ (* (sqrt eps) (* (pow x 2) (sqrt -1))) (* (sqrt (/ 1 eps)) (* x (* (sqrt -1) (- (* (sqrt eps) (* (pow x 2) (sqrt -1))) (* eps x)))))) (* eps x)) eps)))>
#<alt (+ (* -1 (* (sqrt eps) (sqrt -1))) (* -1 (/ (- (+ (* -1 (/ (- (* (pow x 2) (- (* (sqrt eps) (* (pow x 2) (sqrt -1))) (* eps x))) (* (sqrt eps) (* x (* (sqrt -1) (- (* (sqrt eps) (* (pow x 2) (sqrt -1))) (* eps x)))))) eps)) (* (sqrt eps) (* (pow x 2) (sqrt -1)))) (* eps x)) eps)))>
#<alt eps>
#<alt (+ eps (pow x 2))>
#<alt (+ eps (pow x 2))>
#<alt (+ eps (pow x 2))>
#<alt (pow x 2)>
#<alt (* (pow x 2) (+ 1 (/ eps (pow x 2))))>
#<alt (* (pow x 2) (+ 1 (/ eps (pow x 2))))>
#<alt (* (pow x 2) (+ 1 (/ eps (pow x 2))))>
#<alt (pow x 2)>
#<alt (* (pow x 2) (+ 1 (/ eps (pow x 2))))>
#<alt (* (pow x 2) (+ 1 (/ eps (pow x 2))))>
#<alt (* (pow x 2) (+ 1 (/ eps (pow x 2))))>
#<alt (pow x 2)>
#<alt (+ eps (pow x 2))>
#<alt (+ eps (pow x 2))>
#<alt (+ eps (pow x 2))>
#<alt eps>
#<alt (* eps (+ 1 (/ (pow x 2) eps)))>
#<alt (* eps (+ 1 (/ (pow x 2) eps)))>
#<alt (* eps (+ 1 (/ (pow x 2) eps)))>
#<alt eps>
#<alt (* -1 (* eps (- (* -1 (/ (pow x 2) eps)) 1)))>
#<alt (* -1 (* eps (- (* -1 (/ (pow x 2) eps)) 1)))>
#<alt (* -1 (* eps (- (* -1 (/ (pow x 2) eps)) 1)))>
#<alt (* (sqrt eps) (sqrt -1))>
#<alt (+ x (* (sqrt eps) (sqrt -1)))>
#<alt (+ x (* (sqrt eps) (sqrt -1)))>
#<alt (+ x (* (sqrt eps) (sqrt -1)))>
#<alt x>
#<alt (* x (+ 1 (* (sqrt eps) (/ (sqrt -1) x))))>
#<alt (* x (+ 1 (* (sqrt eps) (/ (sqrt -1) x))))>
#<alt (* x (+ 1 (* (sqrt eps) (/ (sqrt -1) x))))>
#<alt x>
#<alt (* -1 (* x (- (* -1 (* (sqrt eps) (/ (sqrt -1) x))) 1)))>
#<alt (* -1 (* x (- (* -1 (* (sqrt eps) (/ (sqrt -1) x))) 1)))>
#<alt (* -1 (* x (- (* -1 (* (sqrt eps) (/ (sqrt -1) x))) 1)))>
#<alt (+ x (* (sqrt eps) (sqrt -1)))>
#<alt (+ x (* (sqrt eps) (sqrt -1)))>
#<alt (+ x (* (sqrt eps) (sqrt -1)))>
#<alt (+ x (* (sqrt eps) (sqrt -1)))>
#<alt (* (sqrt eps) (sqrt -1))>
#<alt (* eps (+ (* (sqrt (/ 1 eps)) (sqrt -1)) (/ x eps)))>
#<alt (* eps (+ (* (sqrt (/ 1 eps)) (sqrt -1)) (/ x eps)))>
#<alt (* eps (+ (* (sqrt (/ 1 eps)) (sqrt -1)) (/ x eps)))>
#<alt (* -1 (* (sqrt eps) (sqrt -1)))>
#<alt (* -1 (* eps (+ (* -1 (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))>
#<alt (* -1 (* eps (+ (* -1 (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))>
#<alt (* -1 (* eps (+ (* -1 (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))>
#<alt (* (sqrt eps) (sqrt -1))>
#<alt (* (sqrt eps) (sqrt -1))>
#<alt (* (sqrt eps) (sqrt -1))>
#<alt (* (sqrt eps) (sqrt -1))>
#<alt (* (sqrt eps) (sqrt -1))>
#<alt (* (sqrt eps) (sqrt -1))>
#<alt (* (sqrt eps) (sqrt -1))>
#<alt (* (sqrt eps) (sqrt -1))>
#<alt (* -1 (* (sqrt eps) (sqrt -1)))>
#<alt (* -1 (* (sqrt eps) (sqrt -1)))>
#<alt (* -1 (* (sqrt eps) (sqrt -1)))>
#<alt (* -1 (* (sqrt eps) (sqrt -1)))>
#<alt (* 1/2 (/ eps x))>
#<alt (* 1/2 (/ eps x))>
#<alt (* 1/2 (/ eps x))>
#<alt (* 1/2 (/ eps x))>
#<alt (* 1/2 (/ eps x))>
#<alt (* 1/2 (/ eps x))>
#<alt (* 1/2 (/ eps x))>
#<alt (* 1/2 (/ eps x))>
#<alt (* 1/2 (/ eps x))>
#<alt (* 1/2 (/ eps x))>
#<alt (* 1/2 (/ eps x))>
#<alt (* 1/2 (/ eps x))>
#<alt (* 1/2 (/ eps x))>
#<alt (* 1/2 (/ eps x))>
#<alt (* 1/2 (/ eps x))>
#<alt (* 1/2 (/ eps x))>
#<alt (* 1/2 (/ eps x))>
#<alt (* 1/2 (/ eps x))>
#<alt (* 1/2 (/ eps x))>
#<alt (* 1/2 (/ eps x))>
#<alt (* 1/2 (/ eps x))>
#<alt (* 1/2 (/ eps x))>
#<alt (* 1/2 (/ eps x))>
#<alt (* 1/2 (/ eps x))>
#<alt (/ 1/2 x)>
#<alt (/ 1/2 x)>
#<alt (/ 1/2 x)>
#<alt (/ 1/2 x)>
#<alt (/ 1/2 x)>
#<alt (/ 1/2 x)>
#<alt (/ 1/2 x)>
#<alt (/ 1/2 x)>
#<alt (/ 1/2 x)>
#<alt (/ 1/2 x)>
#<alt (/ 1/2 x)>
#<alt (/ 1/2 x)>
#<alt (* 1/2 (/ eps x))>
#<alt (* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))>
#<alt (* eps (+ (* eps (+ (* 1/32 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))>
#<alt (* eps (+ (* eps (+ (* eps (+ (* 1/128 (/ eps (pow x 7))) (* 1/32 (/ 1 (pow x 5))))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))>
#<alt (* -2 x)>
#<alt (+ (* -8 (/ (pow x 3) eps)) (* -2 x))>
#<alt (- (+ (* -32 (/ (pow x 5) (pow eps 2))) (* -2 x)) (* 8 (/ (pow x 3) eps)))>
#<alt (- (+ (* -128 (/ (pow x 7) (pow eps 3))) (* -2 x)) (+ (* 8 (/ (pow x 3) eps)) (* 32 (/ (pow x 5) (pow eps 2)))))>
#<alt (* -2 x)>
#<alt (+ (* -8 (/ (pow x 3) eps)) (* -2 x))>
#<alt (+ (* -2 x) (* -1 (/ (- (* 32 (/ (pow x 5) eps)) (* -8 (pow x 3))) eps)))>
#<alt (+ (* -2 x) (* -1 (/ (- (* -1 (/ (- (* -128 (/ (pow x 7) eps)) (* 32 (pow x 5))) eps)) (* -8 (pow x 3))) eps)))>
#<alt (* -2 x)>
#<alt (* x (- (* -8 (/ (pow x 2) eps)) 2))>
#<alt (* x (- (* (pow x 2) (- (* -32 (/ (pow x 2) (pow eps 2))) (* 8 (/ 1 eps)))) 2))>
#<alt (* x (- (* (pow x 2) (- (* (pow x 2) (- (* -128 (/ (pow x 2) (pow eps 3))) (* 32 (/ 1 (pow eps 2))))) (* 8 (/ 1 eps)))) 2))>
#<alt (* 1/2 (/ eps x))>
#<alt (/ (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps)) x)>
#<alt (/ (- (+ (* 1/32 (/ (pow eps 3) (pow x 4))) (* 1/2 eps)) (* -1/8 (/ (pow eps 2) (pow x 2)))) x)>
#<alt (/ (- (+ (* 1/128 (/ (pow eps 4) (pow x 6))) (* 1/2 eps)) (+ (* -1/8 (/ (pow eps 2) (pow x 2))) (* -1/32 (/ (pow eps 3) (pow x 4))))) x)>
#<alt (* 1/2 (/ eps x))>
#<alt (* -1 (/ (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2)))) x))>
#<alt (* -1 (/ (- (+ (* -1/2 eps) (* -1/32 (/ (pow eps 3) (pow x 4)))) (* 1/8 (/ (pow eps 2) (pow x 2)))) x))>
#<alt (* -1 (/ (- (+ (* -1/2 eps) (* -1/128 (/ (pow eps 4) (pow x 6)))) (+ (* 1/32 (/ (pow eps 3) (pow x 4))) (* 1/8 (/ (pow eps 2) (pow x 2))))) x))>
#<alt (* 2 (/ x eps))>
#<alt (/ (+ (* -1/2 (/ eps x)) (* 2 x)) eps)>
#<alt (/ (+ (* -1/2 (/ eps x)) (* 2 x)) eps)>
#<alt (/ (+ (* -1/2 (/ eps x)) (* 2 x)) eps)>
#<alt (/ -1/2 x)>
#<alt (- (* 2 (/ x eps)) (* 1/2 (/ 1 x)))>
#<alt (- (* 2 (/ x eps)) (* 1/2 (/ 1 x)))>
#<alt (- (* 2 (/ x eps)) (* 1/2 (/ 1 x)))>
#<alt (/ -1/2 x)>
#<alt (- (* 2 (/ x eps)) (* 1/2 (/ 1 x)))>
#<alt (- (* 2 (/ x eps)) (* 1/2 (/ 1 x)))>
#<alt (- (* 2 (/ x eps)) (* 1/2 (/ 1 x)))>
#<alt (/ -1/2 x)>
#<alt (/ (- (* 2 (/ (pow x 2) eps)) 1/2) x)>
#<alt (/ (- (* 2 (/ (pow x 2) eps)) 1/2) x)>
#<alt (/ (- (* 2 (/ (pow x 2) eps)) 1/2) x)>
#<alt (* 2 (/ x eps))>
#<alt (* x (- (* 2 (/ 1 eps)) (* 1/2 (/ 1 (pow x 2)))))>
#<alt (* x (- (* 2 (/ 1 eps)) (* 1/2 (/ 1 (pow x 2)))))>
#<alt (* x (- (* 2 (/ 1 eps)) (* 1/2 (/ 1 (pow x 2)))))>
#<alt (* 2 (/ x eps))>
#<alt (* -1 (* x (- (* 1/2 (/ 1 (pow x 2))) (* 2 (/ 1 eps)))))>
#<alt (* -1 (* x (- (* 1/2 (/ 1 (pow x 2))) (* 2 (/ 1 eps)))))>
#<alt (* -1 (* x (- (* 1/2 (/ 1 (pow x 2))) (* 2 (/ 1 eps)))))>
#<alt (* 2 x)>
#<alt (+ (* -1/2 (/ eps x)) (* 2 x))>
#<alt (+ (* -1/2 (/ eps x)) (* 2 x))>
#<alt (+ (* -1/2 (/ eps x)) (* 2 x))>
#<alt (* -1/2 (/ eps x))>
#<alt (* eps (- (* 2 (/ x eps)) (* 1/2 (/ 1 x))))>
#<alt (* eps (- (* 2 (/ x eps)) (* 1/2 (/ 1 x))))>
#<alt (* eps (- (* 2 (/ x eps)) (* 1/2 (/ 1 x))))>
#<alt (* -1/2 (/ eps x))>
#<alt (* -1 (* eps (+ (* -2 (/ x eps)) (* 1/2 (/ 1 x)))))>
#<alt (* -1 (* eps (+ (* -2 (/ x eps)) (* 1/2 (/ 1 x)))))>
#<alt (* -1 (* eps (+ (* -2 (/ x eps)) (* 1/2 (/ 1 x)))))>
#<alt (* -1/2 (/ eps x))>
#<alt (/ (+ (* -1/2 eps) (* 2 (pow x 2))) x)>
#<alt (/ (+ (* -1/2 eps) (* 2 (pow x 2))) x)>
#<alt (/ (+ (* -1/2 eps) (* 2 (pow x 2))) x)>
#<alt (* 2 x)>
#<alt (* x (+ 2 (* -1/2 (/ eps (pow x 2)))))>
#<alt (* x (+ 2 (* -1/2 (/ eps (pow x 2)))))>
#<alt (* x (+ 2 (* -1/2 (/ eps (pow x 2)))))>
#<alt (* 2 x)>
#<alt (* -1 (* x (- (* 1/2 (/ eps (pow x 2))) 2)))>
#<alt (* -1 (* x (- (* 1/2 (/ eps (pow x 2))) 2)))>
#<alt (* -1 (* x (- (* 1/2 (/ eps (pow x 2))) 2)))>
#<alt (/ -1/2 x)>
#<alt (/ -1/2 x)>
#<alt (/ -1/2 x)>
#<alt (/ -1/2 x)>
#<alt (/ -1/2 x)>
#<alt (/ -1/2 x)>
#<alt (/ -1/2 x)>
#<alt (/ -1/2 x)>
#<alt (/ -1/2 x)>
#<alt (/ -1/2 x)>
#<alt (/ -1/2 x)>
#<alt (/ -1/2 x)>
#<alt (* 1/2 (/ eps x))>
#<alt (* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))>
#<alt (* eps (+ (* eps (+ (* 1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))>
#<alt (* eps (+ (* eps (+ (* eps (+ (* 3/128 (/ eps (pow x 7))) (* 1/16 (/ 1 (pow x 5))))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))>
#<alt (* -8 (/ (pow x 3) eps))>
#<alt (/ (+ (* -8 (pow x 3)) (* 32 (/ (pow x 5) eps))) eps)>
