Metrics for ENA, Section 1.4, Exercise 4d

start0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated

analyze43.0ms (0.5%)

Memory

-16.3MiB live, 22.7MiB 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)

sample1.7s (19.2%)

Memory

11.9MiB live, 1 679.1MiB allocated

Samples

455.0ms	2 680×	1	valid
415.0ms	590×	2	valid
346.0ms	4 986×	0	valid
23.0ms	152×	0	invalid

Precisions

Click to see histograms. Total time spent on operations: 608.0ms

ival-sub: 132.0ms (21.7% of total)

ival-sqrt: 123.0ms (20.2% of total)

ival-<=: 123.0ms (20.2% of total)

ival-mult: 102.0ms (16.8% of total)

adjust: 83.0ms (13.7% of total)

ival-and: 23.0ms (3.8% of total)

exact: 18.0ms (3% of total)

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

Bogosity

explain110.0ms (1.2%)

Memory

-25.1MiB live, 198.9MiB allocated

FPErrors

Click to see full error table

Ground Truth	Example	Example	Subexpression
111	-	-	`(-.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	111	0

Confusion

	Predicted +	Predicted -
+	111	0
-	0	145

Precision

1.0

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	111	0	0
-	0	0	145

Precision?

1.0

Recall?

1.0

Freqs

test

number	freq
0	145
1	111

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

34.0ms	178×	1	valid
16.0ms	306×	0	valid
4.0ms	28×	2	valid

Compiler

Compiled 84 to 28 computations (66.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 34.0ms

ival-sub: 18.0ms (53.7% of total)

ival-sqrt: 6.0ms (17.9% of total)

ival-mult: 5.0ms (14.9% of total)

adjust: 4.0ms (11.9% of total)

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

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

preprocess40.0ms (0.5%)

Memory

-5.1MiB live, 33.3MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	46
1	43	44
2	118	41
3	280	41
4	498	41
5	572	41
6	586	41
0	6	8
0	10	8
1	14	8
2	22	8
3	34	8
4	52	8
5	96	8
6	163	8
7	213	8
8	301	8
9	333	8
10	349	8
0	349	8

Stop Event

1×	iter limit
1×	saturated
1×	iter limit
1×	saturated

Calls

Call 1

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

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

Compiler

Compiled 8 to 6 computations (25% saved)

eval0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated
Compiler: Compiled 0 to 2 computations (-∞% saved)

prune0.0ms (0%)

Memory

0.9MiB live, 0.9MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	61.2%	(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))

Compiler

Compiled 8 to 6 computations (25% saved)

simplify9.0ms (0.1%)

Memory

24.6MiB live, 24.6MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

New	Metric	Score	Program
cost-diff	0	(*.f64 x x)
cost-diff	0	(-.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)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	24
0	10	24
1	14	24
2	22	24
3	34	24
4	52	24
5	96	24
6	163	24
7	213	24
8	301	24
9	333	24
10	349	24
0	349	24

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize28.0ms (0.3%)

Memory

-24.7MiB live, 52.3MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0.0	(*.f64 x x)
accuracy	0.01171875	(-.f64 (*.f64 x x) eps)
accuracy	0.01171875	(sqrt.f64 (-.f64 (*.f64 x x) eps))
accuracy	24.83594137359021	(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))

Samples

12.0ms	89×	1	valid
8.0ms	153×	0	valid
2.0ms	14×	2	valid

Compiler

Compiled 50 to 14 computations (72% saved)

Precisions

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

ival-sub: 4.0ms (33.1% of total)

ival-mult: 4.0ms (33.1% of total)

ival-sqrt: 3.0ms (24.8% of total)

adjust: 2.0ms (16.5% of total)

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

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

series8.0ms (0.1%)

Memory

16.9MiB live, 16.9MiB allocated

Counts

4 → 49

Calls

Call 1

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

Outputs
(* -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)))
(* (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)))))))))
(* -1 eps)
(- (pow x 2) eps)
(pow x 2)
(* 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)
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)))))))
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))
(* 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 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))))))))
(* 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))))
(+ 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)))))
(+ (* -1 eps) (pow x 2))
(* 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)))))
(* 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))))))
(* eps (- (/ (pow x 2) eps) 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 (* 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 (+ 1 (* -1 (/ (pow x 2) eps)))))

Calls

6 calls:

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

simplify245.0ms (2.8%)

Memory

0.7MiB live, 234.6MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	257	1067
1	784	1053
2	2629	1015
3	7085	1012
0	8084	948

Stop Event

1×	iter limit
1×	node limit

Counts

49 → 48

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)))
(* (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)))))))))
(* -1 eps)
(- (pow x 2) eps)
(pow x 2)
(* 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)
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)))))))
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))
(* 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 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))))))))
(* 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))))
(+ 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)))))
(+ (* -1 eps) (pow x 2))
(* 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)))))
(* 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))))))
(* eps (- (/ (pow x 2) eps) 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 (* 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 (+ 1 (* -1 (/ (pow x 2) eps)))))

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

rewrite203.0ms (2.3%)

Memory

-8.1MiB live, 114.1MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	22
0	10	22
1	42	22
2	310	22
3	3602	22
0	8540	22

Stop Event

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

Counts

4 → 224

Calls

Call 1

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

Outputs
(.f64 (/.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 3/2 binary64))) (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 (fma.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x (-.f64 (.f64 x x) eps)) #s(literal 2 binary64)))) (-.f64 (-.f64 (fma.f64 x x eps) (.f64 x x)) (.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)))
(.f64 (/.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 3/2 binary64))) (+.f64 (pow.f64 (fma.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x (-.f64 (.f64 x x) eps)) #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64)))) (fma.f64 (fma.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x (-.f64 (.f64 x x) eps)) (-.f64 (fma.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x (-.f64 (.f64 x x) eps)) (*.f64 x x)) (pow.f64 x #s(literal 4 binary64))))
(.f64 (/.f64 (-.f64 (fma.f64 x x eps) (.f64 x x)) (-.f64 (fma.f64 x x eps) (.f64 x x))) (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))))
(.f64 (/.f64 (-.f64 (fma.f64 x x eps) (.f64 x x)) (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 3/2 binary64)))) (-.f64 (fma.f64 x x (-.f64 (.f64 x x) eps)) (.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x)))
(.f64 (pow.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) #s(literal -1 binary64)) (-.f64 (fma.f64 x x eps) (*.f64 x x)))
(.f64 (pow.f64 (fma.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x (fma.f64 x x (-.f64 (.f64 x x) eps))) #s(literal -1 binary64)) (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 3/2 binary64))))
(.f64 (neg.f64 (-.f64 (fma.f64 x x eps) (.f64 x x))) (pow.f64 (neg.f64 (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)) #s(literal -1 binary64)))
(.f64 (neg.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 3/2 binary64)))) (pow.f64 (neg.f64 (fma.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x (fma.f64 x x (-.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 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) (/.f64 (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x)))
(.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) (.f64 (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) (pow.f64 (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x) #s(literal -1 binary64))))
(.f64 (-.f64 (fma.f64 x x eps) (.f64 x x)) (pow.f64 (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x) #s(literal -1 binary64)))
(.f64 (fma.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x (fma.f64 x x (-.f64 (.f64 x x) eps))) (/.f64 (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) (fma.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x (fma.f64 x x (-.f64 (.f64 x x) eps)))))
(.f64 (fma.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x (fma.f64 x x (-.f64 (.f64 x x) eps))) (.f64 (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) (pow.f64 (fma.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x (fma.f64 x x (-.f64 (*.f64 x x) eps))) #s(literal -1 binary64))))
(.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 3/2 binary64))) (pow.f64 (fma.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x (fma.f64 x x (-.f64 (.f64 x x) eps))) #s(literal -1 binary64)))
(pow.f64 (/.f64 (pow.f64 (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) #s(literal -1 binary64)) #s(literal 1 binary64)) #s(literal -1 binary64))
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(/.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 eps #s(literal 3 binary64))) (fma.f64 eps eps (-.f64 (pow.f64 x #s(literal 4 binary64)) (.f64 (neg.f64 eps) (.f64 x x)))))
(/.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 eps #s(literal 3 binary64))) (pow.f64 (fma.f64 (fma.f64 x x eps) eps (pow.f64 x #s(literal 4 binary64))) #s(literal 1 binary64)))
(/.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 eps #s(literal 3 binary64))) (fma.f64 (fma.f64 x x eps) eps (pow.f64 x #s(literal 4 binary64))))
(neg.f64 (neg.f64 (-.f64 (*.f64 x x) eps)))
(fma.f64 (/.f64 (pow.f64 x #s(literal 6 binary64)) (-.f64 (pow.f64 x #s(literal 8 binary64)) (pow.f64 (.f64 (fma.f64 x x eps) eps) #s(literal 2 binary64)))) (-.f64 (pow.f64 x #s(literal 4 binary64)) (.f64 (fma.f64 x x eps) eps)) (neg.f64 (/.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 (fma.f64 x x eps) eps (pow.f64 x #s(literal 4 binary64))))))
(fma.f64 (/.f64 (pow.f64 x #s(literal 6 binary64)) (+.f64 (pow.f64 (.f64 (fma.f64 x x eps) eps) #s(literal 3 binary64)) (pow.f64 x #s(literal 12 binary64)))) (fma.f64 (.f64 (fma.f64 x x eps) eps) (-.f64 (*.f64 (fma.f64 x x eps) eps) (pow.f64 x #s(literal 4 binary64))) (pow.f64 x #s(literal 8 binary64))) (neg.f64 (/.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 (fma.f64 x x eps) eps (pow.f64 x #s(literal 4 binary64))))))
(fma.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 eps #s(literal 3 binary64)))) (fma.f64 eps (-.f64 eps (.f64 x x)) (pow.f64 x #s(literal 4 binary64))) (neg.f64 (.f64 eps (/.f64 eps (fma.f64 x x eps)))))
(fma.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 (neg.f64 eps) eps (pow.f64 x #s(literal 4 binary64)))) (-.f64 (.f64 x x) eps) (neg.f64 (.f64 eps (/.f64 eps (fma.f64 x x eps)))))
(fma.f64 #s(literal -1 binary64) eps (*.f64 x x))
(fma.f64 (pow.f64 x #s(literal 4 binary64)) (/.f64 (*.f64 x x) (fma.f64 (fma.f64 x x eps) eps (pow.f64 x #s(literal 4 binary64)))) (neg.f64 (/.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 (fma.f64 x x eps) eps (pow.f64 x #s(literal 4 binary64))))))
(fma.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 (fma.f64 x x eps) #s(literal -1 binary64)) (neg.f64 (*.f64 eps (/.f64 eps (fma.f64 x x eps)))))
(fma.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 (fma.f64 (fma.f64 x x eps) eps (pow.f64 x #s(literal 4 binary64))) #s(literal -1 binary64)) (neg.f64 (/.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 (fma.f64 x x eps) eps (pow.f64 x #s(literal 4 binary64))))))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (fma.f64 x x eps) eps (pow.f64 x #s(literal 4 binary64)))) (neg.f64 (/.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 (fma.f64 x x eps) eps (pow.f64 x #s(literal 4 binary64))))))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) (/.f64 x (fma.f64 x x eps)) (neg.f64 (*.f64 eps (/.f64 eps (fma.f64 x x eps)))))
(fma.f64 eps #s(literal -1 binary64) (*.f64 x x))
(fma.f64 (*.f64 x x) (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 (fma.f64 x x eps) eps (pow.f64 x #s(literal 4 binary64)))) (neg.f64 (/.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 (fma.f64 x x eps) eps (pow.f64 x #s(literal 4 binary64))))))
(fma.f64 (.f64 x x) (/.f64 (.f64 x x) (fma.f64 x x eps)) (neg.f64 (*.f64 eps (/.f64 eps (fma.f64 x x eps)))))
(fma.f64 x (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 x x eps)) (neg.f64 (*.f64 eps (/.f64 eps (fma.f64 x x eps)))))
(fma.f64 x x (neg.f64 eps))
(sqrt.f64 (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 2 binary64)))
(-.f64 (fma.f64 x x #s(literal 0 binary64)) eps)
(-.f64 #s(literal 0 binary64) (-.f64 eps (*.f64 x x)))
(-.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 x x eps)) (*.f64 eps (/.f64 eps (fma.f64 x x eps))))
(-.f64 (/.f64 (pow.f64 x #s(literal 6 binary64)) (fma.f64 (fma.f64 x x eps) eps (pow.f64 x #s(literal 4 binary64)))) (/.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 (fma.f64 x x eps) eps (pow.f64 x #s(literal 4 binary64)))))
(-.f64 (*.f64 x x) eps)
(fabs.f64 (-.f64 (*.f64 x x) eps))
(exp.f64 (.f64 (neg.f64 (log.f64 (-.f64 (.f64 x x) eps))) #s(literal -1 binary64)))
(exp.f64 (.f64 (log.f64 (neg.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)))) #s(literal 2 binary64)))
(exp.f64 (log.f64 (-.f64 (*.f64 x x) eps)))
(+.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 x x eps)) (neg.f64 (*.f64 eps (/.f64 eps (fma.f64 x x eps)))))
(+.f64 (/.f64 (pow.f64 x #s(literal 6 binary64)) (fma.f64 (fma.f64 x x eps) eps (pow.f64 x #s(literal 4 binary64)))) (neg.f64 (/.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 (fma.f64 x x eps) eps (pow.f64 x #s(literal 4 binary64))))))
(+.f64 (neg.f64 eps) (*.f64 x x))
(+.f64 (*.f64 x x) (neg.f64 eps))
(*.f64 x x)
(pow.f64 (exp.f64 #s(literal 2 binary64)) (log.f64 x))
(pow.f64 (*.f64 x x) #s(literal 1 binary64))
(pow.f64 x #s(literal 2 binary64))
(exp.f64 (.f64 (.f64 (log.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)))
(exp.f64 (*.f64 (log.f64 x) #s(literal 2 binary64)))

eval56.0ms (0.6%)

Memory: 28.5MiB live, 65.9MiB allocated
Compiler: Compiled 7 015 to 1 083 computations (84.6% saved)

prune34.0ms (0.4%)

Memory

-16.5MiB live, 21.6MiB allocated

Pruning

15 alts after pruning (14 fresh and 1 done)

	Pruned	Kept	Total
New	255	14	269
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	255	15	270

Accuracy

99.5%

Counts

270 → 15

Alt Table

Click to see full alt table

Status	Accuracy	Program
	46.8%	(fma.f64 (.f64 x x) (/.f64 x (fma.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x (fma.f64 x x (-.f64 (.f64 x x) eps)))) (neg.f64 (/.f64 (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 3/2 binary64)) (fma.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x (fma.f64 x x (-.f64 (.f64 x x) eps))))))
▶	60.9%	(fma.f64 (sqrt.f64 x) (sqrt.f64 x) (neg.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps))))
	60.7%	(fma.f64 x (/.f64 x (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x)) (neg.f64 (/.f64 (-.f64 (.f64 x x) eps) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))))
	60.8%	(/.f64 (-.f64 (fma.f64 x x eps) (.f64 x x)) (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x))
	60.8%	(/.f64 (-.f64 (-.f64 (.f64 x x) eps) (.f64 x x)) (-.f64 (neg.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps))) x))
▶	61.1%	(/.f64 #s(literal 1 binary64) (pow.f64 (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) #s(literal -1 binary64)))
	60.6%	(-.f64 x (/.f64 (-.f64 (.f64 x x) eps) (sqrt.f64 (-.f64 (.f64 x x) eps))))
✓	61.2%	(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
	56.3%	(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))))
▶	7.6%	(-.f64 x #s(approx (sqrt (- (* x x) eps)) (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) x)))
▶	3.5%	(-.f64 x #s(approx (sqrt (- (* x x) eps)) (neg.f64 x)))
	23.8%	#s(approx (- x (sqrt (- (* x x) eps))) (/.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 (.f64 (/.f64 eps x) #s(literal 1/8 binary64)) (/.f64 eps x) (.f64 (pow.f64 eps #s(literal 3 binary64)) (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 4 binary64)))))) x))
	28.7%	#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (fma.f64 (fma.f64 (/.f64 eps (pow.f64 x #s(literal 5 binary64))) #s(literal 1/16 binary64) (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64)))) eps (/.f64 #s(literal 1/2 binary64) x)) eps))
▶	40.4%	#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (fma.f64 (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64))) eps (/.f64 #s(literal 1/2 binary64) x)) eps))
	45.1%	#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (/.f64 #s(literal 1/2 binary64) x) eps))

Compiler

Compiled 586 to 334 computations (43% saved)

simplify109.0ms (1.2%)

Memory

8.0MiB live, 46.4MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 19 expressions of interest:

New	Metric	Score
cost-diff	0	(/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64)))
cost-diff	0	(fma.f64 (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64))) eps (/.f64 #s(literal 1/2 binary64) x))
cost-diff	0	(*.f64 (fma.f64 (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64))) eps (/.f64 #s(literal 1/2 binary64) x)) eps)
cost-diff	0	#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (fma.f64 (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64))) eps (/.f64 #s(literal 1/2 binary64) x)) eps))
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	(/.f64 eps x)
cost-diff	0	(fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) x)
cost-diff	0	#s(approx (sqrt (- (* x x) eps)) (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) x))
cost-diff	0	(-.f64 x #s(approx (sqrt (- (* x x) eps)) (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) x)))
cost-diff	0	(neg.f64 x)
cost-diff	0	#s(approx (sqrt (- (* x x) eps)) (neg.f64 x))
cost-diff	0	(-.f64 x #s(approx (sqrt (- (* x x) eps)) (neg.f64 x)))
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	(pow.f64 (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) #s(literal -1 binary64))
cost-diff	7168	(/.f64 #s(literal 1 binary64) (pow.f64 (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) #s(literal -1 binary64)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	34	207
0	58	199
1	84	199
2	157	199
3	335	199
4	759	199
5	1515	199
6	1923	199
7	4385	199
8	7293	199
0	8050	199

Stop Event

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

Calls

Call 1

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

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

localize149.0ms (1.7%)

Memory

1.8MiB live, 159.5MiB allocated

Localize:

Found 19 expressions of interest:

New	Metric	Score
accuracy	0.09765625	(/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64)))
accuracy	7.8454875885979565	(*.f64 (fma.f64 (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64))) eps (/.f64 #s(literal 1/2 binary64) x)) eps)
accuracy	8.02420380341758	(fma.f64 (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64))) eps (/.f64 #s(literal 1/2 binary64) x))
accuracy	35.978824811219866	#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (fma.f64 (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64))) eps (/.f64 #s(literal 1/2 binary64) x)) eps))
accuracy	0.0	(neg.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)))
accuracy	0.01171875	(-.f64 (*.f64 x x) eps)
accuracy	0.01171875	(sqrt.f64 (-.f64 (*.f64 x x) eps))
accuracy	24.96949242837854	(fma.f64 (sqrt.f64 x) (sqrt.f64 x) (neg.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps))))
accuracy	0.0	(/.f64 eps x)
accuracy	0.0078125	(fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) x)
accuracy	24.83594137359021	(-.f64 x #s(approx (sqrt (- (* x x) eps)) (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) x)))
accuracy	34.24342411992151	#s(approx (sqrt (- (* x x) eps)) (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) x))
accuracy	0.0	(neg.f64 x)
accuracy	24.83594137359021	(-.f64 x #s(approx (sqrt (- (* x x) eps)) (neg.f64 x)))
accuracy	62.396341972704136	#s(approx (sqrt (- (* x x) eps)) (neg.f64 x))
accuracy	0.01171875	(sqrt.f64 (-.f64 (*.f64 x x) eps))
accuracy	0.28125	(/.f64 #s(literal 1 binary64) (pow.f64 (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) #s(literal -1 binary64)))
accuracy	0.296875	(pow.f64 (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) #s(literal -1 binary64))
accuracy	24.83594137359021	(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))

Samples

50.0ms	151×	0	valid
35.0ms	90×	1	valid
8.0ms	15×	2	valid

Compiler

Compiled 387 to 64 computations (83.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 69.0ms

ival-mult: 25.0ms (36.1% of total)

ival-pow: 12.0ms (17.3% of total)

ival-div: 8.0ms (11.6% of total)

adjust: 6.0ms (8.7% of total)

ival-sqrt: 6.0ms (8.7% of total)

ival-add: 5.0ms (7.2% of total)

ival-sub: 4.0ms (5.8% of total)

ival-neg: 3.0ms (4.3% of total)

exact: 1.0ms (1.4% of total)

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

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

series48.0ms (0.5%)

Memory

1.1MiB live, 50.7MiB allocated

Counts

19 → 114

Calls

Call 1

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

Outputs
(* -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 (* (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))))))
(* (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)))))))))
(* -1 x)
(* -1/2 (/ eps x))
(/ (+ (* -1/2 eps) (pow x 2)) x)
(/ eps x)
(sqrt x)
(- (* -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)))
(* 1/8 (/ (pow eps 2) (pow x 3)))
(/ (+ (* 1/8 (pow eps 2)) (* 1/2 (* eps (pow x 2)))) (pow x 3))
(* 1/8 (/ eps (pow x 3)))
(/ (+ (* 1/8 eps) (* 1/2 (pow x 2))) (pow x 3))
(/ 1/8 (pow x 3))
(* -1 eps)
(- (pow x 2) 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)
(/ (- (* 1/2 (/ (+ (* 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 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)))))))
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)))))))
(* 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)))))))
(/ (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps)) x)
(/ 1/2 x)
(/ (+ 1/2 (* 1/8 (/ eps (pow x 2)))) x)
(pow x 2)
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))
(* 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 (- (+ (* 1/16 (/ (pow eps 3) (pow x 6))) (+ (* 1/8 (/ (pow eps 2) (pow x 4))) (* 1/2 (/ eps (pow x 2))))) 2)))
(* -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))
(* -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 (* 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))))))))
(* -1 (* x (- (* 1/2 (/ eps (pow x 2))) 1)))
(* -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 (* (sqrt x) (pow (sqrt -1) 2)))
(* -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 (/ (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2)))) 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))))
(/ (+ (* -1/2 (/ 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)
(+ 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)))))
(- (* 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)
(+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))
(+ (* -1 eps) (pow x 2))
(* 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)))))
(/ (+ (* -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)
(* 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))))))
(* eps (- (/ x eps) (* 1/2 (/ 1 x))))
(* 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))))))
(* (pow eps 2) (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))))
(* eps (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))))
(* eps (- (/ (pow x 2) eps) 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 (/ 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 (* 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 (+ (* -1 (/ x eps)) (* 1/2 (/ 1 x)))))
(* -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)))))))
(* eps (+ (* 1/8 (/ 1 (pow x 3))) (* 1/2 (/ 1 (* eps x)))))
(* -1 (* eps (+ 1 (* -1 (/ (pow x 2) eps)))))

Calls

6 calls:

Time	Variable		Point	Expression
26.0ms	x	@	inf	((/ 1 (pow (- x (sqrt (- (* x x) eps))) -1)) (pow (- x (sqrt (- (* x x) eps))) -1) (- x (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps)) (- x (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps)) (neg x) (- x (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps)) (+ (* (/ eps x) -1/2) x) (/ eps x) (+ (* (sqrt x) (sqrt x)) (neg (sqrt (- (* x x) eps)))) (sqrt x) (neg (sqrt (- (* x x) eps))) (- x (sqrt (- (* x x) eps))) (* (+ (* (/ 1/8 (pow x 3)) eps) (/ 1/2 x)) eps) (+ (* (/ 1/8 (pow x 3)) eps) (/ 1/2 x)) (/ 1/8 (pow x 3)) (- (* x x) eps))
6.0ms	eps	@	inf	((/ 1 (pow (- x (sqrt (- (* x x) eps))) -1)) (pow (- x (sqrt (- (* x x) eps))) -1) (- x (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps)) (- x (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps)) (neg x) (- x (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps)) (+ (* (/ eps x) -1/2) x) (/ eps x) (+ (* (sqrt x) (sqrt x)) (neg (sqrt (- (* x x) eps)))) (sqrt x) (neg (sqrt (- (* x x) eps))) (- x (sqrt (- (* x x) eps))) (* (+ (* (/ 1/8 (pow x 3)) eps) (/ 1/2 x)) eps) (+ (* (/ 1/8 (pow x 3)) eps) (/ 1/2 x)) (/ 1/8 (pow x 3)) (- (* x x) eps))
4.0ms	eps	@	-inf	((/ 1 (pow (- x (sqrt (- (* x x) eps))) -1)) (pow (- x (sqrt (- (* x x) eps))) -1) (- x (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps)) (- x (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps)) (neg x) (- x (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps)) (+ (* (/ eps x) -1/2) x) (/ eps x) (+ (* (sqrt x) (sqrt x)) (neg (sqrt (- (* x x) eps)))) (sqrt x) (neg (sqrt (- (* x x) eps))) (- x (sqrt (- (* x x) eps))) (* (+ (* (/ 1/8 (pow x 3)) eps) (/ 1/2 x)) eps) (+ (* (/ 1/8 (pow x 3)) eps) (/ 1/2 x)) (/ 1/8 (pow x 3)) (- (* x x) eps))
4.0ms	x	@	-inf	((/ 1 (pow (- x (sqrt (- (* x x) eps))) -1)) (pow (- x (sqrt (- (* x x) eps))) -1) (- x (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps)) (- x (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps)) (neg x) (- x (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps)) (+ (* (/ eps x) -1/2) x) (/ eps x) (+ (* (sqrt x) (sqrt x)) (neg (sqrt (- (* x x) eps)))) (sqrt x) (neg (sqrt (- (* x x) eps))) (- x (sqrt (- (* x x) eps))) (* (+ (* (/ 1/8 (pow x 3)) eps) (/ 1/2 x)) eps) (+ (* (/ 1/8 (pow x 3)) eps) (/ 1/2 x)) (/ 1/8 (pow x 3)) (- (* x x) eps))
4.0ms	x	@	0	((/ 1 (pow (- x (sqrt (- (* x x) eps))) -1)) (pow (- x (sqrt (- (* x x) eps))) -1) (- x (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps)) (- x (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps)) (neg x) (- x (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps)) (+ (* (/ eps x) -1/2) x) (/ eps x) (+ (* (sqrt x) (sqrt x)) (neg (sqrt (- (* x x) eps)))) (sqrt x) (neg (sqrt (- (* x x) eps))) (- x (sqrt (- (* x x) eps))) (* (+ (* (/ 1/8 (pow x 3)) eps) (/ 1/2 x)) eps) (+ (* (/ 1/8 (pow x 3)) eps) (/ 1/2 x)) (/ 1/8 (pow x 3)) (- (* x x) eps))

simplify161.0ms (1.8%)

Memory

-3.0MiB live, 266.5MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	508	2547
1	1559	2433
2	5439	2399
0	8389	2273

Stop Event

1×	iter limit
1×	node limit

Counts

114 → 113

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 (* (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))))))
(* (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)))))))))
(* -1 x)
(* -1/2 (/ eps x))
(/ (+ (* -1/2 eps) (pow x 2)) x)
(/ eps x)
(sqrt x)
(- (* -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)))
(* 1/8 (/ (pow eps 2) (pow x 3)))
(/ (+ (* 1/8 (pow eps 2)) (* 1/2 (* eps (pow x 2)))) (pow x 3))
(* 1/8 (/ eps (pow x 3)))
(/ (+ (* 1/8 eps) (* 1/2 (pow x 2))) (pow x 3))
(/ 1/8 (pow x 3))
(* -1 eps)
(- (pow x 2) 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)
(/ (- (* 1/2 (/ (+ (* 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 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)))))))
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)))))))
(* 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)))))))
(/ (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps)) x)
(/ 1/2 x)
(/ (+ 1/2 (* 1/8 (/ eps (pow x 2)))) x)
(pow x 2)
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))
(* 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 (- (+ (* 1/16 (/ (pow eps 3) (pow x 6))) (+ (* 1/8 (/ (pow eps 2) (pow x 4))) (* 1/2 (/ eps (pow x 2))))) 2)))
(* -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))
(* -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 (* 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))))))))
(* -1 (* x (- (* 1/2 (/ eps (pow x 2))) 1)))
(* -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 (* (sqrt x) (pow (sqrt -1) 2)))
(* -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 (/ (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2)))) 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))))
(/ (+ (* -1/2 (/ 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)
(+ 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)))))
(- (* 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)
(+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))
(+ (* -1 eps) (pow x 2))
(* 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)))))
(/ (+ (* -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)
(* 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))))))
(* eps (- (/ x eps) (* 1/2 (/ 1 x))))
(* 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))))))
(* (pow eps 2) (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))))
(* eps (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))))
(* eps (- (/ (pow x 2) eps) 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 (/ 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 (* 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 (+ (* -1 (/ x eps)) (* 1/2 (/ 1 x)))))
(* -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)))))))
(* eps (+ (* 1/8 (/ 1 (pow x 3))) (* 1/2 (/ 1 (* eps x)))))
(* -1 (* eps (+ 1 (* -1 (/ (pow x 2) eps)))))