#<alt (/ (- (+ (* -256 (/ (pow x 7) (pow eps 2))) (* -8 (pow x 3))) (* -32 (/ (pow x 5) eps))) eps)>
#<alt (/ (- (+ (* -8 (pow x 3)) (* -1 (/ (+ (* -1024 (pow x 9)) (* -512 (pow x 9))) (pow eps 3)))) (+ (* -32 (/ (pow x 5) eps)) (* 256 (/ (pow x 7) (pow eps 2))))) eps)>
#<alt (* -8 (/ (pow x 3) eps))>
#<alt (* -1 (/ (+ (* -32 (/ (pow x 5) eps)) (* 8 (pow x 3))) eps))>
#<alt (* -1 (/ (+ (* -1 (/ (- (* -256 (/ (pow x 7) eps)) (* -32 (pow x 5))) eps)) (* 8 (pow x 3))) eps))>
#<alt (* -1 (/ (+ (* -1 (/ (- (* -1 (/ (- (+ (* -1024 (/ (pow x 9) eps)) (* -512 (/ (pow x 9) eps))) (* -256 (pow x 7))) eps)) (* -32 (pow x 5))) eps)) (* 8 (pow x 3))) eps))>
#<alt (* -8 (/ (pow x 3) eps))>
#<alt (* (pow x 3) (- (* 32 (/ (pow x 2) (pow eps 2))) (* 8 (/ 1 eps))))>
#<alt (* (pow x 3) (- (* (pow x 2) (+ (* -256 (/ (pow x 2) (pow eps 3))) (* 32 (/ 1 (pow eps 2))))) (* 8 (/ 1 eps))))>
#<alt (* (pow x 3) (- (* (pow x 2) (+ (* (pow x 2) (- (* 1536 (/ (pow x 2) (pow eps 4))) (* 256 (/ 1 (pow eps 3))))) (* 32 (/ 1 (pow eps 2))))) (* 8 (/ 1 eps))))>
#<alt (* 1/2 (/ eps x))>
#<alt (/ (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps)) x)>
#<alt (/ (- (+ (* 1/16 (/ (pow eps 3) (pow x 4))) (* 1/2 eps)) (* -1/8 (/ (pow eps 2) (pow x 2)))) x)>
#<alt (/ (- (+ (* -1 (/ (+ (* -1/64 (pow eps 4)) (* -1/128 (pow eps 4))) (pow x 6))) (* 1/2 eps)) (+ (* -1/8 (/ (pow eps 2) (pow x 2))) (* -1/16 (/ (pow eps 3) (pow x 4))))) x)>
#<alt (* 1/2 (/ eps x))>
#<alt (* -1 (/ (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2)))) x))>
#<alt (* -1 (/ (- (+ (* -1/2 eps) (* -1/16 (/ (pow eps 3) (pow x 4)))) (* 1/8 (/ (pow eps 2) (pow x 2)))) x))>
#<alt (* -1 (/ (- (+ (* -1 (/ (+ (* 1/128 (pow eps 4)) (* 1/64 (pow eps 4))) (pow x 6))) (* -1/2 eps)) (+ (* 1/16 (/ (pow eps 3) (pow x 4))) (* 1/8 (/ (pow eps 2) (pow x 2))))) x))>
#<alt (* -1/8 (/ (pow eps 2) (pow x 3)))>
#<alt (/ (+ (* -1/2 (* eps (pow x 2))) (* -1/8 (pow eps 2))) (pow x 3))>
#<alt (/ (+ (* -1/8 (pow eps 2)) (* (pow x 2) (+ (* -1/2 eps) (* 2 (pow x 2))))) (pow x 3))>
#<alt (/ (+ (* -1/8 (pow eps 2)) (* (pow x 2) (+ (* -1/2 eps) (* 2 (pow x 2))))) (pow x 3))>
#<alt (* 2 x)>
#<alt (* x (+ 2 (* -1/2 (/ eps (pow x 2)))))>
#<alt (* x (+ 2 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4))))))>
#<alt (* x (+ 2 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4))))))>
#<alt (* 2 x)>
#<alt (* -1 (* x (- (* 1/2 (/ eps (pow x 2))) 2)))>
#<alt (* -1 (* x (- (+ (* 1/8 (/ (pow eps 2) (pow x 4))) (* 1/2 (/ eps (pow x 2)))) 2)))>
#<alt (* -1 (* x (- (+ (* 1/8 (/ (pow eps 2) (pow x 4))) (* 1/2 (/ eps (pow x 2)))) 2)))>
#<alt (* 2 x)>
#<alt (+ (* -1/2 (/ eps x)) (* 2 x))>
#<alt (+ (* 2 x) (* eps (- (* -1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))))>
#<alt (+ (* 2 x) (* eps (- (* -1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))))>
#<alt (* -1/8 (/ (pow eps 2) (pow x 3)))>
#<alt (* -1 (* (pow eps 2) (+ (* 1/8 (/ 1 (pow x 3))) (* 1/2 (/ 1 (* eps x))))))>
#<alt (* (pow eps 2) (- (* 2 (/ x (pow eps 2))) (+ (* 1/8 (/ 1 (pow x 3))) (/ 1/2 (* eps x)))))>
#<alt (* (pow eps 2) (- (* 2 (/ x (pow eps 2))) (+ (* 1/8 (/ 1 (pow x 3))) (/ 1/2 (* eps x)))))>
#<alt (* -1/8 (/ (pow eps 2) (pow x 3)))>
#<alt (* -1 (* (pow eps 2) (+ (* 1/8 (/ 1 (pow x 3))) (* 1/2 (/ 1 (* eps x))))))>
#<alt (* (pow eps 2) (- (* -1 (/ (+ (* -2 (/ x eps)) (* 1/2 (/ 1 x))) eps)) (* 1/8 (/ 1 (pow x 3)))))>
#<alt (* (pow eps 2) (- (* -1 (/ (+ (* -2 (/ x eps)) (* 1/2 (/ 1 x))) eps)) (* 1/8 (/ 1 (pow x 3)))))>
#<alt x>
#<alt (+ x (* -1/2 (/ eps x)))>
#<alt (+ x (* eps (- (* -1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))))>
#<alt (+ x (* eps (- (* -1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))))>
#<alt (* -1/8 (/ (pow eps 2) (pow x 3)))>
#<alt (* -1 (* (pow eps 2) (+ (* 1/8 (/ 1 (pow x 3))) (* 1/2 (/ 1 (* eps x))))))>
#<alt (* (pow eps 2) (- (/ x (pow eps 2)) (+ (* 1/8 (/ 1 (pow x 3))) (/ 1/2 (* eps x)))))>
#<alt (* (pow eps 2) (- (/ x (pow eps 2)) (+ (* 1/8 (/ 1 (pow x 3))) (/ 1/2 (* eps x)))))>
#<alt (* -1/8 (/ (pow eps 2) (pow x 3)))>
#<alt (* -1 (* (pow eps 2) (+ (* 1/8 (/ 1 (pow x 3))) (* 1/2 (/ 1 (* eps x))))))>
#<alt (* (pow eps 2) (- (* -1 (/ (+ (* -1 (/ x eps)) (* 1/2 (/ 1 x))) eps)) (* 1/8 (/ 1 (pow x 3)))))>
#<alt (* (pow eps 2) (- (* -1 (/ (+ (* -1 (/ x eps)) (* 1/2 (/ 1 x))) eps)) (* 1/8 (/ 1 (pow x 3)))))>
#<alt (* -1/8 (/ (pow eps 2) (pow x 3)))>
#<alt (/ (+ (* -1/2 (* eps (pow x 2))) (* -1/8 (pow eps 2))) (pow x 3))>
#<alt (/ (+ (* -1/8 (pow eps 2)) (* (pow x 2) (+ (* -1/2 eps) (pow x 2)))) (pow x 3))>
#<alt (/ (+ (* -1/8 (pow eps 2)) (* (pow x 2) (+ (* -1/2 eps) (pow x 2)))) (pow x 3))>
#<alt x>
#<alt (* x (+ 1 (* -1/2 (/ eps (pow x 2)))))>
#<alt (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4))))))>
#<alt (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4))))))>
#<alt x>
#<alt (* -1 (* x (- (* 1/2 (/ eps (pow x 2))) 1)))>
#<alt (* -1 (* x (- (+ (* 1/8 (/ (pow eps 2) (pow x 4))) (* 1/2 (/ eps (pow x 2)))) 1)))>
#<alt (* -1 (* x (- (+ (* 1/8 (/ (pow eps 2) (pow x 4))) (* 1/2 (/ eps (pow x 2)))) 1)))>
#<alt (/ -1/2 x)>
#<alt (- (* -1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))>
#<alt (- (* -1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))>
#<alt (- (* -1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))>
#<alt (* -1/8 (/ eps (pow x 3)))>
#<alt (* -1 (* eps (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3))))))>
#<alt (* -1 (* eps (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3))))))>
#<alt (* -1 (* eps (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3))))))>
#<alt (* -1/8 (/ eps (pow x 3)))>
#<alt (* -1 (* eps (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3))))))>
#<alt (* -1 (* eps (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3))))))>
#<alt (* -1 (* eps (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3))))))>
#<alt (* -1/8 (/ eps (pow x 3)))>
#<alt (/ (+ (* -1/2 (pow x 2)) (* -1/8 eps)) (pow x 3))>
#<alt (/ (+ (* -1/2 (pow x 2)) (* -1/8 eps)) (pow x 3))>
#<alt (/ (+ (* -1/2 (pow x 2)) (* -1/8 eps)) (pow x 3))>
#<alt (/ -1/2 x)>
#<alt (/ (- (* -1/8 (/ eps (pow x 2))) 1/2) x)>
#<alt (/ (- (* -1/8 (/ eps (pow x 2))) 1/2) x)>
#<alt (/ (- (* -1/8 (/ eps (pow x 2))) 1/2) x)>
#<alt (/ -1/2 x)>
#<alt (* -1 (/ (+ 1/2 (* 1/8 (/ eps (pow x 2)))) x))>
#<alt (* -1 (/ (+ 1/2 (* 1/8 (/ eps (pow x 2)))) x))>
#<alt (* -1 (/ (+ 1/2 (* 1/8 (/ eps (pow x 2)))) x))>
#<alt (* -1 eps)>
#<alt (* -1 eps)>
#<alt (* -1 eps)>
#<alt (* -1 eps)>
#<alt (* -1 eps)>
#<alt (* -1 eps)>
#<alt (* -1 eps)>
#<alt (* -1 eps)>
#<alt (* -1 eps)>
#<alt (* -1 eps)>
#<alt (* -1 eps)>
#<alt (* -1 eps)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt -1/2>
#<alt (- (* -1/8 (/ eps (pow x 2))) 1/2)>
#<alt (- (* -1/8 (/ eps (pow x 2))) 1/2)>
#<alt (- (* -1/8 (/ eps (pow x 2))) 1/2)>
#<alt (* -1/8 (/ eps (pow x 2)))>
#<alt (* -1 (* eps (+ (* 1/8 (/ 1 (pow x 2))) (* 1/2 (/ 1 eps)))))>
#<alt (* -1 (* eps (+ (* 1/8 (/ 1 (pow x 2))) (* 1/2 (/ 1 eps)))))>
#<alt (* -1 (* eps (+ (* 1/8 (/ 1 (pow x 2))) (* 1/2 (/ 1 eps)))))>
#<alt (* -1/8 (/ eps (pow x 2)))>
#<alt (* -1 (* eps (+ (* 1/2 (/ 1 eps)) (* 1/8 (/ 1 (pow x 2))))))>
#<alt (* -1 (* eps (+ (* 1/2 (/ 1 eps)) (* 1/8 (/ 1 (pow x 2))))))>
#<alt (* -1 (* eps (+ (* 1/2 (/ 1 eps)) (* 1/8 (/ 1 (pow x 2))))))>
#<alt (* -1/8 (/ eps (pow x 2)))>
#<alt (/ (+ (* -1/2 (pow x 2)) (* -1/8 eps)) (pow x 2))>
#<alt (/ (+ (* -1/2 (pow x 2)) (* -1/8 eps)) (pow x 2))>
#<alt (/ (+ (* -1/2 (pow x 2)) (* -1/8 eps)) (pow x 2))>
#<alt -1/2>
#<alt (- (* -1/8 (/ eps (pow x 2))) 1/2)>
#<alt (- (* -1/8 (/ eps (pow x 2))) 1/2)>
#<alt (- (* -1/8 (/ eps (pow x 2))) 1/2)>
#<alt -1/2>
#<alt (- (* -1/8 (/ eps (pow x 2))) 1/2)>
#<alt (- (* -1/8 (/ eps (pow x 2))) 1/2)>
#<alt (- (* -1/8 (/ eps (pow x 2))) 1/2)>
#<alt (/ -1/8 (pow x 2))>
#<alt (/ -1/8 (pow x 2))>
#<alt (/ -1/8 (pow x 2))>
#<alt (/ -1/8 (pow x 2))>
#<alt (/ -1/8 (pow x 2))>
#<alt (/ -1/8 (pow x 2))>
#<alt (/ -1/8 (pow x 2))>
#<alt (/ -1/8 (pow x 2))>
#<alt (/ -1/8 (pow x 2))>
#<alt (/ -1/8 (pow x 2))>
#<alt (/ -1/8 (pow x 2))>
#<alt (/ -1/8 (pow x 2))>