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

rewrite240.0ms (2.7%)

Memory

14.2MiB live, 254.5MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	34	169
0	58	161
1	204	161
2	1476	161
0	8267	161

Stop Event

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

Counts

19 → 812

Calls

Call 1

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

Outputs
(.f64 (pow.f64 (pow.f64 (-.f64 (.f64 x x) (-.f64 (.f64 x x) eps)) #s(literal -1 binary64)) #s(literal -1 binary64)) (pow.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) #s(literal -1 binary64)))
(.f64 (pow.f64 (pow.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 3/2 binary64))) #s(literal -1 binary64)) #s(literal -1 binary64)) (pow.f64 (fma.f64 x x (fma.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x (-.f64 (.f64 x x) eps))) #s(literal -1 binary64)))
(.f64 (pow.f64 (pow.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 3/2 binary64))) #s(literal -1 binary64)) #s(literal -1 binary64)) (pow.f64 (-.f64 (fma.f64 x x (-.f64 (.f64 x x) eps)) (.f64 (neg.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps))) x)) #s(literal -1 binary64)))
(.f64 (pow.f64 (sqrt.f64 (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps)))) #s(literal 1 binary64)) (pow.f64 (sqrt.f64 (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))) #s(literal 1 binary64)))
(.f64 (pow.f64 (-.f64 (.f64 x x) (-.f64 (.f64 x x) eps)) #s(literal 1 binary64)) (pow.f64 (pow.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) #s(literal -1 binary64)) #s(literal 1 binary64)))
(.f64 (pow.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 3/2 binary64))) #s(literal 1 binary64)) (pow.f64 (pow.f64 (fma.f64 x x (fma.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x (-.f64 (.f64 x x) eps))) #s(literal -1 binary64)) #s(literal 1 binary64)))
(.f64 (pow.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 3/2 binary64))) #s(literal 1 binary64)) (pow.f64 (pow.f64 (-.f64 (fma.f64 x x (-.f64 (.f64 x x) eps)) (.f64 (neg.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps))) x)) #s(literal -1 binary64)) #s(literal 1 binary64)))
(.f64 (sqrt.f64 (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps)))) (pow.f64 (/.f64 (pow.f64 (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) #s(literal -1/2 binary64)) #s(literal 1 binary64)) #s(literal -1 binary64)))
(.f64 (sqrt.f64 (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps)))) (sqrt.f64 (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))))
(.f64 (-.f64 (.f64 x x) (-.f64 (.f64 x x) eps)) (pow.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) #s(literal -1 binary64)))
(.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 3/2 binary64))) (pow.f64 (fma.f64 x x (fma.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x (-.f64 (.f64 x x) eps))) #s(literal -1 binary64)))
(.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 3/2 binary64))) (pow.f64 (-.f64 (fma.f64 x x (-.f64 (.f64 x x) eps)) (.f64 (neg.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps))) x)) #s(literal -1 binary64)))
(.f64 #s(literal -1 binary64) (pow.f64 (pow.f64 (/.f64 #s(literal -1 binary64) (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps)))) #s(literal -1 binary64)) #s(literal 1 binary64)))
(.f64 #s(literal -1 binary64) (pow.f64 (/.f64 #s(literal -1 binary64) (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps)))) #s(literal -1 binary64)))
(.f64 (-.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))))
(pow.f64 (.f64 (pow.f64 (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) #s(literal -1 binary64)) (pow.f64 (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) #s(literal -1 binary64))) #s(literal -1/2 binary64))
(pow.f64 (/.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) (-.f64 (.f64 x x) (-.f64 (*.f64 x x) eps))) #s(literal -1 binary64))
(pow.f64 (/.f64 (fma.f64 x x (fma.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x (-.f64 (.f64 x x) eps))) (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 3/2 binary64)))) #s(literal -1 binary64))
(pow.f64 (/.f64 (-.f64 (fma.f64 x x (-.f64 (.f64 x x) eps)) (.f64 (neg.f64 (sqrt.f64 (-.f64 (.f64 x x) eps))) x)) (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 3/2 binary64)))) #s(literal -1 binary64))
(pow.f64 (neg.f64 (/.f64 #s(literal -1 binary64) (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))) #s(literal -1 binary64))
(pow.f64 (pow.f64 (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) #s(literal 2 binary64)) #s(literal 1/2 binary64))
(pow.f64 (sqrt.f64 (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))) #s(literal 2 binary64))
(pow.f64 (pow.f64 (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) #s(literal -1/2 binary64)) #s(literal -2 binary64))
(pow.f64 (pow.f64 (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) #s(literal -1 binary64)) #s(literal -1 binary64))
(pow.f64 (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) #s(literal 1 binary64))
(/.f64 (neg.f64 (sqrt.f64 (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))))) (neg.f64 (pow.f64 (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) #s(literal -1/2 binary64))))
(/.f64 (neg.f64 (-.f64 (-.f64 (.f64 x x) eps) (.f64 x x))) (neg.f64 (-.f64 (neg.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps))) x)))
(/.f64 (neg.f64 (neg.f64 (-.f64 (.f64 x x) (-.f64 (.f64 x x) eps)))) (neg.f64 (neg.f64 (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))))
(/.f64 (neg.f64 (neg.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 3/2 binary64))))) (neg.f64 (neg.f64 (fma.f64 x x (fma.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x (-.f64 (*.f64 x x) eps))))))
(/.f64 (neg.f64 (neg.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 3/2 binary64))))) (neg.f64 (neg.f64 (-.f64 (fma.f64 x x (-.f64 (.f64 x x) eps)) (.f64 (neg.f64 (sqrt.f64 (-.f64 (.f64 x x) eps))) x)))))
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(pow.f64 (exp.f64 (log.f64 (/.f64 #s(literal 1/2 binary64) x))) #s(literal 3 binary64))
(pow.f64 (pow.f64 (*.f64 x #s(literal 2 binary64)) #s(literal -3/2 binary64)) #s(literal 2 binary64))
(pow.f64 (/.f64 (*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 8 binary64)) #s(literal 1 binary64)) #s(literal -1 binary64))
(pow.f64 (*.f64 x #s(literal 2 binary64)) #s(literal -3 binary64))
(pow.f64 (*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 8 binary64)) #s(literal -1 binary64))
(pow.f64 (pow.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 2 binary64)) #s(literal 3/2 binary64))
(pow.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 3 binary64))
(/.f64 (neg.f64 (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3/2 binary64)))) (neg.f64 (pow.f64 x #s(literal 3/2 binary64))))
(/.f64 (neg.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 x x))) (neg.f64 x))
(/.f64 (neg.f64 (/.f64 #s(literal 1/8 binary64) x)) (neg.f64 (*.f64 x x)))
(/.f64 (pow.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) #s(literal 3 binary64)) (pow.f64 x #s(literal 3/2 binary64)))
(/.f64 (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3/2 binary64))) (pow.f64 x #s(literal 3/2 binary64)))
(/.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) x)
(/.f64 (/.f64 #s(literal 1/8 binary64) x) (*.f64 x x))
(/.f64 #s(literal -1/8 binary64) (neg.f64 (neg.f64 (pow.f64 (neg.f64 x) #s(literal 3 binary64)))))
(/.f64 #s(literal -1/8 binary64) (pow.f64 (neg.f64 x) #s(literal 3 binary64)))
(/.f64 #s(literal 1/8 binary64) (pow.f64 (neg.f64 (neg.f64 x)) #s(literal 3 binary64)))
(/.f64 #s(literal 1/8 binary64) (neg.f64 (pow.f64 (neg.f64 x) #s(literal 3 binary64))))
(/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64)))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 8 binary64)) #s(literal 1 binary64))))
(/.f64 #s(literal -1 binary64) (pow.f64 (neg.f64 (*.f64 x #s(literal 2 binary64))) #s(literal 3 binary64)))
(/.f64 #s(literal -1 binary64) (neg.f64 (*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 8 binary64))))
(/.f64 #s(literal 1 binary64) (neg.f64 (neg.f64 (*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 8 binary64)))))
(/.f64 #s(literal 1 binary64) (pow.f64 (/.f64 (*.f64 x #s(literal 2 binary64)) #s(literal 1 binary64)) #s(literal 3 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 8 binary64)) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 8 binary64)))
(neg.f64 (pow.f64 (/.f64 #s(literal -1/2 binary64) x) #s(literal 3 binary64)))
(neg.f64 (/.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal 3 binary64))))
(exp.f64 (.f64 (log.f64 (.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 8 binary64))) #s(literal -1 binary64)))
(exp.f64 (*.f64 (log.f64 (/.f64 #s(literal 1/2 binary64) x)) #s(literal 3 binary64)))
(.f64 (pow.f64 (.f64 (neg.f64 (sqrt.f64 (-.f64 (.f64 x x) eps))) #s(literal -1 binary64)) #s(literal 1 binary64)) (sqrt.f64 (-.f64 (.f64 x x) eps)))
(.f64 (pow.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (.f64 eps eps)) #s(literal 1 binary64)) (pow.f64 (pow.f64 (fma.f64 x x eps) #s(literal -1 binary64)) #s(literal 1 binary64)))
(*.f64 (pow.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 eps #s(literal 3 binary64))) #s(literal 1 binary64)) (pow.f64 (pow.f64 (fma.f64 eps (fma.f64 x x eps) (pow.f64 x #s(literal 4 binary64))) #s(literal -1 binary64)) #s(literal 1 binary64)))
(.f64 (.f64 (neg.f64 (sqrt.f64 (-.f64 (.f64 x x) eps))) #s(literal -1 binary64)) (sqrt.f64 (-.f64 (.f64 x x) eps)))
(.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (.f64 eps eps)) (pow.f64 (fma.f64 x x eps) #s(literal -1 binary64)))
(*.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 eps #s(literal 3 binary64))) (pow.f64 (fma.f64 eps (fma.f64 x x eps) (pow.f64 x #s(literal 4 binary64))) #s(literal -1 binary64)))
(.f64 (neg.f64 (sqrt.f64 (-.f64 (.f64 x x) eps))) (neg.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps))))
(.f64 #s(literal -1 binary64) (pow.f64 (.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) (neg.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)))) #s(literal 1 binary64)))
(.f64 #s(literal -1 binary64) (.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) (neg.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)))))
(.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) (sqrt.f64 (-.f64 (*.f64 x x) eps)))
(.f64 (-.f64 (.f64 x x) eps) #s(literal 1 binary64))
(.f64 #s(literal 1 binary64) (-.f64 (.f64 x x) eps))
(pow.f64 (/.f64 (fma.f64 x x eps) (-.f64 (pow.f64 x #s(literal 4 binary64)) (*.f64 eps eps))) #s(literal -1 binary64))
(pow.f64 (/.f64 (fma.f64 eps (fma.f64 x x eps) (pow.f64 x #s(literal 4 binary64))) (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 eps #s(literal 3 binary64)))) #s(literal -1 binary64))
(pow.f64 (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 2 binary64)) #s(literal 1/2 binary64))
(pow.f64 (neg.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps))) #s(literal 2 binary64))
(pow.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) #s(literal 2 binary64))
(pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1 binary64))
(/.f64 (fma.f64 #s(literal -1 binary64) (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64))) (fma.f64 eps eps (-.f64 (pow.f64 x #s(literal 4 binary64)) (.f64 (neg.f64 eps) (.f64 x x)))))
(/.f64 (neg.f64 (neg.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (*.f64 eps eps)))) (neg.f64 (neg.f64 (fma.f64 x x eps))))
(/.f64 (neg.f64 (neg.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 eps #s(literal 3 binary64))))) (neg.f64 (neg.f64 (fma.f64 eps (fma.f64 x x eps) (pow.f64 x #s(literal 4 binary64))))))
(/.f64 (-.f64 (.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 x x eps)) (.f64 (fma.f64 x x eps) (.f64 eps eps))) (.f64 (fma.f64 x x eps) (fma.f64 x x eps)))
(/.f64 (-.f64 (.f64 (pow.f64 x #s(literal 6 binary64)) (fma.f64 eps (fma.f64 x x eps) (pow.f64 x #s(literal 4 binary64)))) (.f64 (fma.f64 eps (fma.f64 x x eps) (pow.f64 x #s(literal 4 binary64))) (pow.f64 eps #s(literal 3 binary64)))) (*.f64 (fma.f64 eps (fma.f64 x x eps) (pow.f64 x #s(literal 4 binary64))) (fma.f64 eps (fma.f64 x x eps) (pow.f64 x #s(literal 4 binary64)))))
(/.f64 (neg.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (.f64 eps eps))) (neg.f64 (-.f64 (.f64 x x) (neg.f64 eps))))
(/.f64 (neg.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (*.f64 eps eps))) (neg.f64 (fma.f64 x x eps)))
(/.f64 (neg.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 eps #s(literal 3 binary64)))) (neg.f64 (+.f64 (pow.f64 x #s(literal 4 binary64)) (-.f64 (.f64 eps eps) (.f64 (*.f64 x x) (neg.f64 eps))))))
(/.f64 (neg.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 eps #s(literal 3 binary64)))) (neg.f64 (fma.f64 eps (fma.f64 x x eps) (pow.f64 x #s(literal 4 binary64)))))
(/.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (.f64 eps eps)) (-.f64 (.f64 x x) (neg.f64 eps)))
(/.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (*.f64 eps eps)) (fma.f64 x x eps))
(/.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 eps #s(literal 3 binary64))) (+.f64 (pow.f64 x #s(literal 4 binary64)) (-.f64 (.f64 eps eps) (.f64 (*.f64 x x) (neg.f64 eps)))))
(/.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 eps #s(literal 3 binary64))) (fma.f64 eps (fma.f64 x x eps) (pow.f64 x #s(literal 4 binary64))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (fma.f64 x x eps) (-.f64 (pow.f64 x #s(literal 4 binary64)) (*.f64 eps eps)))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (fma.f64 eps (fma.f64 x x eps) (pow.f64 x #s(literal 4 binary64))) (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 eps #s(literal 3 binary64))))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 x x eps) (-.f64 (pow.f64 x #s(literal 4 binary64)) (*.f64 eps eps))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 eps (fma.f64 x x eps) (pow.f64 x #s(literal 4 binary64))) (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 eps #s(literal 3 binary64)))))
(neg.f64 (.f64 (neg.f64 (sqrt.f64 (-.f64 (.f64 x x) eps))) (sqrt.f64 (-.f64 (*.f64 x x) eps))))
(neg.f64 (.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) (neg.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)))))
(fma.f64 (pow.f64 (pow.f64 x #s(literal 1/4 binary64)) #s(literal 4 binary64)) (pow.f64 (pow.f64 x #s(literal 1/4 binary64)) #s(literal 4 binary64)) (neg.f64 eps))
(fma.f64 (pow.f64 x #s(literal 3/2 binary64)) (sqrt.f64 x) (neg.f64 eps))
(fma.f64 (sqrt.f64 x) (pow.f64 x #s(literal 3/2 binary64)) (neg.f64 eps))
(fma.f64 (neg.f64 x) (neg.f64 x) (neg.f64 eps))
(fma.f64 #s(literal -1 binary64) eps (*.f64 x x))
(fma.f64 x x (neg.f64 eps))
(sqrt.f64 (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 2 binary64)))
(-.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (-.f64 (.f64 x x) (neg.f64 eps))) (/.f64 (.f64 eps eps) (-.f64 (*.f64 x x) (neg.f64 eps))))
(-.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 x x eps)) (/.f64 (*.f64 eps eps) (fma.f64 x x eps)))
(-.f64 (/.f64 (pow.f64 x #s(literal 6 binary64)) (fma.f64 eps (fma.f64 x x eps) (pow.f64 x #s(literal 4 binary64)))) (/.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 eps (fma.f64 x x eps) (pow.f64 x #s(literal 4 binary64)))))
(-.f64 (*.f64 x x) eps)
(fabs.f64 (-.f64 (*.f64 x x) eps))
(exp.f64 (.f64 (log.f64 (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 2 binary64))) #s(literal 1/2 binary64)))
(exp.f64 (.f64 (log.f64 (neg.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)))) #s(literal 2 binary64)))
(exp.f64 (.f64 (log.f64 (sqrt.f64 (-.f64 (.f64 x x) eps))) #s(literal 2 binary64)))
(exp.f64 (.f64 (log.f64 (-.f64 (.f64 x x) eps)) #s(literal 1 binary64)))
(exp.f64 (log.f64 (-.f64 (*.f64 x x) eps)))
(+.f64 (neg.f64 eps) (*.f64 x x))
(+.f64 (*.f64 x x) (neg.f64 eps))

eval173.0ms (1.9%)