Calls

90 calls:

Time	Variable		Point	Expression
1.0ms	eps	@	inf	(/ (+ (* x x) eps) (+ x (sqrt (neg eps))))
1.0ms	eps	@	-inf	(/ (+ (* x x) eps) (+ x (sqrt (neg eps))))
1.0ms	x	@	0	(/ (+ (* x x) eps) (+ x (sqrt (neg eps))))
0.0ms	x	@	inf	(/ (+ (* x x) eps) (+ x (sqrt (neg eps))))
0.0ms	eps	@	0	(/ (+ (* x x) eps) (+ x (sqrt (neg eps))))

rewrite468.0ms (4.7%)

Memory

8.0MiB live, 477.4MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

4 122×	`/-lowering-/.f32`
4 122×	`/-lowering-/.f64`
3 432×	`-lowering-.f32`
3 432×	`-lowering-.f64`
2 832×	`accelerator-lowering-fma.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	28	149
1	188	147
2	1615	114
0	8802	105

Stop Event

1×	iter limit
1×	node limit

Counts

18 → 1 004

Calls

Call 1

Inputs
(/ (+ (* x x) eps) (+ x (sqrt (neg eps))))
(+ (* x x) eps)
(+ x (sqrt (neg eps)))
(sqrt (neg eps))
(* (/ 1/2 x) eps)
(/ 1/2 x)
(/ 1 (/ (+ (* eps (/ -1/2 x)) (+ x x)) eps))
(/ (+ (* eps (/ -1/2 x)) (+ x x)) eps)
(+ (* eps (/ -1/2 x)) (+ x x))
(/ -1/2 x)
(/ eps (+ x (+ (* eps (/ (+ (* eps (/ -1/8 (* x x))) -1/2) x)) x)))
(+ x (+ (* eps (/ (+ (* eps (/ -1/8 (* x x))) -1/2) x)) x))
(+ (* eps (/ (+ (* eps (/ -1/8 (* x x))) -1/2) x)) x)
(/ (+ (* eps (/ -1/8 (* x x))) -1/2) x)
(neg eps)
(+ x x)
(+ (* eps (/ -1/8 (* x x))) -1/2)
(/ -1/8 (* x x))