Memory: -17.6MiB live, 249.5MiB allocated
Compiler: Compiled 25 217 to 3 608 computations (85.7% saved)

prune22.0ms (0.2%)

Memory

30.7MiB live, 68.4MiB allocated

Pruning

13 alts after pruning (10 fresh and 3 done)

	Pruned	Kept	Total
New	889	8	897
Fresh	7	2	9
Picked	3	2	5
Done	0	1	1
Total	899	13	912

Accuracy

100.0%

Counts

912 → 13

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	61.1%	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))))
	45.1%	(/.f64 #s(literal 1 binary64) #s(approx (pow (- x (sqrt (- (* x x) eps))) -1) (/.f64 (fma.f64 #s(literal 2 binary64) x (*.f64 (/.f64 (fma.f64 (/.f64 (/.f64 eps x) x) #s(literal -1/8 binary64) #s(literal -1/2 binary64)) x) eps)) eps)))
▶	46.3%	(/.f64 #s(literal 1 binary64) #s(approx (pow (- x (sqrt (- (* x x) eps))) -1) (/.f64 (fma.f64 #s(literal 2 binary64) x (*.f64 (/.f64 eps x) #s(literal -1/2 binary64))) eps)))
▶	45.1%	(/.f64 #s(literal 1 binary64) #s(approx (pow (- x (sqrt (- (* x x) eps))) -1) (*.f64 (/.f64 x eps) #s(literal 2 binary64))))
	45.9%	(/.f64 #s(literal 1 binary64) #s(approx (pow (- x (sqrt (- (* x x) eps))) -1) (.f64 (-.f64 (/.f64 #s(literal 2 binary64) eps) (/.f64 #s(literal 1/2 binary64) (.f64 x x))) x)))
	60.6%	(-.f64 x (/.f64 (-.f64 (.f64 x x) eps) (sqrt.f64 (-.f64 (.f64 x x) eps))))
✓	61.2%	(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
▶	56.3%	(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))))
✓	7.6%	(-.f64 x #s(approx (sqrt (- (* x x) eps)) (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) x)))
✓	3.5%	(-.f64 x #s(approx (sqrt (- (* x x) eps)) (neg.f64 x)))
	33.2%	#s(approx (/ 1 (pow (- x (sqrt (- (* x x) eps))) -1)) (/.f64 (fma.f64 (/.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 4 binary64))) #s(literal 1/16 binary64) (-.f64 (.f64 #s(literal 1/2 binary64) eps) (.f64 (/.f64 #s(literal -1/8 binary64) x) (/.f64 (*.f64 eps eps) x)))) x))
	45.1%	#s(approx (/ 1 (pow (- x (sqrt (- (* x x) eps))) -1)) (*.f64 (/.f64 #s(literal 1/2 binary64) x) eps))
▶	44.1%	#s(approx (- x (sqrt (- (* x x) eps))) #s(approx (* (+ (* (/ 1/8 (pow x 3)) eps) (/ 1/2 x)) eps) (/.f64 (fma.f64 (/.f64 #s(literal -1/8 binary64) x) (/.f64 (.f64 eps eps) x) (.f64 #s(literal -1/2 binary64) eps)) (neg.f64 x))))

Compiler

Compiled 484 to 346 computations (28.5% saved)

simplify290.0ms (3.3%)

Memory

5.4MiB live, 124.9MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score
cost-diff	0	#s(approx (* (+ (* (/ 1/8 (pow x 3)) eps) (/ 1/2 x)) eps) (/.f64 (fma.f64 (/.f64 #s(literal -1/8 binary64) x) (/.f64 (.f64 eps eps) x) (.f64 #s(literal -1/2 binary64) eps)) (neg.f64 x)))
cost-diff	0	#s(approx (- x (sqrt (- (* x x) eps))) #s(approx (* (+ (* (/ 1/8 (pow x 3)) eps) (/ 1/2 x)) eps) (/.f64 (fma.f64 (/.f64 #s(literal -1/8 binary64) x) (/.f64 (.f64 eps eps) x) (.f64 #s(literal -1/2 binary64) eps)) (neg.f64 x))))
cost-diff	128	(/.f64 (fma.f64 (/.f64 #s(literal -1/8 binary64) x) (/.f64 (.f64 eps eps) x) (.f64 #s(literal -1/2 binary64) eps)) (neg.f64 x))
cost-diff	320	(fma.f64 (/.f64 #s(literal -1/8 binary64) x) (/.f64 (.f64 eps eps) x) (.f64 #s(literal -1/2 binary64) eps))
cost-diff	0	(fma.f64 #s(literal 2 binary64) x (*.f64 (/.f64 eps x) #s(literal -1/2 binary64)))
cost-diff	0	#s(approx (pow (- x (sqrt (- (* x x) eps))) -1) (/.f64 (fma.f64 #s(literal 2 binary64) x (*.f64 (/.f64 eps x) #s(literal -1/2 binary64))) eps))
cost-diff	0	(/.f64 #s(literal 1 binary64) #s(approx (pow (- x (sqrt (- (* x x) eps))) -1) (/.f64 (fma.f64 #s(literal 2 binary64) x (*.f64 (/.f64 eps x) #s(literal -1/2 binary64))) eps)))
cost-diff	320	(/.f64 (fma.f64 #s(literal 2 binary64) x (*.f64 (/.f64 eps x) #s(literal -1/2 binary64))) eps)
cost-diff	0	(/.f64 x eps)
cost-diff	0	(*.f64 (/.f64 x eps) #s(literal 2 binary64))
cost-diff	0	#s(approx (pow (- x (sqrt (- (* x x) eps))) -1) (*.f64 (/.f64 x eps) #s(literal 2 binary64)))
cost-diff	0	(/.f64 #s(literal 1 binary64) #s(approx (pow (- x (sqrt (- (* x x) eps))) -1) (*.f64 (/.f64 x eps) #s(literal 2 binary64))))
cost-diff	0	(neg.f64 eps)
cost-diff	0	#s(approx (- (* x x) eps) (neg.f64 eps))
cost-diff	0	(sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps)))
cost-diff	0	(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))))
cost-diff	0	(-.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	7168	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	50	314
0	78	310
1	118	310
2	189	306
3	313	306
4	638	303
5	1201	303
6	2062	303
7	3537	303
8	4897	303
9	5421	303
10	5603	303
11	5730	303
12	5831	303
13	5849	303
14	6166	303
15	6370	303
16	6396	303
17	6404	303
18	6404	303
19	6404	303
20	6557	300
21	6803	300
22	7555	300
0	8045	291

Stop Event

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

Calls

Call 1

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

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

localize173.0ms (1.9%)

Memory

-19.7MiB live, 354.9MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0.12109375	(/.f64 (fma.f64 (/.f64 #s(literal -1/8 binary64) x) (/.f64 (.f64 eps eps) x) (.f64 #s(literal -1/2 binary64) eps)) (neg.f64 x))
accuracy	3.53239878457418	(fma.f64 (/.f64 #s(literal -1/8 binary64) x) (/.f64 (.f64 eps eps) x) (.f64 #s(literal -1/2 binary64) eps))
accuracy	12.52495948577733	(/.f64 (*.f64 eps eps) x)
accuracy	35.978824811219866	#s(approx (- x (sqrt (- (* x x) eps))) #s(approx (* (+ (* (/ 1/8 (pow x 3)) eps) (/ 1/2 x)) eps) (/.f64 (fma.f64 (/.f64 #s(literal -1/8 binary64) x) (/.f64 (.f64 eps eps) x) (.f64 #s(literal -1/2 binary64) eps)) (neg.f64 x))))
accuracy	0.0	(*.f64 (/.f64 eps x) #s(literal -1/2 binary64))
accuracy	0.16796875	(/.f64 (fma.f64 #s(literal 2 binary64) x (*.f64 (/.f64 eps x) #s(literal -1/2 binary64))) eps)
accuracy	0.28125	(/.f64 #s(literal 1 binary64) #s(approx (pow (- x (sqrt (- (* x x) eps))) -1) (/.f64 (fma.f64 #s(literal 2 binary64) x (*.f64 (/.f64 eps x) #s(literal -1/2 binary64))) eps)))
accuracy	34.22060995420228	#s(approx (pow (- x (sqrt (- (* x x) eps))) -1) (/.f64 (fma.f64 #s(literal 2 binary64) x (*.f64 (/.f64 eps x) #s(literal -1/2 binary64))) eps))
accuracy	0.0	(/.f64 x eps)
accuracy	0.0	(*.f64 (/.f64 x eps) #s(literal 2 binary64))
accuracy	0.28125	(/.f64 #s(literal 1 binary64) #s(approx (pow (- x (sqrt (- (* x x) eps))) -1) (*.f64 (/.f64 x eps) #s(literal 2 binary64))))
accuracy	35.01724428250855	#s(approx (pow (- x (sqrt (- (* x x) eps))) -1) (*.f64 (/.f64 x eps) #s(literal 2 binary64)))
accuracy	0.0	(neg.f64 eps)
accuracy	0.01171875	(sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps)))
accuracy	24.83594137359021	(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))))
accuracy	26.890546346853938	#s(approx (- (* x x) eps) (neg.f64 eps))
accuracy	0.01171875	(sqrt.f64 (-.f64 (*.f64 x x) eps))
accuracy	0.28125	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))))
accuracy	0.296875	(/.f64 #s(literal 1 binary64) (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))
accuracy	24.83594137359021	(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))

Samples

76.0ms	87×	1	valid
55.0ms	156×	0	valid
8.0ms	13×	2	valid

Compiler

Compiled 545 to 92 computations (83.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 113.0ms

ival-div: 38.0ms (33.7% of total)

adjust: 24.0ms (21.3% of total)

ival-pow: 19.0ms (16.8% of total)

ival-mult: 14.0ms (12.4% of total)

ival-add: 6.0ms (5.3% of total)

ival-sub: 4.0ms (3.5% of total)

ival-sqrt: 3.0ms (2.7% of total)

ival-neg: 2.0ms (1.8% of total)

exact: 1.0ms (0.9% of total)

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

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

series372.0ms (4.2%)

Memory

-10.4MiB live, 67.4MiB allocated

Counts

23 → 96

Calls

Call 1

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

Outputs
(* -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)))
(* (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)))))))))
(* -1 eps)
(- (pow x 2) eps)
(* -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 eps)
(/ -1/2 x)
(/ (- (* 2 (/ (pow x 2) eps)) 1/2) x)
(* -1/2 (/ eps x))
(/ (+ (* -1/2 eps) (* 2 (pow x 2))) x)
(* -1/8 (/ (pow eps 2) (pow x 2)))
(/ (+ (* -1/2 (* eps (pow x 2))) (* -1/8 (pow eps 2))) (pow x 2))
(* 1/8 (/ (pow eps 2) (pow x 3)))
(/ (+ (* 1/8 (pow eps 2)) (* 1/2 (* eps (pow x 2)))) (pow x 3))
(/ (pow eps 2) x)
(* 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)
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)))))))
(pow x 2)
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))
(* 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)))))))
(* 2 x)
(* x (+ 2 (* -1/2 (/ eps (pow x 2)))))
(* -1/2 eps)
(+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2))))
(/ (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps)) 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 (- (+ (* 1/16 (/ (pow eps 3) (pow x 6))) (+ (* 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))) (+ 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 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))))))))
(/ 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))
(* -1 (* x (- (* 1/2 (/ 1 (pow x 2))) (* 2 (/ 1 eps)))))
(* -1 (/ (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2)))) 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))))
(+ 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)))))
(+ (* -1 eps) (pow x 2))
(/ (+ (* -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)
(+ (* -1/2 (/ eps x)) (* 2 x))
(* eps (- (* -1/8 (/ eps (pow x 2))) 1/2))
(* 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)))))
(* 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))))))
(* eps (- (/ (pow x 2) eps) 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)
(- (* 2 (/ x eps)) (* 1/2 (/ 1 x)))
(* eps (- (* 2 (/ x eps)) (* 1/2 (/ 1 x))))
(* -1 (* (pow eps 2) (+ (* 1/8 (/ 1 (pow x 2))) (* 1/2 (/ 1 eps)))))
(* (pow eps 2) (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))))
(* -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 (* 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 (+ 1 (* -1 (/ (pow x 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 (* eps (+ (* -2 (/ x eps)) (* 1/2 (/ 1 x)))))

Calls

6 calls:

Time	Variable		Point	Expression
291.0ms	eps	@	inf	((/ 1 (/ 1 (- x (sqrt (- (* x x) eps))))) (- x (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps)) (- (* x x) eps) (- x (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps)) (- (* x x) eps) (neg eps) (/ 1 (pow (- x (sqrt (- (* x x) eps))) -1)) (pow (- x (sqrt (- (* x x) eps))) -1) (* (/ x eps) 2) (/ x eps) (/ (+ (* 2 x) (* (/ eps x) -1/2)) eps) (/ 1 (pow (- x (sqrt (- (* x x) eps))) -1)) (pow (- x (sqrt (- (* x x) eps))) -1) (+ (* 2 x) (* (/ eps x) -1/2)) (+ (* (/ -1/8 x) (/ (* eps eps) x)) (* -1/2 eps)) (/ (+ (* (/ -1/8 x) (/ (* eps eps) x)) (* -1/2 eps)) (neg x)) (- x (sqrt (- (* x x) eps))) (* (+ (* (/ 1/8 (pow x 3)) eps) (/ 1/2 x)) eps) (/ 1 (- x (sqrt (- (* x x) eps)))) (* (/ eps x) -1/2) (/ (* eps eps) x))
64.0ms	x	@	0	((/ 1 (/ 1 (- x (sqrt (- (* x x) eps))))) (- x (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps)) (- (* x x) eps) (- x (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps)) (- (* x x) eps) (neg eps) (/ 1 (pow (- x (sqrt (- (* x x) eps))) -1)) (pow (- x (sqrt (- (* x x) eps))) -1) (* (/ x eps) 2) (/ x eps) (/ (+ (* 2 x) (* (/ eps x) -1/2)) eps) (/ 1 (pow (- x (sqrt (- (* x x) eps))) -1)) (pow (- x (sqrt (- (* x x) eps))) -1) (+ (* 2 x) (* (/ eps x) -1/2)) (+ (* (/ -1/8 x) (/ (* eps eps) x)) (* -1/2 eps)) (/ (+ (* (/ -1/8 x) (/ (* eps eps) x)) (* -1/2 eps)) (neg x)) (- x (sqrt (- (* x x) eps))) (* (+ (* (/ 1/8 (pow x 3)) eps) (/ 1/2 x)) eps) (/ 1 (- x (sqrt (- (* x x) eps)))) (* (/ eps x) -1/2) (/ (* eps eps) x))
4.0ms	eps	@	-inf	((/ 1 (/ 1 (- x (sqrt (- (* x x) eps))))) (- x (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps)) (- (* x x) eps) (- x (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps)) (- (* x x) eps) (neg eps) (/ 1 (pow (- x (sqrt (- (* x x) eps))) -1)) (pow (- x (sqrt (- (* x x) eps))) -1) (* (/ x eps) 2) (/ x eps) (/ (+ (* 2 x) (* (/ eps x) -1/2)) eps) (/ 1 (pow (- x (sqrt (- (* x x) eps))) -1)) (pow (- x (sqrt (- (* x x) eps))) -1) (+ (* 2 x) (* (/ eps x) -1/2)) (+ (* (/ -1/8 x) (/ (* eps eps) x)) (* -1/2 eps)) (/ (+ (* (/ -1/8 x) (/ (* eps eps) x)) (* -1/2 eps)) (neg x)) (- x (sqrt (- (* x x) eps))) (* (+ (* (/ 1/8 (pow x 3)) eps) (/ 1/2 x)) eps) (/ 1 (- x (sqrt (- (* x x) eps)))) (* (/ eps x) -1/2) (/ (* eps eps) x))
4.0ms	x	@	inf	((/ 1 (/ 1 (- x (sqrt (- (* x x) eps))))) (- x (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps)) (- (* x x) eps) (- x (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps)) (- (* x x) eps) (neg eps) (/ 1 (pow (- x (sqrt (- (* x x) eps))) -1)) (pow (- x (sqrt (- (* x x) eps))) -1) (* (/ x eps) 2) (/ x eps) (/ (+ (* 2 x) (* (/ eps x) -1/2)) eps) (/ 1 (pow (- x (sqrt (- (* x x) eps))) -1)) (pow (- x (sqrt (- (* x x) eps))) -1) (+ (* 2 x) (* (/ eps x) -1/2)) (+ (* (/ -1/8 x) (/ (* eps eps) x)) (* -1/2 eps)) (/ (+ (* (/ -1/8 x) (/ (* eps eps) x)) (* -1/2 eps)) (neg x)) (- x (sqrt (- (* x x) eps))) (* (+ (* (/ 1/8 (pow x 3)) eps) (/ 1/2 x)) eps) (/ 1 (- x (sqrt (- (* x x) eps)))) (* (/ eps x) -1/2) (/ (* eps eps) x))
3.0ms	x	@	-inf	((/ 1 (/ 1 (- x (sqrt (- (* x x) eps))))) (- x (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps)) (- (* x x) eps) (- x (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps)) (- (* x x) eps) (neg eps) (/ 1 (pow (- x (sqrt (- (* x x) eps))) -1)) (pow (- x (sqrt (- (* x x) eps))) -1) (* (/ x eps) 2) (/ x eps) (/ (+ (* 2 x) (* (/ eps x) -1/2)) eps) (/ 1 (pow (- x (sqrt (- (* x x) eps))) -1)) (pow (- x (sqrt (- (* x x) eps))) -1) (+ (* 2 x) (* (/ eps x) -1/2)) (+ (* (/ -1/8 x) (/ (* eps eps) x)) (* -1/2 eps)) (/ (+ (* (/ -1/8 x) (/ (* eps eps) x)) (* -1/2 eps)) (neg x)) (- x (sqrt (- (* x x) eps))) (* (+ (* (/ 1/8 (pow x 3)) eps) (/ 1/2 x)) eps) (/ 1 (- x (sqrt (- (* x x) eps)))) (* (/ eps x) -1/2) (/ (* eps eps) x))

simplify951.0ms (10.7%)

Memory

19.2MiB live, 137.6MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	462	1990
1	1420	1882
2	4872	1853
0	8120	1750

Stop Event

1×	iter limit
1×	node limit

Counts

96 → 95

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)))
(* (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)))))))))
(* -1 eps)
(- (pow x 2) eps)
(* -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 eps)
(/ -1/2 x)
(/ (- (* 2 (/ (pow x 2) eps)) 1/2) x)
(* -1/2 (/ eps x))
(/ (+ (* -1/2 eps) (* 2 (pow x 2))) x)
(* -1/8 (/ (pow eps 2) (pow x 2)))
(/ (+ (* -1/2 (* eps (pow x 2))) (* -1/8 (pow eps 2))) (pow x 2))
(* 1/8 (/ (pow eps 2) (pow x 3)))
(/ (+ (* 1/8 (pow eps 2)) (* 1/2 (* eps (pow x 2)))) (pow x 3))
(/ (pow eps 2) x)
(* 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)
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)))))))
(pow x 2)
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))
(* 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)))))))
(* 2 x)
(* x (+ 2 (* -1/2 (/ eps (pow x 2)))))
(* -1/2 eps)
(+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2))))
(/ (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps)) 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 (- (+ (* 1/16 (/ (pow eps 3) (pow x 6))) (+ (* 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))) (+ 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 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))))))))
(/ 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))
(* -1 (* x (- (* 1/2 (/ 1 (pow x 2))) (* 2 (/ 1 eps)))))
(* -1 (/ (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2)))) 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))))
(+ 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)))))
(+ (* -1 eps) (pow x 2))
(/ (+ (* -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)
(+ (* -1/2 (/ eps x)) (* 2 x))
(* eps (- (* -1/8 (/ eps (pow x 2))) 1/2))
(* 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)))))
(* 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))))))
(* eps (- (/ (pow x 2) eps) 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)
(- (* 2 (/ x eps)) (* 1/2 (/ 1 x)))
(* eps (- (* 2 (/ x eps)) (* 1/2 (/ 1 x))))
(* -1 (* (pow eps 2) (+ (* 1/8 (/ 1 (pow x 2))) (* 1/2 (/ 1 eps)))))
(* (pow eps 2) (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))))
(* -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 (* 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 (+ 1 (* -1 (/ (pow x 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 (* eps (+ (* -2 (/ x eps)) (* 1/2 (/ 1 x)))))

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

rewrite973.0ms (11%)

Memory

-10.5MiB live, 104.6MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	50	279
0	78	275
1	270	275
2	1913	271
0	8307	265