Outputs
(+.f64 x (neg.f64 (sqrt.f64 (neg.f64 eps))))
(exp.f64 (*.f64 (log.f64 (/.f64 #s(literal 1 binary64) (-.f64 x (sqrt.f64 (neg.f64 eps))))) #s(literal -1 binary64)))
(-.f64 x (sqrt.f64 (neg.f64 eps)))
(neg.f64 (/.f64 (fma.f64 x x eps) (neg.f64 (+.f64 x (sqrt.f64 (neg.f64 eps))))))
(neg.f64 (/.f64 (neg.f64 (fma.f64 x x eps)) (+.f64 x (sqrt.f64 (neg.f64 eps)))))
(/.f64 (fma.f64 x x eps) (+.f64 x (sqrt.f64 (neg.f64 eps))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 x (sqrt.f64 (neg.f64 eps)))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (-.f64 x (sqrt.f64 (neg.f64 eps)))) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (neg.f64 (neg.f64 (/.f64 #s(literal 1 binary64) (-.f64 x (sqrt.f64 (neg.f64 eps)))))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal 1 binary64) (-.f64 x (sqrt.f64 (neg.f64 eps))))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (/.f64 #s(literal 1 binary64) (-.f64 x (sqrt.f64 (neg.f64 eps)))) #s(literal 1 binary64))))
(/.f64 (neg.f64 (fma.f64 x x eps)) (neg.f64 (+.f64 x (sqrt.f64 (neg.f64 eps)))))
(/.f64 (fma.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)) (.f64 eps (.f64 eps eps))) (.f64 (+.f64 x (sqrt.f64 (neg.f64 eps))) (fma.f64 x (.f64 x (.f64 x x)) (.f64 eps (-.f64 eps (*.f64 x x))))))
(/.f64 (.f64 (fma.f64 x x eps) (-.f64 (.f64 x x) eps)) (.f64 (+.f64 x (sqrt.f64 (neg.f64 eps))) (-.f64 (.f64 x x) eps)))
(/.f64 (.f64 (fma.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)) (.f64 eps (.f64 eps eps))) #s(literal 1 binary64)) (.f64 (fma.f64 x (.f64 x (.f64 x x)) (.f64 eps (-.f64 eps (.f64 x x)))) (+.f64 x (sqrt.f64 (neg.f64 eps)))))
(/.f64 (.f64 (.f64 (fma.f64 x x eps) (-.f64 (.f64 x x) eps)) #s(literal 1 binary64)) (.f64 (-.f64 (*.f64 x x) eps) (+.f64 x (sqrt.f64 (neg.f64 eps)))))
(/.f64 (neg.f64 (neg.f64 (fma.f64 x x eps))) (neg.f64 (neg.f64 (+.f64 x (sqrt.f64 (neg.f64 eps))))))
(/.f64 (neg.f64 (fma.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)) (.f64 eps (.f64 eps eps)))) (neg.f64 (.f64 (+.f64 x (sqrt.f64 (neg.f64 eps))) (fma.f64 x (.f64 x (.f64 x x)) (.f64 eps (-.f64 eps (*.f64 x x)))))))
(/.f64 (neg.f64 (.f64 (fma.f64 x x eps) (-.f64 (.f64 x x) eps))) (neg.f64 (.f64 (+.f64 x (sqrt.f64 (neg.f64 eps))) (-.f64 (.f64 x x) eps))))
(/.f64 (-.f64 (.f64 x (.f64 x x)) (.f64 (neg.f64 eps) (sqrt.f64 (neg.f64 eps)))) (fma.f64 x x (+.f64 (neg.f64 eps) (.f64 x (sqrt.f64 (neg.f64 eps))))))
(/.f64 (*.f64 (fma.f64 x x eps) #s(literal 1 binary64)) (+.f64 x (sqrt.f64 (neg.f64 eps))))
(/.f64 (.f64 (fma.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)) (.f64 eps (.f64 eps eps))) (/.f64 #s(literal 1 binary64) (+.f64 x (sqrt.f64 (neg.f64 eps))))) (fma.f64 x (.f64 x (.f64 x x)) (.f64 eps (-.f64 eps (*.f64 x x)))))
(/.f64 (.f64 (.f64 (fma.f64 x x eps) (-.f64 (.f64 x x) eps)) (/.f64 #s(literal 1 binary64) (+.f64 x (sqrt.f64 (neg.f64 eps))))) (-.f64 (.f64 x x) eps))
(/.f64 (neg.f64 (.f64 (fma.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)) (.f64 eps (.f64 eps eps))) #s(literal 1 binary64))) (neg.f64 (.f64 (fma.f64 x (.f64 x (.f64 x x)) (.f64 eps (-.f64 eps (.f64 x x)))) (+.f64 x (sqrt.f64 (neg.f64 eps))))))
(/.f64 (neg.f64 (.f64 (.f64 (fma.f64 x x eps) (-.f64 (.f64 x x) eps)) #s(literal 1 binary64))) (neg.f64 (.f64 (-.f64 (*.f64 x x) eps) (+.f64 x (sqrt.f64 (neg.f64 eps))))))
(/.f64 (neg.f64 (neg.f64 (neg.f64 (fma.f64 x x eps)))) (neg.f64 (neg.f64 (neg.f64 (+.f64 x (sqrt.f64 (neg.f64 eps)))))))
(/.f64 (neg.f64 (*.f64 (fma.f64 x x eps) #s(literal 1 binary64))) (neg.f64 (+.f64 x (sqrt.f64 (neg.f64 eps)))))
(/.f64 (neg.f64 (.f64 (fma.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)) (.f64 eps (.f64 eps eps))) (/.f64 #s(literal 1 binary64) (+.f64 x (sqrt.f64 (neg.f64 eps)))))) (neg.f64 (fma.f64 x (.f64 x (.f64 x x)) (.f64 eps (-.f64 eps (*.f64 x x))))))
(/.f64 (neg.f64 (.f64 (.f64 (fma.f64 x x eps) (-.f64 (.f64 x x) eps)) (/.f64 #s(literal 1 binary64) (+.f64 x (sqrt.f64 (neg.f64 eps)))))) (neg.f64 (-.f64 (.f64 x x) eps)))
(/.f64 (neg.f64 (-.f64 (.f64 x (.f64 x x)) (.f64 (neg.f64 eps) (sqrt.f64 (neg.f64 eps))))) (neg.f64 (fma.f64 x x (+.f64 (neg.f64 eps) (.f64 x (sqrt.f64 (neg.f64 eps)))))))
(pow.f64 (/.f64 #s(literal 1 binary64) (-.f64 x (sqrt.f64 (neg.f64 eps)))) #s(literal -1 binary64))
(pow.f64 (/.f64 (/.f64 #s(literal 1 binary64) (-.f64 x (sqrt.f64 (neg.f64 eps)))) #s(literal 1 binary64)) #s(literal -1 binary64))
(*.f64 (fma.f64 x x eps) (/.f64 #s(literal 1 binary64) (+.f64 x (sqrt.f64 (neg.f64 eps)))))
(*.f64 #s(literal 1 binary64) (-.f64 x (sqrt.f64 (neg.f64 eps))))
(*.f64 (neg.f64 (fma.f64 x x eps)) (/.f64 #s(literal 1 binary64) (neg.f64 (+.f64 x (sqrt.f64 (neg.f64 eps))))))
(*.f64 (/.f64 #s(literal 1 binary64) (+.f64 x (sqrt.f64 (neg.f64 eps)))) (fma.f64 x x eps))
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(.f64 (pow.f64 (/.f64 x (fma.f64 (.f64 eps (.f64 eps eps)) (/.f64 #s(literal -1/512 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))) #s(literal -1/8 binary64))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 (/.f64 (.f64 (.f64 eps #s(literal -1/8 binary64)) (.f64 eps #s(literal -1/8 binary64))) (.f64 x (.f64 x (.f64 x x)))) (-.f64 #s(literal 1/4 binary64) (.f64 eps (.f64 (/.f64 #s(literal -1/8 binary64) (*.f64 x x)) #s(literal -1/2 binary64)))))))
(.f64 (pow.f64 (/.f64 x (+.f64 (/.f64 (.f64 (.f64 eps #s(literal -1/8 binary64)) (.f64 eps #s(literal -1/8 binary64))) (.f64 x (.f64 x (.f64 x x)))) #s(literal -1/4 binary64))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 eps (/.f64 #s(literal -1/8 binary64) (.f64 x x)) #s(literal 1/2 binary64))))
(+.f64 #s(literal 0 binary64) (neg.f64 eps))
(+.f64 (.f64 (neg.f64 eps) x) (.f64 (neg.f64 eps) x))
(+.f64 (.f64 x (neg.f64 eps)) (.f64 x (neg.f64 eps)))
(exp.f64 (log.f64 (neg.f64 eps)))
(exp.f64 (*.f64 (log.f64 (neg.f64 eps)) #s(literal 1 binary64)))
(exp.f64 (.f64 (.f64 #s(literal 1/2 binary64) (log.f64 (neg.f64 eps))) #s(literal 2 binary64)))
(exp.f64 (.f64 (log.f64 (.f64 eps eps)) #s(literal 1/2 binary64)))
(fabs.f64 (neg.f64 eps))
(-.f64 #s(literal 0 binary64) eps)
(sqrt.f64 (*.f64 eps eps))
(fma.f64 x (neg.f64 eps) (*.f64 x (neg.f64 eps)))
(fma.f64 (neg.f64 eps) x (*.f64 (neg.f64 eps) x))
(neg.f64 eps)
(/.f64 eps #s(literal -1 binary64))
(/.f64 (neg.f64 eps) #s(literal 1 binary64))
(/.f64 #s(literal 1 binary64) (/.f64 x (*.f64 eps #s(literal -1/2 binary64))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 x (*.f64 eps #s(literal -1/2 binary64)))))
(/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)
(/.f64 (*.f64 eps #s(literal 1/2 binary64)) (neg.f64 x))
(/.f64 (.f64 (.f64 eps #s(literal -1/2 binary64)) #s(literal 0 binary64)) #s(literal 0 binary64))
(/.f64 (.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 (fma.f64 x x #s(literal 0 binary64)) #s(literal 1 binary64))) (.f64 x (fma.f64 x x #s(literal 0 binary64))))
(/.f64 (neg.f64 (*.f64 eps #s(literal 1/2 binary64))) (neg.f64 (neg.f64 x)))
(/.f64 (neg.f64 (*.f64 eps #s(literal -1/2 binary64))) (neg.f64 x))
(/.f64 (-.f64 #s(literal 0 binary64) (.f64 eps (.f64 eps eps))) (+.f64 #s(literal 0 binary64) (fma.f64 eps eps (*.f64 #s(literal 0 binary64) eps))))
(/.f64 (-.f64 #s(literal 0 binary64) (*.f64 eps eps)) (+.f64 #s(literal 0 binary64) eps))
(/.f64 (*.f64 eps #s(literal 1 binary64)) #s(literal -1 binary64))
(/.f64 (.f64 (neg.f64 eps) (.f64 (fma.f64 x x #s(literal 0 binary64)) #s(literal 1 binary64))) (fma.f64 x x #s(literal 0 binary64)))
(/.f64 (*.f64 (neg.f64 eps) #s(literal 0 binary64)) #s(literal 0 binary64))
(/.f64 (.f64 (.f64 eps #s(literal -1/2 binary64)) #s(literal 1 binary64)) x)
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(/.f64 (neg.f64 (.f64 (neg.f64 eps) (.f64 (fma.f64 x x #s(literal 0 binary64)) #s(literal 1 binary64)))) (neg.f64 (fma.f64 x x #s(literal 0 binary64))))
(/.f64 (neg.f64 (*.f64 (neg.f64 eps) #s(literal 0 binary64))) #s(literal 0 binary64))
(/.f64 (neg.f64 (.f64 (.f64 eps #s(literal -1/2 binary64)) #s(literal 1 binary64))) (neg.f64 x))
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(/.f64 (neg.f64 (neg.f64 (*.f64 eps #s(literal -1/2 binary64)))) (neg.f64 (neg.f64 x)))
(/.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (.f64 eps (.f64 eps eps)))) (neg.f64 (+.f64 #s(literal 0 binary64) (fma.f64 eps eps (*.f64 #s(literal 0 binary64) eps)))))
(/.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (*.f64 eps eps))) (neg.f64 (+.f64 #s(literal 0 binary64) eps)))
(pow.f64 (neg.f64 eps) #s(literal 1 binary64))
(pow.f64 (sqrt.f64 (neg.f64 eps)) #s(literal 2 binary64))
(pow.f64 (*.f64 eps eps) #s(literal 1/2 binary64))
(pow.f64 (/.f64 x (*.f64 eps #s(literal -1/2 binary64))) #s(literal -1 binary64))
(*.f64 eps #s(literal -1 binary64))
(*.f64 (neg.f64 eps) #s(literal 1 binary64))
(*.f64 (sqrt.f64 (neg.f64 eps)) (sqrt.f64 (neg.f64 eps)))
(*.f64 #s(literal 1 binary64) (neg.f64 eps))
(.f64 #s(literal -1/2 binary64) (.f64 (/.f64 #s(literal 1 binary64) x) eps))
(*.f64 #s(literal -1 binary64) eps)
(*.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)))
(.f64 #s(literal -1 binary64) (.f64 eps #s(literal 1 binary64)))
(.f64 (.f64 eps #s(literal -1/2 binary64)) (/.f64 #s(literal 1 binary64) x))
(*.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps)) #s(literal -1 binary64))
(.f64 (.f64 (neg.f64 eps) #s(literal 2 binary64)) x)
(*.f64 (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64)) (pow.f64 (sqrt.f64 eps) #s(literal 2 binary64)))
#s(literal 1 binary64)
(+.f64 #s(literal -1/2 binary64) (/.f64 eps (.f64 (.f64 x x) #s(literal -8 binary64))))
(+.f64 (/.f64 eps (.f64 (.f64 x x) #s(literal -8 binary64))) #s(literal -1/2 binary64))
(-.f64 (/.f64 (/.f64 (.f64 (.f64 eps #s(literal -1/8 binary64)) (.f64 eps #s(literal -1/8 binary64))) (.f64 x (.f64 x (.f64 x x)))) (fma.f64 eps (/.f64 #s(literal -1/8 binary64) (.f64 x x)) #s(literal 1/2 binary64))) (/.f64 #s(literal 1/4 binary64) (fma.f64 eps (/.f64 #s(literal -1/8 binary64) (.f64 x x)) #s(literal 1/2 binary64))))
(fma.f64 eps (/.f64 #s(literal -1/8 binary64) (*.f64 x x)) #s(literal -1/2 binary64))
(fma.f64 #s(literal -1/8 binary64) (.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) eps) #s(literal -1/2 binary64))
(fma.f64 (/.f64 #s(literal -1/8 binary64) (*.f64 x x)) eps #s(literal -1/2 binary64))
(fma.f64 (.f64 eps #s(literal -1/8 binary64)) (/.f64 #s(literal 1 binary64) (.f64 x x)) #s(literal -1/2 binary64))
(fma.f64 (/.f64 eps x) (/.f64 #s(literal -1/8 binary64) x) #s(literal -1/2 binary64))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (/.f64 (.f64 (.f64 eps #s(literal -1/8 binary64)) (.f64 eps #s(literal -1/8 binary64))) (.f64 x (.f64 x (.f64 x x)))) (-.f64 #s(literal 1/4 binary64) (.f64 eps (.f64 (/.f64 #s(literal -1/8 binary64) (.f64 x x)) #s(literal -1/2 binary64))))) (fma.f64 (.f64 eps (.f64 eps eps)) (/.f64 #s(literal -1/512 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))) #s(literal -1/8 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 eps (/.f64 #s(literal -1/8 binary64) (.f64 x x)) #s(literal 1/2 binary64)) (+.f64 (/.f64 (.f64 (.f64 eps #s(literal -1/8 binary64)) (.f64 eps #s(literal -1/8 binary64))) (.f64 x (.f64 x (*.f64 x x)))) #s(literal -1/4 binary64))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (+.f64 (/.f64 (.f64 (.f64 eps #s(literal -1/8 binary64)) (.f64 eps #s(literal -1/8 binary64))) (.f64 x (.f64 x (.f64 x x)))) (-.f64 #s(literal 1/4 binary64) (.f64 eps (.f64 (/.f64 #s(literal -1/8 binary64) (.f64 x x)) #s(literal -1/2 binary64))))) (fma.f64 (.f64 eps (.f64 eps eps)) (/.f64 #s(literal -1/512 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))) #s(literal -1/8 binary64)))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (fma.f64 eps (/.f64 #s(literal -1/8 binary64) (.f64 x x)) #s(literal 1/2 binary64)) (+.f64 (/.f64 (.f64 (.f64 eps #s(literal -1/8 binary64)) (.f64 eps #s(literal -1/8 binary64))) (.f64 x (.f64 x (*.f64 x x)))) #s(literal -1/4 binary64)))))
(/.f64 (fma.f64 (.f64 eps (.f64 eps eps)) (/.f64 #s(literal -1/512 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))) #s(literal -1/8 binary64)) (+.f64 (/.f64 (.f64 (.f64 eps #s(literal -1/8 binary64)) (.f64 eps #s(literal -1/8 binary64))) (.f64 x (.f64 x (.f64 x x)))) (-.f64 #s(literal 1/4 binary64) (.f64 eps (.f64 (/.f64 #s(literal -1/8 binary64) (.f64 x x)) #s(literal -1/2 binary64))))))
(/.f64 (fma.f64 (.f64 eps (.f64 eps eps)) (/.f64 #s(literal -1/512 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))) #s(literal -1/8 binary64)) (+.f64 #s(literal 1/4 binary64) (/.f64 (-.f64 (.f64 (/.f64 eps (.f64 (.f64 x x) #s(literal -8 binary64))) (.f64 eps #s(literal -1/8 binary64))) (.f64 (.f64 eps #s(literal -1/8 binary64)) #s(literal -1/2 binary64))) (.f64 x x))))
(/.f64 (+.f64 (/.f64 (.f64 (.f64 eps #s(literal -1/8 binary64)) (.f64 eps #s(literal -1/8 binary64))) (.f64 x (.f64 x (.f64 x x)))) #s(literal -1/4 binary64)) (fma.f64 eps (/.f64 #s(literal -1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64)))
(/.f64 (neg.f64 (fma.f64 (.f64 eps (.f64 eps eps)) (/.f64 #s(literal -1/512 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))) #s(literal -1/8 binary64))) (neg.f64 (+.f64 (/.f64 (.f64 (.f64 eps #s(literal -1/8 binary64)) (.f64 eps #s(literal -1/8 binary64))) (.f64 x (.f64 x (.f64 x x)))) (-.f64 #s(literal 1/4 binary64) (.f64 eps (.f64 (/.f64 #s(literal -1/8 binary64) (.f64 x x)) #s(literal -1/2 binary64)))))))
(/.f64 (neg.f64 (fma.f64 (.f64 eps (.f64 eps eps)) (/.f64 #s(literal -1/512 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))) #s(literal -1/8 binary64))) (neg.f64 (+.f64 #s(literal 1/4 binary64) (/.f64 (-.f64 (.f64 (/.f64 eps (.f64 (.f64 x x) #s(literal -8 binary64))) (.f64 eps #s(literal -1/8 binary64))) (.f64 (.f64 eps #s(literal -1/8 binary64)) #s(literal -1/2 binary64))) (.f64 x x)))))
(/.f64 (neg.f64 (+.f64 (/.f64 (.f64 (.f64 eps #s(literal -1/8 binary64)) (.f64 eps #s(literal -1/8 binary64))) (.f64 x (.f64 x (.f64 x x)))) #s(literal -1/4 binary64))) (neg.f64 (fma.f64 eps (/.f64 #s(literal -1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64))))
(/.f64 (-.f64 #s(literal 1/4 binary64) (/.f64 (.f64 (.f64 eps #s(literal -1/8 binary64)) (.f64 eps #s(literal -1/8 binary64))) (.f64 x (.f64 x (.f64 x x))))) (-.f64 #s(literal -1/2 binary64) (/.f64 eps (.f64 (.f64 x x) #s(literal -8 binary64)))))
(/.f64 (-.f64 (.f64 (/.f64 (.f64 (.f64 eps #s(literal -1/8 binary64)) (.f64 eps #s(literal -1/8 binary64))) (.f64 x (.f64 x (.f64 x x)))) (fma.f64 eps (/.f64 #s(literal -1/8 binary64) (.f64 x x)) #s(literal 1/2 binary64))) (.f64 (fma.f64 eps (/.f64 #s(literal -1/8 binary64) (.f64 x x)) #s(literal 1/2 binary64)) #s(literal 1/4 binary64))) (.f64 (fma.f64 eps (/.f64 #s(literal -1/8 binary64) (.f64 x x)) #s(literal 1/2 binary64)) (fma.f64 eps (/.f64 #s(literal -1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64))))
(/.f64 (neg.f64 (neg.f64 (fma.f64 (.f64 eps (.f64 eps eps)) (/.f64 #s(literal -1/512 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))) #s(literal -1/8 binary64)))) (neg.f64 (neg.f64 (+.f64 (/.f64 (.f64 (.f64 eps #s(literal -1/8 binary64)) (.f64 eps #s(literal -1/8 binary64))) (.f64 x (.f64 x (.f64 x x)))) (-.f64 #s(literal 1/4 binary64) (.f64 eps (.f64 (/.f64 #s(literal -1/8 binary64) (.f64 x x)) #s(literal -1/2 binary64))))))))
(/.f64 (neg.f64 (neg.f64 (+.f64 (/.f64 (.f64 (.f64 eps #s(literal -1/8 binary64)) (.f64 eps #s(literal -1/8 binary64))) (.f64 x (.f64 x (.f64 x x)))) #s(literal -1/4 binary64)))) (neg.f64 (neg.f64 (fma.f64 eps (/.f64 #s(literal -1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64)))))
(/.f64 (neg.f64 (-.f64 #s(literal 1/4 binary64) (/.f64 (.f64 (.f64 eps #s(literal -1/8 binary64)) (.f64 eps #s(literal -1/8 binary64))) (.f64 x (.f64 x (.f64 x x)))))) (neg.f64 (-.f64 #s(literal -1/2 binary64) (/.f64 eps (.f64 (.f64 x x) #s(literal -8 binary64))))))
(pow.f64 (/.f64 (+.f64 (/.f64 (.f64 (.f64 eps #s(literal -1/8 binary64)) (.f64 eps #s(literal -1/8 binary64))) (.f64 x (.f64 x (.f64 x x)))) (-.f64 #s(literal 1/4 binary64) (.f64 eps (.f64 (/.f64 #s(literal -1/8 binary64) (.f64 x x)) #s(literal -1/2 binary64))))) (fma.f64 (.f64 eps (.f64 eps eps)) (/.f64 #s(literal -1/512 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))) #s(literal -1/8 binary64))) #s(literal -1 binary64))
(pow.f64 (/.f64 (fma.f64 eps (/.f64 #s(literal -1/8 binary64) (.f64 x x)) #s(literal 1/2 binary64)) (+.f64 (/.f64 (.f64 (.f64 eps #s(literal -1/8 binary64)) (.f64 eps #s(literal -1/8 binary64))) (.f64 x (.f64 x (*.f64 x x)))) #s(literal -1/4 binary64))) #s(literal -1 binary64))
(.f64 (fma.f64 (.f64 eps (.f64 eps eps)) (/.f64 #s(literal -1/512 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))) #s(literal -1/8 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 (/.f64 (.f64 (.f64 eps #s(literal -1/8 binary64)) (.f64 eps #s(literal -1/8 binary64))) (.f64 x (.f64 x (.f64 x x)))) (-.f64 #s(literal 1/4 binary64) (.f64 eps (.f64 (/.f64 #s(literal -1/8 binary64) (*.f64 x x)) #s(literal -1/2 binary64)))))))
(.f64 (+.f64 (/.f64 (.f64 (.f64 eps #s(literal -1/8 binary64)) (.f64 eps #s(literal -1/8 binary64))) (.f64 x (.f64 x (.f64 x x)))) #s(literal -1/4 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 eps (/.f64 #s(literal -1/8 binary64) (.f64 x x)) #s(literal 1/2 binary64))))
(exp.f64 (.f64 (log.f64 (.f64 (*.f64 x x) #s(literal -8 binary64))) #s(literal -1 binary64)))
(neg.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 x x)))
(/.f64 #s(literal 1 binary64) (.f64 (.f64 x x) #s(literal -8 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (.f64 (.f64 x x) #s(literal -8 binary64)) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 x (/.f64 #s(literal -1/8 binary64) x)))
(/.f64 #s(literal 1 binary64) (neg.f64 (neg.f64 (.f64 (.f64 x x) #s(literal -8 binary64)))))
(/.f64 #s(literal -1/8 binary64) (*.f64 x x))
(/.f64 #s(literal -1/8 binary64) (neg.f64 (*.f64 x (neg.f64 x))))
(/.f64 #s(literal -1 binary64) (neg.f64 (.f64 (.f64 x x) #s(literal -8 binary64))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (.f64 (.f64 x x) #s(literal -8 binary64)) #s(literal 1 binary64))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 x (/.f64 #s(literal -1/8 binary64) x))))
(/.f64 #s(literal 1/8 binary64) (*.f64 x (neg.f64 x)))
(/.f64 #s(literal 1/8 binary64) (neg.f64 (neg.f64 (*.f64 x (neg.f64 x)))))
(/.f64 (/.f64 #s(literal -1/8 binary64) x) x)
(/.f64 (neg.f64 (/.f64 #s(literal -1/8 binary64) x)) (neg.f64 x))
(/.f64 (neg.f64 (neg.f64 (/.f64 #s(literal -1/8 binary64) x))) (neg.f64 (neg.f64 x)))
(pow.f64 (.f64 (.f64 x x) #s(literal -8 binary64)) #s(literal -1 binary64))
(pow.f64 (/.f64 (.f64 (.f64 x x) #s(literal -8 binary64)) #s(literal 1 binary64)) #s(literal -1 binary64))
(pow.f64 (/.f64 x (/.f64 #s(literal -1/8 binary64) x)) #s(literal -1 binary64))
(.f64 #s(literal 1 binary64) (/.f64 #s(literal -1/8 binary64) (.f64 x x)))
(.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1 binary64) (.f64 x x)))
(.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1 binary64) (.f64 x (neg.f64 x))))
(*.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal -1/8 binary64) x))
(.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) #s(literal -1/8 binary64))
(*.f64 (/.f64 #s(literal -1/8 binary64) x) (/.f64 #s(literal 1 binary64) x))

simplify349.0ms (3.5%)

Memory

15.8MiB live, 649.9MiB allocated

Algorithm

1×	egg-herbie

Rules

9 340×	`accelerator-lowering-fma.f32`
9 340×	`accelerator-lowering-fma.f64`
5 182×	`-lowering-.f32`
5 182×	`-lowering-.f64`
2 772×	`+-lowering-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	532	3926
1	1599	3808
2	4793	3703
0	8787	3456

Stop Event

1×	iter limit
1×	node limit

Counts

360 → 360

Calls

Call 1

Inputs
(* (sqrt eps) (/ 1 (sqrt -1)))
(+ (* -1 (/ x (pow (sqrt -1) 2))) (* (sqrt eps) (/ 1 (sqrt -1))))
(+ (* x (- (* x (- (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1))) (* -1 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))))) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt eps) (/ 1 (sqrt -1))))
(+ (* x (- (* x (- (+ (* -1 (* (sqrt (/ 1 eps)) (/ (* x (- (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1))) (* -1 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))))) (sqrt -1)))) (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))) (* -1 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))))) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt eps) (/ 1 (sqrt -1))))
x
(* x (+ 1 (* -1 (* (sqrt eps) (/ (sqrt -1) x)))))
(* x (- (+ 1 (/ eps (pow x 2))) (+ (* -1 (/ (* eps (pow (sqrt -1) 2)) (pow x 2))) (* (sqrt eps) (/ (sqrt -1) x)))))
(* x (- (+ 1 (+ (* -1 (* (sqrt eps) (/ (* (sqrt -1) (- eps (* -1 (* eps (pow (sqrt -1) 2))))) (pow x 3)))) (/ eps (pow x 2)))) (+ (* -1 (/ (* eps (pow (sqrt -1) 2)) (pow x 2))) (* (sqrt eps) (/ (sqrt -1) x)))))
x
(* -1 (* x (- (* (sqrt eps) (/ (sqrt -1) x)) 1)))
(* -1 (* x (- (* -1 (/ (- (* -1 (/ (- (* -1 eps) (* eps (pow (sqrt -1) 2))) x)) (* (sqrt eps) (sqrt -1))) x)) 1)))
(* -1 (* x (- (* -1 (/ (- (* -1 (/ (- (+ (* -1 eps) (* -1 (* (sqrt eps) (/ (* (sqrt -1) (- (* -1 eps) (* eps (pow (sqrt -1) 2)))) x)))) (* eps (pow (sqrt -1) 2))) x)) (* (sqrt eps) (sqrt -1))) x)) 1)))
(/ (pow x 2) (+ x (* (sqrt eps) (sqrt -1))))
(+ (/ eps (+ x (* (sqrt eps) (sqrt -1)))) (/ (pow x 2) (+ x (* (sqrt eps) (sqrt -1)))))
(+ (/ eps (+ x (* (sqrt eps) (sqrt -1)))) (/ (pow x 2) (+ x (* (sqrt eps) (sqrt -1)))))
(+ (/ eps (+ x (* (sqrt eps) (sqrt -1)))) (/ (pow x 2) (+ x (* (sqrt eps) (sqrt -1)))))
(* (sqrt eps) (/ 1 (sqrt -1)))
(- (+ (* (sqrt eps) (/ 1 (sqrt -1))) (* (sqrt (/ 1 eps)) (/ (pow x 2) (sqrt -1)))) (/ x (pow (sqrt -1) 2)))
(- (+ (* -1 (* (sqrt (/ 1 (pow eps 3))) (/ (* x (- (* (sqrt eps) (/ (pow x 2) (sqrt -1))) (/ (* eps x) (pow (sqrt -1) 2)))) (sqrt -1)))) (+ (* (sqrt eps) (/ 1 (sqrt -1))) (* (sqrt (/ 1 eps)) (/ (pow x 2) (sqrt -1))))) (/ x (pow (sqrt -1) 2)))
(- (+ (* (sqrt eps) (/ 1 (sqrt -1))) (+ (* (sqrt (/ 1 eps)) (/ (pow x 2) (sqrt -1))) (/ (* (pow x 2) (- (* (sqrt eps) (/ (pow x 2) (sqrt -1))) (/ (* eps x) (pow (sqrt -1) 2)))) (* (pow eps 2) (pow (sqrt -1) 2))))) (+ (* (sqrt (/ 1 (pow eps 3))) (/ (* x (- (* (sqrt eps) (/ (pow x 2) (sqrt -1))) (/ (* eps x) (pow (sqrt -1) 2)))) (sqrt -1))) (/ x (pow (sqrt -1) 2))))
(* -1 (* (sqrt eps) (sqrt -1)))
(+ (* -1 (* (sqrt eps) (sqrt -1))) (* -1 (/ (- (* (sqrt eps) (* (pow x 2) (sqrt -1))) (* eps x)) eps)))
(+ (* -1 (* (sqrt eps) (sqrt -1))) (* -1 (/ (- (+ (* (sqrt eps) (* (pow x 2) (sqrt -1))) (* (sqrt (/ 1 eps)) (* x (* (sqrt -1) (- (* (sqrt eps) (* (pow x 2) (sqrt -1))) (* eps x)))))) (* eps x)) eps)))
(+ (* -1 (* (sqrt eps) (sqrt -1))) (* -1 (/ (- (+ (* -1 (/ (- (* (pow x 2) (- (* (sqrt eps) (* (pow x 2) (sqrt -1))) (* eps x))) (* (sqrt eps) (* x (* (sqrt -1) (- (* (sqrt eps) (* (pow x 2) (sqrt -1))) (* eps x)))))) eps)) (* (sqrt eps) (* (pow x 2) (sqrt -1)))) (* eps x)) eps)))
eps
(+ eps (pow x 2))
(+ eps (pow x 2))
(+ eps (pow x 2))
(pow x 2)
(* (pow x 2) (+ 1 (/ eps (pow x 2))))
(* (pow x 2) (+ 1 (/ eps (pow x 2))))
(* (pow x 2) (+ 1 (/ eps (pow x 2))))
(pow x 2)
(* (pow x 2) (+ 1 (/ eps (pow x 2))))
(* (pow x 2) (+ 1 (/ eps (pow x 2))))
(* (pow x 2) (+ 1 (/ eps (pow x 2))))
(pow x 2)
(+ eps (pow x 2))
(+ eps (pow x 2))
(+ eps (pow x 2))
eps
(* eps (+ 1 (/ (pow x 2) eps)))
(* eps (+ 1 (/ (pow x 2) eps)))
(* eps (+ 1 (/ (pow x 2) eps)))
eps
(* -1 (* eps (- (* -1 (/ (pow x 2) eps)) 1)))
(* -1 (* eps (- (* -1 (/ (pow x 2) eps)) 1)))
(* -1 (* eps (- (* -1 (/ (pow x 2) eps)) 1)))
(* (sqrt eps) (sqrt -1))
(+ x (* (sqrt eps) (sqrt -1)))
(+ x (* (sqrt eps) (sqrt -1)))
(+ x (* (sqrt eps) (sqrt -1)))
x
(* x (+ 1 (* (sqrt eps) (/ (sqrt -1) x))))
(* x (+ 1 (* (sqrt eps) (/ (sqrt -1) x))))
(* x (+ 1 (* (sqrt eps) (/ (sqrt -1) x))))
x
(* -1 (* x (- (* -1 (* (sqrt eps) (/ (sqrt -1) x))) 1)))
(* -1 (* x (- (* -1 (* (sqrt eps) (/ (sqrt -1) x))) 1)))
(* -1 (* x (- (* -1 (* (sqrt eps) (/ (sqrt -1) x))) 1)))
(+ x (* (sqrt eps) (sqrt -1)))
(+ x (* (sqrt eps) (sqrt -1)))
(+ x (* (sqrt eps) (sqrt -1)))
(+ x (* (sqrt eps) (sqrt -1)))
(* (sqrt eps) (sqrt -1))
(* eps (+ (* (sqrt (/ 1 eps)) (sqrt -1)) (/ x eps)))
(* eps (+ (* (sqrt (/ 1 eps)) (sqrt -1)) (/ x eps)))
(* eps (+ (* (sqrt (/ 1 eps)) (sqrt -1)) (/ x eps)))
(* -1 (* (sqrt eps) (sqrt -1)))
(* -1 (* eps (+ (* -1 (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* -1 (* eps (+ (* -1 (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* -1 (* eps (+ (* -1 (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* (sqrt eps) (sqrt -1))
(* (sqrt eps) (sqrt -1))
(* (sqrt eps) (sqrt -1))
(* (sqrt eps) (sqrt -1))
(* (sqrt eps) (sqrt -1))
(* (sqrt eps) (sqrt -1))
(* (sqrt eps) (sqrt -1))
(* (sqrt eps) (sqrt -1))
(* -1 (* (sqrt eps) (sqrt -1)))
(* -1 (* (sqrt eps) (sqrt -1)))
(* -1 (* (sqrt eps) (sqrt -1)))
(* -1 (* (sqrt eps) (sqrt -1)))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(/ 1/2 x)
(/ 1/2 x)
(/ 1/2 x)
(/ 1/2 x)
(/ 1/2 x)
(/ 1/2 x)
(/ 1/2 x)
(/ 1/2 x)
(/ 1/2 x)
(/ 1/2 x)
(/ 1/2 x)
(/ 1/2 x)
(* 1/2 (/ eps x))
(* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))
(* eps (+ (* eps (+ (* 1/32 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))
(* eps (+ (* eps (+ (* eps (+ (* 1/128 (/ eps (pow x 7))) (* 1/32 (/ 1 (pow x 5))))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))
(* -2 x)
(+ (* -8 (/ (pow x 3) eps)) (* -2 x))
(- (+ (* -32 (/ (pow x 5) (pow eps 2))) (* -2 x)) (* 8 (/ (pow x 3) eps)))
(- (+ (* -128 (/ (pow x 7) (pow eps 3))) (* -2 x)) (+ (* 8 (/ (pow x 3) eps)) (* 32 (/ (pow x 5) (pow eps 2)))))
(* -2 x)
(+ (* -8 (/ (pow x 3) eps)) (* -2 x))
(+ (* -2 x) (* -1 (/ (- (* 32 (/ (pow x 5) eps)) (* -8 (pow x 3))) eps)))
(+ (* -2 x) (* -1 (/ (- (* -1 (/ (- (* -128 (/ (pow x 7) eps)) (* 32 (pow x 5))) eps)) (* -8 (pow x 3))) eps)))
(* -2 x)
(* x (- (* -8 (/ (pow x 2) eps)) 2))
(* x (- (* (pow x 2) (- (* -32 (/ (pow x 2) (pow eps 2))) (* 8 (/ 1 eps)))) 2))
(* x (- (* (pow x 2) (- (* (pow x 2) (- (* -128 (/ (pow x 2) (pow eps 3))) (* 32 (/ 1 (pow eps 2))))) (* 8 (/ 1 eps)))) 2))
(* 1/2 (/ eps x))
(/ (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps)) x)
(/ (- (+ (* 1/32 (/ (pow eps 3) (pow x 4))) (* 1/2 eps)) (* -1/8 (/ (pow eps 2) (pow x 2)))) x)
(/ (- (+ (* 1/128 (/ (pow eps 4) (pow x 6))) (* 1/2 eps)) (+ (* -1/8 (/ (pow eps 2) (pow x 2))) (* -1/32 (/ (pow eps 3) (pow x 4))))) x)
(* 1/2 (/ eps x))
(* -1 (/ (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2)))) x))
(* -1 (/ (- (+ (* -1/2 eps) (* -1/32 (/ (pow eps 3) (pow x 4)))) (* 1/8 (/ (pow eps 2) (pow x 2)))) x))
(* -1 (/ (- (+ (* -1/2 eps) (* -1/128 (/ (pow eps 4) (pow x 6)))) (+ (* 1/32 (/ (pow eps 3) (pow x 4))) (* 1/8 (/ (pow eps 2) (pow x 2))))) x))
(* 2 (/ x eps))
(/ (+ (* -1/2 (/ eps x)) (* 2 x)) eps)
(/ (+ (* -1/2 (/ eps x)) (* 2 x)) eps)
(/ (+ (* -1/2 (/ eps x)) (* 2 x)) eps)
(/ -1/2 x)
(- (* 2 (/ x eps)) (* 1/2 (/ 1 x)))
(- (* 2 (/ x eps)) (* 1/2 (/ 1 x)))
(- (* 2 (/ x eps)) (* 1/2 (/ 1 x)))
(/ -1/2 x)
(- (* 2 (/ x eps)) (* 1/2 (/ 1 x)))
(- (* 2 (/ x eps)) (* 1/2 (/ 1 x)))
(- (* 2 (/ x eps)) (* 1/2 (/ 1 x)))
(/ -1/2 x)
(/ (- (* 2 (/ (pow x 2) eps)) 1/2) x)
(/ (- (* 2 (/ (pow x 2) eps)) 1/2) x)
(/ (- (* 2 (/ (pow x 2) eps)) 1/2) x)
(* 2 (/ x eps))
(* x (- (* 2 (/ 1 eps)) (* 1/2 (/ 1 (pow x 2)))))
(* x (- (* 2 (/ 1 eps)) (* 1/2 (/ 1 (pow x 2)))))
(* x (- (* 2 (/ 1 eps)) (* 1/2 (/ 1 (pow x 2)))))
(* 2 (/ x eps))
(* -1 (* x (- (* 1/2 (/ 1 (pow x 2))) (* 2 (/ 1 eps)))))
(* -1 (* x (- (* 1/2 (/ 1 (pow x 2))) (* 2 (/ 1 eps)))))
(* -1 (* x (- (* 1/2 (/ 1 (pow x 2))) (* 2 (/ 1 eps)))))
(* 2 x)
(+ (* -1/2 (/ eps x)) (* 2 x))
(+ (* -1/2 (/ eps x)) (* 2 x))
(+ (* -1/2 (/ eps x)) (* 2 x))
(* -1/2 (/ eps x))