Stop Event

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

Counts

23 → 735

Calls

Call 1

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

Outputs
(.f64 (/.f64 (fma.f64 x x (fma.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x (-.f64 (.f64 x x) eps))) #s(literal 1 binary64)) (/.f64 (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) (fma.f64 x x (fma.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x (-.f64 (.f64 x x) eps)))))
(.f64 (/.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) #s(literal 1 binary64)) (/.f64 (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x)))
(.f64 (pow.f64 (pow.f64 (-.f64 (.f64 x x) (-.f64 (.f64 x x) eps)) #s(literal -1 binary64)) #s(literal -1 binary64)) (pow.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) #s(literal -1 binary64)))
(.f64 (pow.f64 (pow.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 3/2 binary64))) #s(literal -1 binary64)) #s(literal -1 binary64)) (pow.f64 (fma.f64 x x (fma.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x (-.f64 (.f64 x x) eps))) #s(literal -1 binary64)))
(.f64 (pow.f64 (pow.f64 (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) #s(literal 1/2 binary64)) #s(literal 1 binary64)) (pow.f64 (pow.f64 (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) #s(literal 1/2 binary64)) #s(literal 1 binary64)))
(.f64 (pow.f64 (-.f64 (.f64 x x) (-.f64 (.f64 x x) eps)) #s(literal 1 binary64)) (pow.f64 (pow.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) #s(literal -1 binary64)) #s(literal 1 binary64)))
(.f64 (pow.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 3/2 binary64))) #s(literal 1 binary64)) (pow.f64 (pow.f64 (fma.f64 x x (fma.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x (-.f64 (.f64 x x) eps))) #s(literal -1 binary64)) #s(literal 1 binary64)))
(.f64 (pow.f64 (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) #s(literal 1/2 binary64)) (pow.f64 (/.f64 (pow.f64 (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) #s(literal -1/2 binary64)) #s(literal 1 binary64)) #s(literal -1 binary64)))
(.f64 (pow.f64 (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) #s(literal 1/2 binary64)) (pow.f64 (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) #s(literal 1/2 binary64)))
(.f64 (-.f64 (.f64 x x) (-.f64 (.f64 x x) eps)) (pow.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) #s(literal -1 binary64)))
(.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 3/2 binary64))) (pow.f64 (fma.f64 x x (fma.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x (-.f64 (.f64 x x) eps))) #s(literal -1 binary64)))
(.f64 #s(literal -1 binary64) (pow.f64 (neg.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 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))))
(pow.f64 (exp.f64 #s(literal -1 binary64)) (neg.f64 (log.f64 (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))))
(pow.f64 (.f64 (pow.f64 (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) #s(literal -1 binary64)) (pow.f64 (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) #s(literal -1 binary64))) #s(literal -1/2 binary64))
(pow.f64 (/.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) (-.f64 (.f64 x x) (-.f64 (*.f64 x x) eps))) #s(literal -1 binary64))
(pow.f64 (/.f64 (fma.f64 x x (fma.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x (-.f64 (.f64 x x) eps))) (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 3/2 binary64)))) #s(literal -1 binary64))
(pow.f64 (pow.f64 (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) #s(literal 2 binary64)) #s(literal 1/2 binary64))
(pow.f64 (pow.f64 (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) #s(literal 1/2 binary64)) #s(literal 2 binary64))
(pow.f64 (pow.f64 (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) #s(literal -1/2 binary64)) #s(literal -2 binary64))
(pow.f64 (pow.f64 (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) #s(literal -1 binary64)) #s(literal -1 binary64))
(pow.f64 (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) #s(literal 1 binary64))
(/.f64 (neg.f64 (pow.f64 (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) #s(literal 1/2 binary64))) (neg.f64 (pow.f64 (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) #s(literal -1/2 binary64))))
(/.f64 (neg.f64 (.f64 #s(literal 1 binary64) (-.f64 (.f64 x x) (-.f64 (.f64 x x) eps)))) (neg.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x)))
(/.f64 (neg.f64 (.f64 #s(literal 1 binary64) (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 3/2 binary64))))) (neg.f64 (fma.f64 x x (fma.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x (-.f64 (.f64 x x) eps)))))
(/.f64 (neg.f64 (neg.f64 (-.f64 (.f64 x x) (-.f64 (.f64 x x) eps)))) (neg.f64 (neg.f64 (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))))
(/.f64 (neg.f64 (neg.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 3/2 binary64))))) (neg.f64 (neg.f64 (fma.f64 x x (fma.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x (-.f64 (*.f64 x x) eps))))))
(/.f64 (-.f64 (.f64 (.f64 x x) (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x)) (.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) (-.f64 (.f64 x x) eps))) (.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)))
(/.f64 (-.f64 (.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 x x (fma.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x (-.f64 (.f64 x x) eps)))) (.f64 (fma.f64 x x (fma.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x (-.f64 (.f64 x x) eps))) (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 3/2 binary64)))) (.f64 (fma.f64 x x (fma.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x (-.f64 (.f64 x x) eps))) (fma.f64 x x (fma.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x (-.f64 (.f64 x x) eps)))))
(/.f64 (-.f64 (.f64 x #s(literal 1 binary64)) (.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 (*.f64 x x) eps)))) #s(literal 1 binary64))
(/.f64 (exp.f64 (log.f64 (-.f64 (.f64 x x) (-.f64 (.f64 x x) eps)))) (exp.f64 (log.f64 (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))))
(/.f64 (exp.f64 (log.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 3/2 binary64))))) (exp.f64 (log.f64 (fma.f64 x x (fma.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x (-.f64 (*.f64 x x) eps))))))
(/.f64 (exp.f64 (log.f64 #s(literal -1 binary64))) (exp.f64 (log.f64 (/.f64 #s(literal -1 binary64) (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))))))
(/.f64 (.f64 #s(literal 1 binary64) (-.f64 (.f64 x x) (-.f64 (.f64 x x) eps))) (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x))
(/.f64 (.f64 #s(literal 1 binary64) (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 3/2 binary64)))) (fma.f64 x x (fma.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x (-.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 (neg.f64 (-.f64 (.f64 x x) (-.f64 (.f64 x x) eps))) (neg.f64 (.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x))))
(/.f64 (neg.f64 (-.f64 (.f64 x x) (-.f64 (.f64 x x) eps))) (neg.f64 (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)))
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(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (/.f64 (neg.f64 x) (fma.f64 #s(literal -1/8 binary64) (pow.f64 (/.f64 eps x) #s(literal 2 binary64)) (*.f64 #s(literal -1/2 binary64) eps))) #s(literal 1 binary64))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (neg.f64 x) (fma.f64 #s(literal -1/8 binary64) (pow.f64 (/.f64 eps x) #s(literal 2 binary64)) (*.f64 #s(literal -1/2 binary64) eps)))))
(/.f64 #s(literal 1 binary64) (neg.f64 (neg.f64 (/.f64 (neg.f64 x) (fma.f64 #s(literal -1/8 binary64) (pow.f64 (/.f64 eps x) #s(literal 2 binary64)) (*.f64 #s(literal -1/2 binary64) eps))))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (neg.f64 x) (fma.f64 #s(literal -1/8 binary64) (pow.f64 (/.f64 eps x) #s(literal 2 binary64)) (*.f64 #s(literal -1/2 binary64) eps))) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (neg.f64 x) (fma.f64 #s(literal -1/8 binary64) (pow.f64 (/.f64 eps x) #s(literal 2 binary64)) (*.f64 #s(literal -1/2 binary64) eps))))
(neg.f64 (/.f64 (fma.f64 #s(literal -1/8 binary64) (pow.f64 (/.f64 eps x) #s(literal 2 binary64)) (*.f64 #s(literal -1/2 binary64) eps)) x))
(-.f64 (/.f64 (.f64 #s(literal 1/64 binary64) (pow.f64 (pow.f64 (/.f64 eps x) #s(literal 2 binary64)) #s(literal 2 binary64))) (.f64 (neg.f64 x) (fma.f64 #s(literal -1/8 binary64) (pow.f64 (/.f64 eps x) #s(literal 2 binary64)) (.f64 #s(literal 1/2 binary64) eps)))) (/.f64 (.f64 #s(literal 1/4 binary64) (.f64 eps eps)) (.f64 (neg.f64 x) (fma.f64 #s(literal -1/8 binary64) (pow.f64 (/.f64 eps x) #s(literal 2 binary64)) (*.f64 #s(literal 1/2 binary64) eps)))))
(-.f64 (/.f64 (/.f64 (.f64 #s(literal 1/64 binary64) (pow.f64 (pow.f64 (/.f64 eps x) #s(literal 2 binary64)) #s(literal 2 binary64))) (fma.f64 #s(literal -1/8 binary64) (pow.f64 (/.f64 eps x) #s(literal 2 binary64)) (.f64 #s(literal 1/2 binary64) eps))) (neg.f64 x)) (/.f64 (/.f64 (.f64 #s(literal 1/4 binary64) (.f64 eps eps)) (fma.f64 #s(literal -1/8 binary64) (pow.f64 (/.f64 eps x) #s(literal 2 binary64)) (*.f64 #s(literal 1/2 binary64) eps))) (neg.f64 x)))
(-.f64 (/.f64 #s(literal 0 binary64) x) (/.f64 (fma.f64 #s(literal -1/8 binary64) (pow.f64 (/.f64 eps x) #s(literal 2 binary64)) (*.f64 #s(literal -1/2 binary64) eps)) x))
(-.f64 #s(literal 0 binary64) (/.f64 (fma.f64 #s(literal -1/8 binary64) (pow.f64 (/.f64 eps x) #s(literal 2 binary64)) (*.f64 #s(literal -1/2 binary64) eps)) x))
(exp.f64 (.f64 (log.f64 (/.f64 (neg.f64 x) (fma.f64 #s(literal -1/8 binary64) (pow.f64 (/.f64 eps x) #s(literal 2 binary64)) (.f64 #s(literal -1/2 binary64) eps)))) #s(literal -1 binary64)))
#s(approx (- x (sqrt (- (* x x) eps))) #s(approx (* (+ (* (/ 1/8 (pow x 3)) eps) (/ 1/2 x)) eps) (/.f64 (fma.f64 #s(literal -1/8 binary64) (pow.f64 (/.f64 eps x) #s(literal 2 binary64)) (*.f64 #s(literal -1/2 binary64) eps)) (neg.f64 x))))
#s(approx (* (+ (* (/ 1/8 (pow x 3)) eps) (/ 1/2 x)) eps) (/.f64 (fma.f64 #s(literal -1/8 binary64) (pow.f64 (/.f64 eps x) #s(literal 2 binary64)) (*.f64 #s(literal -1/2 binary64) eps)) (neg.f64 x)))
(.f64 (pow.f64 (pow.f64 (-.f64 (.f64 x x) (-.f64 (.f64 x x) eps)) #s(literal -1 binary64)) #s(literal 1 binary64)) (pow.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) #s(literal 1 binary64)))
(.f64 (pow.f64 (pow.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 3/2 binary64))) #s(literal -1 binary64)) #s(literal 1 binary64)) (pow.f64 (fma.f64 x x (fma.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x (-.f64 (.f64 x x) eps))) #s(literal 1 binary64)))
(.f64 (pow.f64 (pow.f64 (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) #s(literal 1/2 binary64)) #s(literal -1 binary64)) (pow.f64 (pow.f64 (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) #s(literal 1/2 binary64)) #s(literal -1 binary64)))
(.f64 (pow.f64 (-.f64 (.f64 x x) (-.f64 (.f64 x x) eps)) #s(literal -1 binary64)) (pow.f64 (pow.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) #s(literal -1 binary64)) #s(literal -1 binary64)))
(.f64 (pow.f64 (-.f64 (.f64 x x) (-.f64 (.f64 x x) eps)) #s(literal -1 binary64)) (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x))
(.f64 (pow.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 3/2 binary64))) #s(literal -1 binary64)) (pow.f64 (pow.f64 (fma.f64 x x (fma.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x (-.f64 (.f64 x x) eps))) #s(literal -1 binary64)) #s(literal -1 binary64)))
(.f64 (pow.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 3/2 binary64))) #s(literal -1 binary64)) (fma.f64 x x (fma.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x (-.f64 (.f64 x x) eps))))
(.f64 (pow.f64 (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) #s(literal -1/2 binary64)) (pow.f64 (/.f64 (pow.f64 (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) #s(literal -1/2 binary64)) #s(literal 1 binary64)) #s(literal 1 binary64)))
(.f64 (pow.f64 (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) #s(literal -1/2 binary64)) (/.f64 (pow.f64 (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) #s(literal -1/2 binary64)) #s(literal 1 binary64)))
(.f64 (pow.f64 (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) #s(literal -1/2 binary64)) (pow.f64 (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) #s(literal -1/2 binary64)))
(.f64 #s(literal -1 binary64) (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 #s(literal -1 binary64) (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps)))))
(.f64 (pow.f64 (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) #s(literal -1 binary64)) #s(literal 1 binary64))
(.f64 #s(literal 1 binary64) (pow.f64 (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) #s(literal -1 binary64)))
(pow.f64 (exp.f64 #s(literal -1 binary64)) (log.f64 (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))))
(pow.f64 (.f64 (pow.f64 (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) #s(literal -1 binary64)) (pow.f64 (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) #s(literal -1 binary64))) #s(literal 1/2 binary64))
(pow.f64 (pow.f64 (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) #s(literal 2 binary64)) #s(literal -1/2 binary64))
(pow.f64 (pow.f64 (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) #s(literal -1/2 binary64)) #s(literal 2 binary64))
(pow.f64 (pow.f64 (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) #s(literal -1 binary64)) #s(literal 1 binary64))
(pow.f64 (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) #s(literal -1 binary64))
(/.f64 (/.f64 #s(literal -1 binary64) (-.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 (pow.f64 (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) #s(literal -1 binary64)) #s(literal 1 binary64))
(/.f64 #s(literal 1 binary64) (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))
(neg.f64 (/.f64 #s(literal -1 binary64) (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))))
(-.f64 #s(literal 0 binary64) (/.f64 (pow.f64 (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) #s(literal -1 binary64)) #s(literal -1 binary64)))
(exp.f64 (fma.f64 (log.f64 (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps)))) #s(literal -1/2 binary64) (.f64 (log.f64 (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))) #s(literal -1/2 binary64))))
(exp.f64 (.f64 (.f64 (log.f64 (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))) #s(literal -1/2 binary64)) #s(literal 2 binary64)))
(exp.f64 (.f64 (log.f64 (pow.f64 (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) #s(literal 2 binary64))) #s(literal -1/2 binary64)))
(exp.f64 (.f64 (log.f64 (pow.f64 (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) #s(literal -1/2 binary64))) #s(literal 2 binary64)))
(exp.f64 (.f64 (neg.f64 (log.f64 (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))))) #s(literal 1 binary64)))
(exp.f64 (neg.f64 (log.f64 (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))))
(*.f64 (/.f64 eps #s(literal -1 binary64)) (/.f64 #s(literal 1/2 binary64) x))
(*.f64 (/.f64 #s(literal -1/2 binary64) x) (/.f64 eps #s(literal 1 binary64)))
(*.f64 (/.f64 eps #s(literal 1 binary64)) (/.f64 #s(literal -1/2 binary64) x))
(*.f64 (/.f64 (neg.f64 eps) x) #s(literal 1/2 binary64))
(*.f64 #s(literal 1/2 binary64) (/.f64 (neg.f64 eps) x))
(.f64 (.f64 #s(literal -1/2 binary64) eps) (pow.f64 x #s(literal -1 binary64)))
(*.f64 #s(literal -1/2 binary64) (/.f64 eps x))
(*.f64 (/.f64 eps x) #s(literal -1/2 binary64))
(.f64 eps (.f64 (pow.f64 x #s(literal -1 binary64)) #s(literal -1/2 binary64)))
(*.f64 eps (/.f64 #s(literal -1/2 binary64) x))
(pow.f64 (*.f64 #s(literal -2 binary64) (/.f64 x eps)) #s(literal -1 binary64))
(/.f64 (neg.f64 (*.f64 #s(literal -1/2 binary64) (neg.f64 eps))) x)
(/.f64 (neg.f64 (*.f64 (neg.f64 eps) #s(literal -1/2 binary64))) x)
(/.f64 (neg.f64 (neg.f64 (*.f64 #s(literal -1/2 binary64) eps))) x)
(/.f64 (*.f64 #s(literal -1/2 binary64) (neg.f64 eps)) (neg.f64 x))
(/.f64 (*.f64 (neg.f64 eps) #s(literal -1/2 binary64)) (neg.f64 x))
(/.f64 (neg.f64 (*.f64 #s(literal -1/2 binary64) eps)) (neg.f64 x))
(/.f64 #s(literal 1/2 binary64) (neg.f64 (/.f64 x eps)))
(/.f64 (*.f64 #s(literal -1/2 binary64) eps) x)
(/.f64 #s(literal -1/2 binary64) (/.f64 x eps))
(/.f64 #s(literal -1 binary64) (neg.f64 (*.f64 #s(literal -2 binary64) (/.f64 x eps))))
(/.f64 #s(literal 1 binary64) (*.f64 #s(literal -2 binary64) (/.f64 x eps)))
(*.f64 (/.f64 eps (pow.f64 (neg.f64 eps) #s(literal -1 binary64))) (/.f64 #s(literal -1 binary64) x))
(*.f64 (/.f64 eps (pow.f64 eps #s(literal -1 binary64))) (pow.f64 x #s(literal -1 binary64)))
(.f64 (/.f64 (.f64 eps eps) #s(literal 1 binary64)) (pow.f64 x #s(literal -1 binary64)))
(.f64 (/.f64 (.f64 eps eps) #s(literal -1 binary64)) (/.f64 #s(literal -1 binary64) x))
(*.f64 (/.f64 eps #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (/.f64 (neg.f64 x) eps)))
(*.f64 (/.f64 eps #s(literal -1 binary64)) (/.f64 (neg.f64 eps) x))
(*.f64 (/.f64 eps #s(literal 1 binary64)) (/.f64 eps x))
(*.f64 (/.f64 (neg.f64 eps) x) (/.f64 #s(literal 1 binary64) (pow.f64 (neg.f64 eps) #s(literal -1 binary64))))
(*.f64 (/.f64 (neg.f64 eps) x) (/.f64 eps #s(literal -1 binary64)))
(.f64 (/.f64 #s(literal -1 binary64) x) (/.f64 (.f64 eps eps) #s(literal -1 binary64)))
(*.f64 (pow.f64 x #s(literal -1 binary64)) (pow.f64 (pow.f64 eps #s(literal -2 binary64)) #s(literal -1 binary64)))
(.f64 (pow.f64 x #s(literal -1 binary64)) (.f64 eps eps))
(.f64 (.f64 (neg.f64 eps) eps) (/.f64 #s(literal -1 binary64) x))
(.f64 (.f64 eps eps) (pow.f64 x #s(literal -1 binary64)))
(*.f64 (/.f64 eps x) (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal -1 binary64))))
(*.f64 (/.f64 eps x) (/.f64 eps #s(literal 1 binary64)))
(*.f64 (/.f64 eps x) eps)
(*.f64 eps (/.f64 eps x))
(.f64 #s(literal 1 binary64) (.f64 (/.f64 eps x) eps))
(pow.f64 (/.f64 (/.f64 (/.f64 x eps) eps) #s(literal 1 binary64)) #s(literal -1 binary64))
(pow.f64 (/.f64 (/.f64 x eps) eps) #s(literal -1 binary64))
(/.f64 (neg.f64 (/.f64 (*.f64 (neg.f64 eps) eps) #s(literal -1 binary64))) (neg.f64 x))
(/.f64 (neg.f64 (neg.f64 (*.f64 (neg.f64 eps) eps))) (neg.f64 x))
(/.f64 (neg.f64 (.f64 (.f64 eps eps) #s(literal 1 binary64))) (neg.f64 x))
(/.f64 (neg.f64 (*.f64 eps #s(literal 1 binary64))) (neg.f64 (/.f64 x eps)))
(/.f64 (/.f64 (*.f64 (neg.f64 eps) eps) #s(literal -1 binary64)) x)
(/.f64 (*.f64 eps #s(literal 1 binary64)) (/.f64 x eps))
(/.f64 (neg.f64 (*.f64 (neg.f64 eps) eps)) x)
(/.f64 (.f64 (.f64 eps eps) #s(literal 1 binary64)) x)
(/.f64 (*.f64 (neg.f64 eps) eps) (neg.f64 x))
(/.f64 (*.f64 eps eps) x)
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (/.f64 (/.f64 x eps) eps) #s(literal 1 binary64))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (/.f64 x eps) eps)))
(/.f64 (neg.f64 eps) (neg.f64 (/.f64 x eps)))
(/.f64 eps (/.f64 x eps))
(/.f64 #s(literal 1 binary64) (neg.f64 (neg.f64 (/.f64 (/.f64 x eps) eps))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (/.f64 x eps) eps) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 x eps) eps))
(neg.f64 (/.f64 (*.f64 (neg.f64 eps) eps) x))
(-.f64 (/.f64 #s(literal 0 binary64) x) (/.f64 (*.f64 (neg.f64 eps) eps) x))
(exp.f64 (*.f64 (log.f64 (/.f64 (/.f64 x eps) eps)) #s(literal -1 binary64)))

eval267.0ms (3%)