(* eps (- (* 2 (/ x eps)) (* 1/2 (/ 1 x))))
(* eps (- (* 2 (/ x eps)) (* 1/2 (/ 1 x))))
(* eps (- (* 2 (/ x eps)) (* 1/2 (/ 1 x))))
(* -1/2 (/ eps x))
(* -1 (* eps (+ (* -2 (/ x eps)) (* 1/2 (/ 1 x)))))
(* -1 (* eps (+ (* -2 (/ x eps)) (* 1/2 (/ 1 x)))))
(* -1 (* eps (+ (* -2 (/ x eps)) (* 1/2 (/ 1 x)))))
(* -1/2 (/ eps x))
(/ (+ (* -1/2 eps) (* 2 (pow x 2))) x)
(/ (+ (* -1/2 eps) (* 2 (pow x 2))) x)
(/ (+ (* -1/2 eps) (* 2 (pow x 2))) x)
(* 2 x)
(* x (+ 2 (* -1/2 (/ eps (pow x 2)))))
(* x (+ 2 (* -1/2 (/ eps (pow x 2)))))
(* x (+ 2 (* -1/2 (/ eps (pow x 2)))))
(* 2 x)
(* -1 (* x (- (* 1/2 (/ eps (pow x 2))) 2)))
(* -1 (* x (- (* 1/2 (/ eps (pow x 2))) 2)))
(* -1 (* x (- (* 1/2 (/ eps (pow x 2))) 2)))
(/ -1/2 x)
(/ -1/2 x)
(/ -1/2 x)
(/ -1/2 x)
(/ -1/2 x)
(/ -1/2 x)
(/ -1/2 x)
(/ -1/2 x)
(/ -1/2 x)
(/ -1/2 x)
(/ -1/2 x)
(/ -1/2 x)
(* 1/2 (/ eps x))
(* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))
(* eps (+ (* eps (+ (* 1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))
(* eps (+ (* eps (+ (* eps (+ (* 3/128 (/ eps (pow x 7))) (* 1/16 (/ 1 (pow x 5))))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))
(* -8 (/ (pow x 3) eps))
(/ (+ (* -8 (pow x 3)) (* 32 (/ (pow x 5) eps))) eps)
(/ (- (+ (* -256 (/ (pow x 7) (pow eps 2))) (* -8 (pow x 3))) (* -32 (/ (pow x 5) eps))) eps)
(/ (- (+ (* -8 (pow x 3)) (* -1 (/ (+ (* -1024 (pow x 9)) (* -512 (pow x 9))) (pow eps 3)))) (+ (* -32 (/ (pow x 5) eps)) (* 256 (/ (pow x 7) (pow eps 2))))) eps)
(* -8 (/ (pow x 3) eps))
(* -1 (/ (+ (* -32 (/ (pow x 5) eps)) (* 8 (pow x 3))) eps))
(* -1 (/ (+ (* -1 (/ (- (* -256 (/ (pow x 7) eps)) (* -32 (pow x 5))) eps)) (* 8 (pow x 3))) eps))
(* -1 (/ (+ (* -1 (/ (- (* -1 (/ (- (+ (* -1024 (/ (pow x 9) eps)) (* -512 (/ (pow x 9) eps))) (* -256 (pow x 7))) eps)) (* -32 (pow x 5))) eps)) (* 8 (pow x 3))) eps))
(* -8 (/ (pow x 3) eps))
(* (pow x 3) (- (* 32 (/ (pow x 2) (pow eps 2))) (* 8 (/ 1 eps))))
(* (pow x 3) (- (* (pow x 2) (+ (* -256 (/ (pow x 2) (pow eps 3))) (* 32 (/ 1 (pow eps 2))))) (* 8 (/ 1 eps))))
(* (pow x 3) (- (* (pow x 2) (+ (* (pow x 2) (- (* 1536 (/ (pow x 2) (pow eps 4))) (* 256 (/ 1 (pow eps 3))))) (* 32 (/ 1 (pow eps 2))))) (* 8 (/ 1 eps))))
(* 1/2 (/ eps x))
(/ (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps)) x)
(/ (- (+ (* 1/16 (/ (pow eps 3) (pow x 4))) (* 1/2 eps)) (* -1/8 (/ (pow eps 2) (pow x 2)))) x)
(/ (- (+ (* -1 (/ (+ (* -1/64 (pow eps 4)) (* -1/128 (pow eps 4))) (pow x 6))) (* 1/2 eps)) (+ (* -1/8 (/ (pow eps 2) (pow x 2))) (* -1/16 (/ (pow eps 3) (pow x 4))))) x)
(* 1/2 (/ eps x))
(* -1 (/ (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2)))) x))
(* -1 (/ (- (+ (* -1/2 eps) (* -1/16 (/ (pow eps 3) (pow x 4)))) (* 1/8 (/ (pow eps 2) (pow x 2)))) x))
(* -1 (/ (- (+ (* -1 (/ (+ (* 1/128 (pow eps 4)) (* 1/64 (pow eps 4))) (pow x 6))) (* -1/2 eps)) (+ (* 1/16 (/ (pow eps 3) (pow x 4))) (* 1/8 (/ (pow eps 2) (pow x 2))))) x))
(* -1/8 (/ (pow eps 2) (pow x 3)))
(/ (+ (* -1/2 (* eps (pow x 2))) (* -1/8 (pow eps 2))) (pow x 3))
(/ (+ (* -1/8 (pow eps 2)) (* (pow x 2) (+ (* -1/2 eps) (* 2 (pow x 2))))) (pow x 3))
(/ (+ (* -1/8 (pow eps 2)) (* (pow x 2) (+ (* -1/2 eps) (* 2 (pow x 2))))) (pow x 3))
(* 2 x)
(* x (+ 2 (* -1/2 (/ eps (pow x 2)))))
(* x (+ 2 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4))))))
(* x (+ 2 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4))))))
(* 2 x)
(* -1 (* x (- (* 1/2 (/ eps (pow x 2))) 2)))
(* -1 (* x (- (+ (* 1/8 (/ (pow eps 2) (pow x 4))) (* 1/2 (/ eps (pow x 2)))) 2)))
(* -1 (* x (- (+ (* 1/8 (/ (pow eps 2) (pow x 4))) (* 1/2 (/ eps (pow x 2)))) 2)))
(* 2 x)
(+ (* -1/2 (/ eps x)) (* 2 x))
(+ (* 2 x) (* eps (- (* -1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))))
(+ (* 2 x) (* eps (- (* -1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))))
(* -1/8 (/ (pow eps 2) (pow x 3)))
(* -1 (* (pow eps 2) (+ (* 1/8 (/ 1 (pow x 3))) (* 1/2 (/ 1 (* eps x))))))
(* (pow eps 2) (- (* 2 (/ x (pow eps 2))) (+ (* 1/8 (/ 1 (pow x 3))) (/ 1/2 (* eps x)))))
(* (pow eps 2) (- (* 2 (/ x (pow eps 2))) (+ (* 1/8 (/ 1 (pow x 3))) (/ 1/2 (* eps x)))))
(* -1/8 (/ (pow eps 2) (pow x 3)))
(* -1 (* (pow eps 2) (+ (* 1/8 (/ 1 (pow x 3))) (* 1/2 (/ 1 (* eps x))))))
(* (pow eps 2) (- (* -1 (/ (+ (* -2 (/ x eps)) (* 1/2 (/ 1 x))) eps)) (* 1/8 (/ 1 (pow x 3)))))
(* (pow eps 2) (- (* -1 (/ (+ (* -2 (/ x eps)) (* 1/2 (/ 1 x))) eps)) (* 1/8 (/ 1 (pow x 3)))))
x
(+ x (* -1/2 (/ eps x)))
(+ x (* eps (- (* -1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))))
(+ x (* eps (- (* -1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))))
(* -1/8 (/ (pow eps 2) (pow x 3)))
(* -1 (* (pow eps 2) (+ (* 1/8 (/ 1 (pow x 3))) (* 1/2 (/ 1 (* eps x))))))
(* (pow eps 2) (- (/ x (pow eps 2)) (+ (* 1/8 (/ 1 (pow x 3))) (/ 1/2 (* eps x)))))
(* (pow eps 2) (- (/ x (pow eps 2)) (+ (* 1/8 (/ 1 (pow x 3))) (/ 1/2 (* eps x)))))
(* -1/8 (/ (pow eps 2) (pow x 3)))
(* -1 (* (pow eps 2) (+ (* 1/8 (/ 1 (pow x 3))) (* 1/2 (/ 1 (* eps x))))))
(* (pow eps 2) (- (* -1 (/ (+ (* -1 (/ x eps)) (* 1/2 (/ 1 x))) eps)) (* 1/8 (/ 1 (pow x 3)))))
(* (pow eps 2) (- (* -1 (/ (+ (* -1 (/ x eps)) (* 1/2 (/ 1 x))) eps)) (* 1/8 (/ 1 (pow x 3)))))
(* -1/8 (/ (pow eps 2) (pow x 3)))
(/ (+ (* -1/2 (* eps (pow x 2))) (* -1/8 (pow eps 2))) (pow x 3))
(/ (+ (* -1/8 (pow eps 2)) (* (pow x 2) (+ (* -1/2 eps) (pow x 2)))) (pow x 3))
(/ (+ (* -1/8 (pow eps 2)) (* (pow x 2) (+ (* -1/2 eps) (pow x 2)))) (pow x 3))
x
(* x (+ 1 (* -1/2 (/ eps (pow x 2)))))
(* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4))))))
(* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4))))))
x
(* -1 (* x (- (* 1/2 (/ eps (pow x 2))) 1)))
(* -1 (* x (- (+ (* 1/8 (/ (pow eps 2) (pow x 4))) (* 1/2 (/ eps (pow x 2)))) 1)))
(* -1 (* x (- (+ (* 1/8 (/ (pow eps 2) (pow x 4))) (* 1/2 (/ eps (pow x 2)))) 1)))
(/ -1/2 x)
(- (* -1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))
(- (* -1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))
(- (* -1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))
(* -1/8 (/ eps (pow x 3)))
(* -1 (* eps (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3))))))
(* -1 (* eps (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3))))))
(* -1 (* eps (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3))))))
(* -1/8 (/ eps (pow x 3)))
(* -1 (* eps (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3))))))
(* -1 (* eps (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3))))))
(* -1 (* eps (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3))))))
(* -1/8 (/ eps (pow x 3)))
(/ (+ (* -1/2 (pow x 2)) (* -1/8 eps)) (pow x 3))
(/ (+ (* -1/2 (pow x 2)) (* -1/8 eps)) (pow x 3))
(/ (+ (* -1/2 (pow x 2)) (* -1/8 eps)) (pow x 3))
(/ -1/2 x)
(/ (- (* -1/8 (/ eps (pow x 2))) 1/2) x)
(/ (- (* -1/8 (/ eps (pow x 2))) 1/2) x)
(/ (- (* -1/8 (/ eps (pow x 2))) 1/2) x)
(/ -1/2 x)
(* -1 (/ (+ 1/2 (* 1/8 (/ eps (pow x 2)))) x))
(* -1 (/ (+ 1/2 (* 1/8 (/ eps (pow x 2)))) x))
(* -1 (/ (+ 1/2 (* 1/8 (/ eps (pow x 2)))) x))
(* -1 eps)
(* -1 eps)
(* -1 eps)
(* -1 eps)
(* -1 eps)
(* -1 eps)
(* -1 eps)
(* -1 eps)
(* -1 eps)
(* -1 eps)
(* -1 eps)
(* -1 eps)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
-1/2
(- (* -1/8 (/ eps (pow x 2))) 1/2)
(- (* -1/8 (/ eps (pow x 2))) 1/2)
(- (* -1/8 (/ eps (pow x 2))) 1/2)
(* -1/8 (/ eps (pow x 2)))
(* -1 (* eps (+ (* 1/8 (/ 1 (pow x 2))) (* 1/2 (/ 1 eps)))))
(* -1 (* eps (+ (* 1/8 (/ 1 (pow x 2))) (* 1/2 (/ 1 eps)))))
(* -1 (* eps (+ (* 1/8 (/ 1 (pow x 2))) (* 1/2 (/ 1 eps)))))
(* -1/8 (/ eps (pow x 2)))
(* -1 (* eps (+ (* 1/2 (/ 1 eps)) (* 1/8 (/ 1 (pow x 2))))))
(* -1 (* eps (+ (* 1/2 (/ 1 eps)) (* 1/8 (/ 1 (pow x 2))))))
(* -1 (* eps (+ (* 1/2 (/ 1 eps)) (* 1/8 (/ 1 (pow x 2))))))
(* -1/8 (/ eps (pow x 2)))
(/ (+ (* -1/2 (pow x 2)) (* -1/8 eps)) (pow x 2))
(/ (+ (* -1/2 (pow x 2)) (* -1/8 eps)) (pow x 2))
(/ (+ (* -1/2 (pow x 2)) (* -1/8 eps)) (pow x 2))
-1/2
(- (* -1/8 (/ eps (pow x 2))) 1/2)
(- (* -1/8 (/ eps (pow x 2))) 1/2)
(- (* -1/8 (/ eps (pow x 2))) 1/2)
-1/2
(- (* -1/8 (/ eps (pow x 2))) 1/2)
(- (* -1/8 (/ eps (pow x 2))) 1/2)
(- (* -1/8 (/ eps (pow x 2))) 1/2)
(/ -1/8 (pow x 2))
(/ -1/8 (pow x 2))
(/ -1/8 (pow x 2))
(/ -1/8 (pow x 2))
(/ -1/8 (pow x 2))
(/ -1/8 (pow x 2))
(/ -1/8 (pow x 2))
(/ -1/8 (pow x 2))
(/ -1/8 (pow x 2))
(/ -1/8 (pow x 2))
(/ -1/8 (pow x 2))
(/ -1/8 (pow x 2))