Memory: -26.3MiB live, 140.0MiB allocated
Compiler: Compiled 22 907 to 3 278 computations (85.7% saved)

prune19.0ms (0.2%)

Memory

2.7MiB live, 42.0MiB allocated

Pruning

14 alts after pruning (9 fresh and 5 done)

	Pruned	Kept	Total
New	735	7	742
Fresh	3	2	5
Picked	3	2	5
Done	0	3	3
Total	741	14	755

Accuracy

100.0%

Counts

755 → 14

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	55.9%	(/.f64 (-.f64 (.f64 x x) #s(approx (- ( x x) eps) (neg.f64 eps))) (+.f64 (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))) x))
▶	45.1%	(/.f64 #s(literal 1 binary64) #s(approx (pow (- x (sqrt (- (* x x) eps))) -1) (/.f64 (fma.f64 (/.f64 (fma.f64 (/.f64 (/.f64 eps x) x) #s(literal -1/8 binary64) #s(literal -1/2 binary64)) x) eps (*.f64 #s(literal 2 binary64) x)) eps)))
✓	46.3%	(/.f64 #s(literal 1 binary64) #s(approx (pow (- x (sqrt (- (* x x) eps))) -1) (/.f64 (fma.f64 #s(literal 2 binary64) x (*.f64 (/.f64 eps x) #s(literal -1/2 binary64))) eps)))
	46.3%	(/.f64 #s(literal 1 binary64) #s(approx (pow (- x (sqrt (- (* x x) eps))) -1) (/.f64 #s(approx (+ (* 2 x) (* (/ eps x) -1/2)) (/.f64 (fma.f64 (.f64 x x) #s(literal 2 binary64) (.f64 #s(literal -1/2 binary64) eps)) x)) eps)))
	45.2%	(/.f64 #s(literal 1 binary64) #s(approx (pow (- x (sqrt (- (* x x) eps))) -1) (/.f64 #s(literal 2 binary64) (/.f64 eps x))))
▶	45.1%	(/.f64 #s(literal 1 binary64) #s(approx (pow (- x (sqrt (- (* x x) eps))) -1) (*.f64 x (/.f64 #s(literal 2 binary64) eps))))
▶	46.3%	(/.f64 #s(literal 1 binary64) #s(approx (pow (- x (sqrt (- (* x x) eps))) -1) #s(approx (/ (+ (* 2 x) (* (/ eps x) -1/2)) eps) (fma.f64 (/.f64 x eps) #s(literal 2 binary64) (/.f64 #s(literal -1/2 binary64) x)))))
✓	61.2%	(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
✓	56.3%	(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))))
✓	7.6%	(-.f64 x #s(approx (sqrt (- (* x x) eps)) (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) x)))
✓	3.5%	(-.f64 x #s(approx (sqrt (- (* x x) eps)) (neg.f64 x)))
	33.2%	#s(approx (/ 1 (pow (- x (sqrt (- (* x x) eps))) -1)) (/.f64 (fma.f64 (/.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 4 binary64))) #s(literal 1/16 binary64) (-.f64 (.f64 #s(literal 1/2 binary64) eps) (.f64 (/.f64 #s(literal -1/8 binary64) x) (/.f64 (*.f64 eps eps) x)))) x))
▶	45.1%	#s(approx (/ 1 (pow (- x (sqrt (- (* x x) eps))) -1)) (*.f64 (/.f64 #s(literal 1/2 binary64) x) eps))
	45.3%	#s(approx (- x (sqrt (- (* x x) eps))) #s(approx (* (+ (* (/ 1/8 (pow x 3)) eps) (/ 1/2 x)) eps) (/.f64 #s(approx (+ (* (/ -1/8 x) (/ (* eps eps) x)) (* -1/2 eps)) (*.f64 #s(literal -1/2 binary64) eps)) (neg.f64 x))))

Compiler

Compiled 580 to 409 computations (29.5% saved)

simplify339.0ms (3.8%)

Memory

32.3MiB live, 114.7MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 19 expressions of interest:

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	48	374
0	74	374
1	111	370
2	147	370
3	197	370
4	290	370
5	544	370
6	935	370
7	1739	370
8	3758	370
9	4934	370
10	5622	370
11	5968	370
12	5998	370
13	6012	370
14	6152	370
15	6694	370
16	7012	370
17	7099	370
18	7165	370
19	7187	370
20	7371	370
21	7915	370
22	7915	370
23	7972	370
24	7996	370
0	8050	367

Stop Event

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

Calls

Call 1

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

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

localize267.0ms (3%)

Memory

-3.7MiB live, 187.5MiB allocated

Localize:

Found 19 expressions of interest:

New	Metric	Score
accuracy	0.24609375	(/.f64 (/.f64 eps x) x)
accuracy	0.28125	(/.f64 #s(literal 1 binary64) #s(approx (pow (- x (sqrt (- (* x x) eps))) -1) (/.f64 (fma.f64 (/.f64 (fma.f64 (/.f64 (/.f64 eps x) x) #s(literal -1/8 binary64) #s(literal -1/2 binary64)) x) eps (*.f64 #s(literal 2 binary64) x)) eps)))
accuracy	7.728300088597955	(fma.f64 (/.f64 (fma.f64 (/.f64 (/.f64 eps x) x) #s(literal -1/8 binary64) #s(literal -1/2 binary64)) x) eps (*.f64 #s(literal 2 binary64) x))
accuracy	36.03969387928187	#s(approx (pow (- x (sqrt (- (* x x) eps))) -1) (/.f64 (fma.f64 (/.f64 (fma.f64 (/.f64 (/.f64 eps x) x) #s(literal -1/8 binary64) #s(literal -1/2 binary64)) x) eps (*.f64 #s(literal 2 binary64) x)) eps))
accuracy	0.0	#s(approx (/ (+ (* 2 x) (* (/ eps x) -1/2)) eps) (fma.f64 (/.f64 x eps) #s(literal 2 binary64) (/.f64 #s(literal -1/2 binary64) x)))
accuracy	0.0234375	(fma.f64 (/.f64 x eps) #s(literal 2 binary64) (/.f64 #s(literal -1/2 binary64) x))
accuracy	0.28125	(/.f64 #s(literal 1 binary64) #s(approx (pow (- x (sqrt (- (* x x) eps))) -1) #s(approx (/ (+ (* 2 x) (* (/ eps x) -1/2)) eps) (fma.f64 (/.f64 x eps) #s(literal 2 binary64) (/.f64 #s(literal -1/2 binary64) x)))))
accuracy	34.22060995420228	#s(approx (pow (- x (sqrt (- (* x x) eps))) -1) #s(approx (/ (+ (* 2 x) (* (/ eps x) -1/2)) eps) (fma.f64 (/.f64 x eps) #s(literal 2 binary64) (/.f64 #s(literal -1/2 binary64) x))))
accuracy	0.0	(/.f64 #s(literal 2 binary64) eps)
accuracy	0.28125	(/.f64 #s(literal 1 binary64) #s(approx (pow (- x (sqrt (- (* x x) eps))) -1) (*.f64 x (/.f64 #s(literal 2 binary64) eps))))
accuracy	0.30859375	(*.f64 x (/.f64 #s(literal 2 binary64) eps))
accuracy	35.01724428250855	#s(approx (pow (- x (sqrt (- (* x x) eps))) -1) (*.f64 x (/.f64 #s(literal 2 binary64) eps)))
accuracy	0.0	(/.f64 #s(literal 1/2 binary64) x)
accuracy	0.3203125	(*.f64 (/.f64 #s(literal 1/2 binary64) x) eps)
accuracy	35.02399119166812	#s(approx (/ 1 (pow (- x (sqrt (- (* x x) eps))) -1)) (*.f64 (/.f64 #s(literal 1/2 binary64) x) eps))
accuracy	0.015625	(+.f64 (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))) x)
accuracy	0.31640625	(/.f64 (-.f64 (.f64 x x) #s(approx (- ( x x) eps) (neg.f64 eps))) (+.f64 (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))) x))
accuracy	24.507468809455123	(-.f64 (.f64 x x) #s(approx (- ( x x) eps) (neg.f64 eps)))
accuracy	26.890546346853938	#s(approx (- (* x x) eps) (neg.f64 eps))

Samples

105.0ms	156×	0	valid
51.0ms	87×	1	valid
8.0ms	13×	2	valid

Compiler

Compiled 634 to 91 computations (85.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 137.0ms

ival-div: 83.0ms (60.8% of total)

ival-sub: 13.0ms (9.5% of total)

ival-mult: 13.0ms (9.5% of total)

ival-pow: 9.0ms (6.6% of total)

adjust: 7.0ms (5.1% of total)

ival-add: 7.0ms (5.1% of total)

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

exact: 1.0ms (0.7% of total)

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

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

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

series32.0ms (0.4%)

Memory

13.3MiB live, 51.2MiB allocated

Counts

21 → 105

Calls

Call 1

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

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

Calls

6 calls:

Time	Variable		Point	Expression
7.0ms	x	@	inf	((/ (- (* x x) (- (* x x) eps)) (+ (sqrt (- (* x x) eps)) x)) (- (* x x) (- (* x x) eps)) (* x x) (- (* x x) eps) (/ 1 (pow (- x (sqrt (- (* x x) eps))) -1)) (* (/ 1/2 x) eps) (/ 1/2 x) (/ 1 (pow (- x (sqrt (- (* x x) eps))) -1)) (pow (- x (sqrt (- (* x x) eps))) -1) (* x (/ 2 eps)) (/ 2 eps) (/ 1 (pow (- x (sqrt (- (* x x) eps))) -1)) (pow (- x (sqrt (- (* x x) eps))) -1) (/ (+ (* 2 x) (* (/ eps x) -1/2)) eps) (+ (* (/ x eps) 2) (/ -1/2 x)) (/ 1 (pow (- x (sqrt (- (* x x) eps))) -1)) (pow (- x (sqrt (- (* x x) eps))) -1) (/ (+ (* (/ (+ (* (/ (/ eps x) x) -1/8) -1/2) x) eps) (* 2 x)) eps) (+ (* (/ (+ (* (/ (/ eps x) x) -1/8) -1/2) x) eps) (* 2 x)) (+ (sqrt (- (* x x) eps)) x) (/ (/ eps x) x))
7.0ms	eps	@	0	((/ (- (* x x) (- (* x x) eps)) (+ (sqrt (- (* x x) eps)) x)) (- (* x x) (- (* x x) eps)) (* x x) (- (* x x) eps) (/ 1 (pow (- x (sqrt (- (* x x) eps))) -1)) (* (/ 1/2 x) eps) (/ 1/2 x) (/ 1 (pow (- x (sqrt (- (* x x) eps))) -1)) (pow (- x (sqrt (- (* x x) eps))) -1) (* x (/ 2 eps)) (/ 2 eps) (/ 1 (pow (- x (sqrt (- (* x x) eps))) -1)) (pow (- x (sqrt (- (* x x) eps))) -1) (/ (+ (* 2 x) (* (/ eps x) -1/2)) eps) (+ (* (/ x eps) 2) (/ -1/2 x)) (/ 1 (pow (- x (sqrt (- (* x x) eps))) -1)) (pow (- x (sqrt (- (* x x) eps))) -1) (/ (+ (* (/ (+ (* (/ (/ eps x) x) -1/8) -1/2) x) eps) (* 2 x)) eps) (+ (* (/ (+ (* (/ (/ eps x) x) -1/8) -1/2) x) eps) (* 2 x)) (+ (sqrt (- (* x x) eps)) x) (/ (/ eps x) x))
4.0ms	eps	@	-inf	((/ (- (* x x) (- (* x x) eps)) (+ (sqrt (- (* x x) eps)) x)) (- (* x x) (- (* x x) eps)) (* x x) (- (* x x) eps) (/ 1 (pow (- x (sqrt (- (* x x) eps))) -1)) (* (/ 1/2 x) eps) (/ 1/2 x) (/ 1 (pow (- x (sqrt (- (* x x) eps))) -1)) (pow (- x (sqrt (- (* x x) eps))) -1) (* x (/ 2 eps)) (/ 2 eps) (/ 1 (pow (- x (sqrt (- (* x x) eps))) -1)) (pow (- x (sqrt (- (* x x) eps))) -1) (/ (+ (* 2 x) (* (/ eps x) -1/2)) eps) (+ (* (/ x eps) 2) (/ -1/2 x)) (/ 1 (pow (- x (sqrt (- (* x x) eps))) -1)) (pow (- x (sqrt (- (* x x) eps))) -1) (/ (+ (* (/ (+ (* (/ (/ eps x) x) -1/8) -1/2) x) eps) (* 2 x)) eps) (+ (* (/ (+ (* (/ (/ eps x) x) -1/8) -1/2) x) eps) (* 2 x)) (+ (sqrt (- (* x x) eps)) x) (/ (/ eps x) x))
4.0ms	eps	@	inf	((/ (- (* x x) (- (* x x) eps)) (+ (sqrt (- (* x x) eps)) x)) (- (* x x) (- (* x x) eps)) (* x x) (- (* x x) eps) (/ 1 (pow (- x (sqrt (- (* x x) eps))) -1)) (* (/ 1/2 x) eps) (/ 1/2 x) (/ 1 (pow (- x (sqrt (- (* x x) eps))) -1)) (pow (- x (sqrt (- (* x x) eps))) -1) (* x (/ 2 eps)) (/ 2 eps) (/ 1 (pow (- x (sqrt (- (* x x) eps))) -1)) (pow (- x (sqrt (- (* x x) eps))) -1) (/ (+ (* 2 x) (* (/ eps x) -1/2)) eps) (+ (* (/ x eps) 2) (/ -1/2 x)) (/ 1 (pow (- x (sqrt (- (* x x) eps))) -1)) (pow (- x (sqrt (- (* x x) eps))) -1) (/ (+ (* (/ (+ (* (/ (/ eps x) x) -1/8) -1/2) x) eps) (* 2 x)) eps) (+ (* (/ (+ (* (/ (/ eps x) x) -1/8) -1/2) x) eps) (* 2 x)) (+ (sqrt (- (* x x) eps)) x) (/ (/ eps x) x))
4.0ms	x	@	0	((/ (- (* x x) (- (* x x) eps)) (+ (sqrt (- (* x x) eps)) x)) (- (* x x) (- (* x x) eps)) (* x x) (- (* x x) eps) (/ 1 (pow (- x (sqrt (- (* x x) eps))) -1)) (* (/ 1/2 x) eps) (/ 1/2 x) (/ 1 (pow (- x (sqrt (- (* x x) eps))) -1)) (pow (- x (sqrt (- (* x x) eps))) -1) (* x (/ 2 eps)) (/ 2 eps) (/ 1 (pow (- x (sqrt (- (* x x) eps))) -1)) (pow (- x (sqrt (- (* x x) eps))) -1) (/ (+ (* 2 x) (* (/ eps x) -1/2)) eps) (+ (* (/ x eps) 2) (/ -1/2 x)) (/ 1 (pow (- x (sqrt (- (* x x) eps))) -1)) (pow (- x (sqrt (- (* x x) eps))) -1) (/ (+ (* (/ (+ (* (/ (/ eps x) x) -1/8) -1/2) x) eps) (* 2 x)) eps) (+ (* (/ (+ (* (/ (/ eps x) x) -1/8) -1/2) x) eps) (* 2 x)) (+ (sqrt (- (* x x) eps)) x) (/ (/ eps x) x))

simplify176.0ms (2%)