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

eval197.0ms (2%)

Memory: 11.5MiB live, 517.6MiB allocated
Compiler: Compiled 34 058 to 4 472 computations (86.9% saved)

prune213.0ms (2.1%)

Memory

-36.5MiB live, 336.6MiB allocated

Pruning

15 alts after pruning (6 fresh and 9 done)

	Pruned	Kept	Total
New	1 358	6	1 364
Fresh	1	0	1
Picked	1	4	5
Done	1	5	6
Total	1 361	15	1 376

Accuracy

100.0%

Counts

1 376 → 15

Alt Table

Click to see full alt table

Status	Accuracy	Program
	45.0%	(/.f64 eps (fma.f64 eps (/.f64 (fma.f64 eps (/.f64 #s(literal -1/8 binary64) (.f64 x x)) #s(literal -1/2 binary64)) x) (.f64 x #s(literal 2 binary64))))
✓	45.0%	(/.f64 eps (+.f64 x (fma.f64 eps (/.f64 (fma.f64 eps (/.f64 #s(literal -1/8 binary64) (*.f64 x x)) #s(literal -1/2 binary64)) x) x)))
	46.3%	(/.f64 eps (+.f64 x (fma.f64 eps (/.f64 #s(literal -1/2 binary64) x) x)))
	58.9%	(/.f64 eps (+.f64 x (sqrt.f64 (neg.f64 eps))))
	45.6%	(/.f64 eps (+.f64 x x))
✓	46.1%	(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 eps (/.f64 #s(literal -1/2 binary64) x) (+.f64 x x)) eps))
✓	60.3%	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))))
✓	6.7%	(-.f64 x (fma.f64 eps (/.f64 #s(literal -1/2 binary64) x) x))
✓	60.4%	(-.f64 x (sqrt.f64 (fma.f64 x x (neg.f64 eps))))
✓	56.2%	(-.f64 x (sqrt.f64 (neg.f64 eps)))
✓	45.5%	(*.f64 (/.f64 #s(literal 1/2 binary64) x) eps)
	5.1%	(*.f64 x #s(literal -2 binary64))
	7.8%	(*.f64 eps #s(literal 1 binary64))
✓	3.7%	x
✓	4.3%	#s(literal 0 binary64)

Compiler

Compiled 455 to 184 computations (59.6% saved)

regimes30.0ms (0.3%)

Memory

19.5MiB live, 55.8MiB allocated

Counts

30 → 2

Calls

Call 1

Inputs
#s(literal 0 binary64)
x
(+.f64 x x)
(-.f64 x x)
(*.f64 eps #s(literal 1 binary64))
(*.f64 x #s(literal -2 binary64))
(-.f64 x (neg.f64 x))
(/.f64 eps (+.f64 x x))
(-.f64 x (sqrt.f64 (neg.f64 eps)))
(*.f64 (/.f64 #s(literal 1/2 binary64) x) eps)
(/.f64 (*.f64 eps #s(literal 1/2 binary64)) x)
(-.f64 x (fma.f64 eps (/.f64 #s(literal -1/2 binary64) x) x))
(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
(-.f64 x (sqrt.f64 (fma.f64 x x (neg.f64 eps))))
(/.f64 eps (+.f64 x (sqrt.f64 (neg.f64 eps))))
(/.f64 eps (+.f64 x (fma.f64 eps (/.f64 #s(literal -1/2 binary64) x) x)))
(/.f64 (fma.f64 x x eps) (+.f64 x (sqrt.f64 (neg.f64 eps))))
(-.f64 x (/.f64 (-.f64 (.f64 x x) eps) (sqrt.f64 (-.f64 (.f64 x x) eps))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 eps (/.f64 #s(literal -1/2 binary64) x) (+.f64 x x)) eps))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))))
(/.f64 (fma.f64 eps #s(literal 1/2 binary64) (/.f64 (.f64 #s(literal 1/8 binary64) (.f64 eps eps)) (*.f64 x x))) x)
(/.f64 (-.f64 (fma.f64 x x eps) (.f64 x x)) (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))))
(fma.f64 (sqrt.f64 x) (sqrt.f64 x) (neg.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps))))
(/.f64 eps (+.f64 x (fma.f64 eps (/.f64 (fma.f64 eps (/.f64 #s(literal -1/8 binary64) (*.f64 x x)) #s(literal -1/2 binary64)) x) x)))
(/.f64 eps (fma.f64 eps (/.f64 (fma.f64 eps (/.f64 #s(literal -1/8 binary64) (.f64 x x)) #s(literal -1/2 binary64)) x) (.f64 x #s(literal 2 binary64))))
(.f64 (/.f64 #s(literal 1 binary64) (+.f64 x (fma.f64 eps (/.f64 (fma.f64 eps (/.f64 #s(literal -1/8 binary64) (.f64 x x)) #s(literal -1/2 binary64)) x) x))) eps)
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 eps (/.f64 (fma.f64 eps (/.f64 #s(literal -1/8 binary64) (*.f64 x x)) #s(literal -1/2 binary64)) x) (+.f64 x x)) eps))
(fma.f64 (sqrt.f64 (sqrt.f64 (-.f64 (.f64 x x) eps))) (neg.f64 (sqrt.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)))) x)
(/.f64 (fma.f64 #s(literal 1/8 binary64) (/.f64 (.f64 eps eps) (.f64 x x)) (fma.f64 (.f64 eps (.f64 eps eps)) (/.f64 #s(literal 1/16 binary64) (.f64 (.f64 x x) (.f64 x x))) (.f64 eps #s(literal 1/2 binary64)))) x)
(.f64 eps (fma.f64 eps (fma.f64 eps (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 5 binary64))) (/.f64 #s(literal 1/8 binary64) (.f64 x (*.f64 x x)))) (/.f64 #s(literal 1/2 binary64) x)))

Outputs
(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
(/.f64 eps (+.f64 x (fma.f64 eps (/.f64 (fma.f64 eps (/.f64 #s(literal -1/8 binary64) (*.f64 x x)) #s(literal -1/2 binary64)) x) x)))

Calls

3 calls:

11.0ms	eps
9.0ms	x
8.0ms	(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))

Results

Accuracy	Segments	Branch
92.3%	2	`x`
82.7%	2	`eps`
99.6%	2	`(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))`

Compiler

Compiled 16 to 10 computations (37.5% saved)

regimes11.0ms (0.1%)

Memory

-27.5MiB live, 16.9MiB allocated

Counts

23 → 2

Calls

Call 1

Inputs
#s(literal 0 binary64)
x
(+.f64 x x)
(-.f64 x x)
(*.f64 eps #s(literal 1 binary64))
(*.f64 x #s(literal -2 binary64))
(-.f64 x (neg.f64 x))
(/.f64 eps (+.f64 x x))
(-.f64 x (sqrt.f64 (neg.f64 eps)))
(*.f64 (/.f64 #s(literal 1/2 binary64) x) eps)
(/.f64 (*.f64 eps #s(literal 1/2 binary64)) x)
(-.f64 x (fma.f64 eps (/.f64 #s(literal -1/2 binary64) x) x))
(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
(-.f64 x (sqrt.f64 (fma.f64 x x (neg.f64 eps))))
(/.f64 eps (+.f64 x (sqrt.f64 (neg.f64 eps))))
(/.f64 eps (+.f64 x (fma.f64 eps (/.f64 #s(literal -1/2 binary64) x) x)))
(/.f64 (fma.f64 x x eps) (+.f64 x (sqrt.f64 (neg.f64 eps))))
(-.f64 x (/.f64 (-.f64 (.f64 x x) eps) (sqrt.f64 (-.f64 (.f64 x x) eps))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 eps (/.f64 #s(literal -1/2 binary64) x) (+.f64 x x)) eps))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))))
(/.f64 (fma.f64 eps #s(literal 1/2 binary64) (/.f64 (.f64 #s(literal 1/8 binary64) (.f64 eps eps)) (*.f64 x x))) x)
(/.f64 (-.f64 (fma.f64 x x eps) (.f64 x x)) (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))))
(fma.f64 (sqrt.f64 x) (sqrt.f64 x) (neg.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps))))

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

Calls

1 calls:

7.0ms

(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))

Results

Accuracy	Segments	Branch
99.5%	2	`(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))`

Compiler

Compiled 10 to 6 computations (40% saved)

regimes6.0ms (0.1%)

Memory

11.8MiB live, 11.8MiB allocated

Counts

15 → 2

Calls

Call 1

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

Outputs
(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
(/.f64 eps (+.f64 x x))

Calls

1 calls:

5.0ms

(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))

Results

Accuracy	Segments	Branch
99.1%	2	`(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))`

Compiler

Compiled 10 to 6 computations (40% saved)

regimes5.0ms (0%)

Memory

10.2MiB live, 10.2MiB allocated

Counts

12 → 2

Calls

Call 1

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

Outputs
(-.f64 x (sqrt.f64 (neg.f64 eps)))
(/.f64 eps (+.f64 x x))

Calls

1 calls:

4.0ms

(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))

Results

Accuracy	Segments	Branch
97.4%	2	`(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))`

Compiler

Compiled 10 to 6 computations (40% saved)

regimes13.0ms (0.1%)

Memory

-16.4MiB live, 20.3MiB allocated

Counts

8 → 1

Calls

Call 1

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

Outputs
(/.f64 eps (+.f64 x x))

Calls

3 calls:

6.0ms	eps
3.0ms	x
3.0ms	(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))

Results

Accuracy	Segments	Branch
45.6%	1	`eps`
45.6%	1	`x`
45.6%	1	`(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))`

Compiler

Compiled 16 to 10 computations (37.5% saved)

regimes9.0ms (0.1%)

Memory

18.1MiB live, 18.1MiB allocated

Counts

7 → 1

Calls

Call 1

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

Outputs
(*.f64 eps #s(literal 1 binary64))

Calls

3 calls:

3.0ms	x
3.0ms	eps
3.0ms	(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))

Results

Accuracy	Segments	Branch
7.8%	1	`eps`
7.8%	1	`(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))`
7.8%	1	`x`

Compiler

Compiled 16 to 10 computations (37.5% saved)

regimes6.0ms (0.1%)

Memory

14.2MiB live, 14.2MiB allocated

Accuracy

Total -0.7b remaining (-1.2%)

Threshold costs -0.7b (-1.2%)

Counts

4 → 1

Calls

Call 1

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

Outputs
#s(literal 0 binary64)

Calls

3 calls:

2.0ms	x
2.0ms	eps
2.0ms	(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))

Results

Accuracy	Segments	Branch
4.3%	1	`eps`
4.3%	1	`(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))`
4.3%	1	`x`

Compiler

Compiled 16 to 10 computations (37.5% saved)

bsearch0.0ms (0%)

Memory

0.5MiB live, 0.5MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	-5.041996258731469e-154	0.0

Compiler

Compiled 13 to 11 computations (15.4% saved)

bsearch0.0ms (0%)

Memory

0.4MiB live, 0.3MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	-5.041996258731469e-154	0.0

Compiler

Compiled 13 to 11 computations (15.4% saved)

bsearch0.0ms (0%)

Memory

0.3MiB live, 0.3MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	-5.041996258731469e-154	0.0

Compiler

Compiled 13 to 11 computations (15.4% saved)

bsearch0.0ms (0%)

Memory

0.3MiB live, 0.3MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	-5.041996258731469e-154	0.0

Compiler

Compiled 13 to 11 computations (15.4% saved)

simplify13.0ms (0.1%)

Memory

-21.8MiB live, 16.7MiB allocated

Algorithm

1×	egg-herbie

Rules

18×	`unsub-neg_binary64`
18×	`+-commutative_binary64`
18×	`neg-mul-1_binary64`
14×	`sub-neg_binary64`
10×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	32	117
1	45	117
2	63	117
3	70	117
4	75	117
5	86	117
6	104	117

Stop Event

1×

saturated

Calls

Call 1

Inputs
(if (<=.f64 (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) #s(literal -7547924849643083/15095849699286165408966218323953075563667684881665761713504825200982496649568595408344506900710635070165873500123055379599082338519699170530245737005730784174597581307904 binary64)) (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) (/.f64 eps (+.f64 x (fma.f64 eps (/.f64 (fma.f64 eps (/.f64 #s(literal -1/8 binary64) (*.f64 x x)) #s(literal -1/2 binary64)) x) x))))
(if (<=.f64 (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) #s(literal -7547924849643083/15095849699286165408966218323953075563667684881665761713504825200982496649568595408344506900710635070165873500123055379599082338519699170530245737005730784174597581307904 binary64)) (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) (/.f64 eps (+.f64 x (fma.f64 eps (/.f64 #s(literal -1/2 binary64) x) x))))
(if (<=.f64 (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) #s(literal -7547924849643083/15095849699286165408966218323953075563667684881665761713504825200982496649568595408344506900710635070165873500123055379599082338519699170530245737005730784174597581307904 binary64)) (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) (/.f64 eps (+.f64 x x)))
(if (<=.f64 (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) #s(literal -7547924849643083/15095849699286165408966218323953075563667684881665761713504825200982496649568595408344506900710635070165873500123055379599082338519699170530245737005730784174597581307904 binary64)) (-.f64 x (sqrt.f64 (neg.f64 eps))) (/.f64 eps (+.f64 x x)))
(/.f64 eps (+.f64 x x))
(*.f64 eps #s(literal 1 binary64))
#s(literal 0 binary64)

Outputs
(if (<=.f64 (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) #s(literal -7547924849643083/15095849699286165408966218323953075563667684881665761713504825200982496649568595408344506900710635070165873500123055379599082338519699170530245737005730784174597581307904 binary64)) (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) (/.f64 eps (+.f64 x (fma.f64 eps (/.f64 (fma.f64 eps (/.f64 #s(literal -1/8 binary64) (*.f64 x x)) #s(literal -1/2 binary64)) x) x))))
(if (<=.f64 (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) #s(literal -7547924849643083/15095849699286165408966218323953075563667684881665761713504825200982496649568595408344506900710635070165873500123055379599082338519699170530245737005730784174597581307904 binary64)) (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) (/.f64 eps (+.f64 x (fma.f64 eps (/.f64 #s(literal -1/2 binary64) x) x))))
(if (<=.f64 (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) #s(literal -7547924849643083/15095849699286165408966218323953075563667684881665761713504825200982496649568595408344506900710635070165873500123055379599082338519699170530245737005730784174597581307904 binary64)) (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) (/.f64 eps (+.f64 x x)))
(if (<=.f64 (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) #s(literal -7547924849643083/15095849699286165408966218323953075563667684881665761713504825200982496649568595408344506900710635070165873500123055379599082338519699170530245737005730784174597581307904 binary64)) (-.f64 x (sqrt.f64 (neg.f64 eps))) (/.f64 eps (+.f64 x x)))
(/.f64 eps (+.f64 x x))
(*.f64 eps #s(literal 1 binary64))
eps
#s(literal 0 binary64)

soundness910.0ms (9.1%)

Memory

8.2MiB live, 813.3MiB allocated

Rules

11 222×	`accelerator-lowering-fma.f32`
11 222×	`accelerator-lowering-fma.f64`
9 340×	`accelerator-lowering-fma.f32`
9 340×	`accelerator-lowering-fma.f64`
7 830×	`accelerator-lowering-fma.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	478	4837
1	1486	4685
2	5149	4612
0	8380	4376
0	6	22
1	38	22
2	306	22
3	3595	22
0	8551	22
0	28	149
1	188	147
2	1615	114
0	8802	105
0	26	157
1	192	153
2	1767	135
0	8484	123
0	532	3926
1	1599	3808
2	4793	3703
0	8787	3456
0	21	84
1	130	84
0	888	84
0	257	1257
1	784	1238
2	2594	1200
3	6944	1197
0	8091	1129

Stop Event

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

Compiler

Compiled 348 to 172 computations (50.6% saved)

preprocess53.0ms (0.5%)

Memory: 2.1MiB live, 163.9MiB allocated
Compiler: Compiled 282 to 86 computations (69.5% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

Iter	Nodes	Cost
0	21	54
1	49	52
2	125	49
3	290	49
4	522	49
5	609	49
6	617	49
0	6	8
1	10	8
2	18	8
3	30	8
4	48	8
5	90	8
6	157	8
7	203	8
8	285	8
9	315	8
10	331	8
0	331	8

Iter	Nodes	Cost
0	6	24
1	10	24
2	18	24
3	30	24
4	48	24
5	90	24
6	157	24
7	203	24
8	285	24
9	315	24
10	331	24
0	331	24

Iter	Nodes	Cost
0	21	54
1	49	52
2	125	49
3	290	49
4	522	49
5	609	49
6	617	49
0	6	8
1	10	8
2	18	8
3	30	8
4	48	8
5	90	8
6	157	8
7	203	8
8	285	8
9	315	8
10	331	8
0	331	8

Iter	Nodes	Cost
0	6	24
1	10	24
2	18	24
3	30	24
4	48	24
5	90	24
6	157	24
7	203	24
8	285	24
9	315	24
10	331	24
0	331	24

analyze15.0ms (0.1%)

sample1.2s (12.4%)

preprocess35.0ms (0.4%)

explain108.0ms (1.1%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify19.0ms (0.2%)

localize29.0ms (0.3%)

series8.0ms (0.1%)

rewrite386.0ms (3.8%)

simplify716.0ms (7.1%)

eval67.0ms (0.7%)

prune80.0ms (0.8%)

simplify67.0ms (0.7%)

localize98.0ms (1%)

series19.0ms (0.2%)

rewrite124.0ms (1.2%)

simplify369.0ms (3.7%)

eval104.0ms (1%)

prune66.0ms (0.7%)

simplify273.0ms (2.7%)

localize100.0ms (1%)

series24.0ms (0.2%)

rewrite412.0ms (4.1%)

simplify2.5s (25.4%)

eval212.0ms (2.1%)

prune155.0ms (1.5%)

simplify325.0ms (3.2%)

localize126.0ms (1.3%)

series14.0ms (0.1%)

rewrite468.0ms (4.7%)

simplify349.0ms (3.5%)

eval197.0ms (2%)

prune213.0ms (2.1%)

regimes30.0ms (0.3%)

regimes11.0ms (0.1%)

regimes6.0ms (0.1%)

regimes5.0ms (0%)

regimes13.0ms (0.1%)

regimes9.0ms (0.1%)

regimes6.0ms (0.1%)

bsearch0.0ms (0%)

bsearch0.0ms (0%)

bsearch0.0ms (0%)

bsearch0.0ms (0%)

simplify13.0ms (0.1%)

soundness910.0ms (9.1%)

preprocess53.0ms (0.5%)

end0.0ms (0%)

Profiling

Iter	Nodes	Cost
0	21	54
1	49	52
2	125	49
3	290	49
4	522	49
5	609	49
6	617	49
0	6	8
1	10	8
2	18	8
3	30	8
4	48	8
5	90	8
6	157	8
7	203	8
8	285	8
9	315	8
10	331	8
0	331	8

Iter	Nodes	Cost
0	6	24
1	10	24
2	18	24
3	30	24
4	48	24
5	90	24
6	157	24
7	203	24
8	285	24
9	315	24
10	331	24
0	331	24