Memory

-25.0MiB live, 257.9MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	566	2377
1	1777	2179
2	6190	2098
0	8185	1982

Stop Event

1×	iter limit
1×	node limit

Counts

105 → 104

Calls

Call 1

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

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 (- (* -1 (* x (+ (* -1 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3))))))) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt eps) (/ 1 (sqrt -1))))
(fma.f64 (fma.f64 (*.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64))) #s(literal -1/2 binary64)) x #s(literal 1 binary64)) x (/.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64))))
(+ (* x (- (* x (- (* x (- (* 1/2 (/ 1 (* eps (pow (sqrt -1) 4)))) (* -1 (* (sqrt (/ 1 eps)) (/ (+ (* -1 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3))))) (sqrt -1)))))) (+ (* -1 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3))))))) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt eps) (/ 1 (sqrt -1))))
(fma.f64 (fma.f64 (fma.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64))) #s(literal -1/2 binary64) (.f64 (fma.f64 (/.f64 (.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64))) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (/.f64 #s(literal 1/2 binary64) (*.f64 (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64)) eps))) x)) x #s(literal 1 binary64)) x (/.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64))))
eps
(pow x 2)
(*.f64 x x)
(* -1 eps)
(neg.f64 eps)
(- (pow x 2) eps)
(fma.f64 x x (neg.f64 eps))
(* -1 (* (sqrt eps) (sqrt -1)))
(*.f64 (neg.f64 (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 eps))
(- x (* (sqrt eps) (sqrt -1)))
(fma.f64 (neg.f64 (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 eps) x)
(- (* x (+ 1 (* -1/2 (* (sqrt (/ 1 eps)) (/ x (sqrt -1)))))) (* (sqrt eps) (sqrt -1)))
(fma.f64 (neg.f64 (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 eps) (fma.f64 (.f64 x #s(literal -1/2 binary64)) (.f64 (/.f64 x (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))) x))
(- (* 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)))
(fma.f64 (neg.f64 (sqrt.f64 eps)) (sqrt.f64 #s(literal -1 binary64)) (fma.f64 (fma.f64 (.f64 (.f64 (neg.f64 x) (/.f64 x (sqrt.f64 #s(literal -1 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 3 binary64))))) #s(literal 1/8 binary64) (.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64))) #s(literal -1/2 binary64))) (.f64 x x) x))
(* 1/2 (/ eps x))
(*.f64 (/.f64 #s(literal 1/2 binary64) x) eps)
(/ 1/2 x)
(/.f64 #s(literal 1/2 binary64) x)
(* -1 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1))))
(/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (neg.f64 (sqrt.f64 #s(literal -1 binary64))))
(+ (* -1 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))) (* -1 (/ x (* eps (pow (sqrt -1) 2)))))
(-.f64 (/.f64 x eps) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64))))
(+ (* -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))))))
(fma.f64 (fma.f64 (*.f64 x #s(literal -1/2 binary64)) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 3 binary64)))) (neg.f64 (sqrt.f64 #s(literal -1 binary64)))) (/.f64 #s(literal 1 binary64) eps)) x (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (neg.f64 (sqrt.f64 #s(literal -1 binary64)))))
(+ (* -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))))))
(fma.f64 (fma.f64 (fma.f64 (fma.f64 (neg.f64 (.f64 #s(literal 1/2 binary64) (/.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 3 binary64)))) (neg.f64 (sqrt.f64 #s(literal -1 binary64)))) (sqrt.f64 #s(literal -1 binary64))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (/.f64 #s(literal 1/2 binary64) (.f64 (.f64 (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64)) eps) eps))) x (.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 3 binary64)))) (neg.f64 (sqrt.f64 #s(literal -1 binary64)))) #s(literal -1/2 binary64))) x (/.f64 #s(literal 1 binary64) eps)) x (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (neg.f64 (sqrt.f64 #s(literal -1 binary64)))))
(* 2 (/ x eps))
(*.f64 (/.f64 x eps) #s(literal 2 binary64))
(/ -1/2 x)
(/.f64 #s(literal -1/2 binary64) x)
(/ (- (* 2 (/ (pow x 2) eps)) 1/2) x)
(/.f64 (fma.f64 (*.f64 x (/.f64 x eps)) #s(literal 2 binary64) #s(literal -1/2 binary64)) x)
(* -1/8 (/ eps (pow x 3)))
(*.f64 (/.f64 eps (pow.f64 x #s(literal 3 binary64))) #s(literal -1/8 binary64))
(/ (+ (* -1/2 (pow x 2)) (* -1/8 eps)) (pow x 3))
(/.f64 (fma.f64 #s(literal -1/8 binary64) eps (.f64 (.f64 x x) #s(literal -1/2 binary64))) (pow.f64 x #s(literal 3 binary64)))
(/ (+ (* -1/8 eps) (* (pow x 2) (- (* 2 (/ (pow x 2) eps)) 1/2))) (pow x 3))
(/.f64 (fma.f64 (.f64 (fma.f64 (.f64 x (/.f64 x eps)) #s(literal 2 binary64) #s(literal -1/2 binary64)) x) x (*.f64 #s(literal -1/8 binary64) eps)) (pow.f64 x #s(literal 3 binary64)))
(* -1/8 (/ (pow eps 2) (pow x 3)))
(.f64 (.f64 eps (/.f64 eps (pow.f64 x #s(literal 3 binary64)))) #s(literal -1/8 binary64))
(/ (+ (* -1/2 (* eps (pow x 2))) (* -1/8 (pow eps 2))) (pow x 3))
(/.f64 (.f64 eps (fma.f64 #s(literal -1/8 binary64) eps (.f64 (*.f64 x x) #s(literal -1/2 binary64)))) (pow.f64 x #s(literal 3 binary64)))
(/ (+ (* -1/8 (pow eps 2)) (* (pow x 2) (+ (* -1/2 eps) (* 2 (pow x 2))))) (pow x 3))
(/.f64 (fma.f64 eps (fma.f64 #s(literal -1/8 binary64) eps (.f64 (.f64 x x) #s(literal -1/2 binary64))) (*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 2 binary64))) (pow.f64 x #s(literal 3 binary64)))
(* (sqrt eps) (sqrt -1))
(*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 eps))
(+ x (* (sqrt eps) (sqrt -1)))
(fma.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 eps) x)
(+ (* x (+ 1 (* 1/2 (* (sqrt (/ 1 eps)) (/ x (sqrt -1)))))) (* (sqrt eps) (sqrt -1)))
(fma.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 eps) (fma.f64 (.f64 x #s(literal 1/2 binary64)) (.f64 (/.f64 x (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))) x))
(+ (* 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)))
(fma.f64 (fma.f64 (fma.f64 #s(literal -1/8 binary64) (.f64 (.f64 (neg.f64 x) (/.f64 x (sqrt.f64 #s(literal -1 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 3 binary64))))) (.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64))) #s(literal 1/2 binary64))) x #s(literal 1 binary64)) x (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 eps)))
(/ eps (pow x 2))
(/.f64 (/.f64 eps x) x)
(/ (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps)) x)
(*.f64 (fma.f64 (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64))) eps (/.f64 #s(literal 1/2 binary64) x)) eps)
(/ (- (+ (* 1/16 (/ (pow eps 3) (pow x 4))) (* 1/2 eps)) (* -1/8 (/ (pow eps 2) (pow x 2)))) x)
(/.f64 (fma.f64 (/.f64 (.f64 eps eps) x) (/.f64 #s(literal 1/8 binary64) x) (fma.f64 (/.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 4 binary64))) #s(literal 1/16 binary64) (.f64 #s(literal 1/2 binary64) eps))) x)
(/ (- (+ (* -1 (/ (+ (* -1/32 (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)
(/.f64 (.f64 #s(literal -1 binary64) (fma.f64 (pow.f64 eps #s(literal 4 binary64)) (/.f64 #s(literal -5/128 binary64) (pow.f64 x #s(literal 6 binary64))) (fma.f64 #s(literal -1/16 binary64) (/.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 4 binary64))) (fma.f64 (.f64 eps (/.f64 (/.f64 eps x) x)) #s(literal -1/8 binary64) (*.f64 #s(literal -1/2 binary64) eps))))) x)
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))
(.f64 (.f64 (-.f64 #s(literal 1 binary64) (/.f64 (/.f64 eps x) x)) x) x)
(/ (- (* 1/8 (/ (pow eps 2) (pow x 2))) (* -1/2 eps)) x)
(*.f64 (fma.f64 (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64))) eps (/.f64 #s(literal 1/2 binary64) x)) eps)
(/ (- (* 1/16 (/ (pow eps 3) (pow x 4))) (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2))))) x)
(/.f64 (fma.f64 (/.f64 (.f64 eps eps) x) (/.f64 #s(literal 1/8 binary64) x) (fma.f64 (/.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 4 binary64))) #s(literal 1/16 binary64) (.f64 #s(literal 1/2 binary64) eps))) 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) (-.f64 (.f64 (.f64 eps (/.f64 (/.f64 eps x) x)) #s(literal 1/8 binary64)) (/.f64 (*.f64 #s(literal -1/16 binary64) (pow.f64 eps #s(literal 3 binary64))) (pow.f64 x #s(literal 4 binary64))))) x)
(* x (- (* 2 (/ 1 eps)) (* 1/2 (/ 1 (pow x 2)))))
(.f64 (-.f64 (/.f64 #s(literal 2 binary64) eps) (/.f64 #s(literal 1/2 binary64) (.f64 x x))) x)
(* x (- (+ (* -1 (/ (+ (* -1/8 eps) (* 1/4 eps)) (pow x 4))) (* 2 (/ 1 eps))) (* 1/2 (/ 1 (pow x 2)))))
(.f64 (-.f64 (/.f64 #s(literal 2 binary64) eps) (fma.f64 (/.f64 eps (pow.f64 x #s(literal 4 binary64))) #s(literal 1/8 binary64) (/.f64 #s(literal 1/2 binary64) (.f64 x x)))) x)
(* 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)))))))
(.f64 (-.f64 (-.f64 (/.f64 #s(literal 2 binary64) eps) (/.f64 (fma.f64 eps (fma.f64 #s(literal -1/16 binary64) eps (.f64 #s(literal -1/4 binary64) (.f64 #s(literal 1/8 binary64) eps))) (.f64 (/.f64 #s(literal 2 binary64) eps) (/.f64 (.f64 #s(literal 5/64 binary64) (pow.f64 eps #s(literal 4 binary64))) eps))) (pow.f64 x #s(literal 6 binary64)))) (fma.f64 (/.f64 eps (pow.f64 x #s(literal 4 binary64))) #s(literal 1/8 binary64) (/.f64 #s(literal 1/2 binary64) (.f64 x x)))) x)
(* x (- (+ (* -1/8 (/ eps (pow x 4))) (* 2 (/ 1 eps))) (* 1/2 (/ 1 (pow x 2)))))
(.f64 (fma.f64 (/.f64 eps (pow.f64 x #s(literal 4 binary64))) #s(literal -1/8 binary64) (-.f64 (/.f64 #s(literal 2 binary64) eps) (/.f64 #s(literal 1/2 binary64) (.f64 x x)))) x)
(* 2 x)
(*.f64 #s(literal 2 binary64) x)
(* x (+ 2 (* -1/2 (/ eps (pow x 2)))))
(*.f64 (fma.f64 (/.f64 (/.f64 eps x) x) #s(literal -1/2 binary64) #s(literal 2 binary64)) x)
(* x (+ 2 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4))))))
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(/.f64 (fma.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 eps) x) 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))
(/.f64 (fma.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 eps) (fma.f64 (.f64 (.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) x) x) (sqrt.f64 eps)) (/.f64 #s(literal 1/2 binary64) eps) x)) 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))
(/.f64 (fma.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 eps) (fma.f64 (/.f64 (fma.f64 (.f64 (.f64 #s(literal 1/2 binary64) (.f64 (sqrt.f64 (pow.f64 eps #s(literal 3 binary64))) (.f64 x x))) (sqrt.f64 #s(literal -1 binary64))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (.f64 (sqrt.f64 #s(literal -1 binary64)) x) #s(literal -1 binary64)) (.f64 (*.f64 (pow.f64 x #s(literal 3 binary64)) eps) #s(literal -1/2 binary64))) eps) (/.f64 #s(literal -1 binary64) eps) x)) eps)
(* -1 (* eps (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3))))))
(*.f64 (-.f64 (/.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal 3 binary64))) (/.f64 (/.f64 #s(literal 1/2 binary64) x) eps)) eps)
(* -1 (* eps (+ (* -1 (/ (- (* 2 (/ x eps)) (* 1/2 (/ 1 x))) eps)) (* 1/8 (/ 1 (pow x 3))))))
(*.f64 (-.f64 (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64))) (/.f64 (fma.f64 (/.f64 x eps) #s(literal 2 binary64) (/.f64 #s(literal -1/2 binary64) x)) eps)) (neg.f64 eps))
(* (pow eps 2) (- (* -1 (/ (+ (* -2 (/ x eps)) (* 1/2 (/ 1 x))) eps)) (* 1/8 (/ 1 (pow x 3)))))
(.f64 (-.f64 (/.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal 3 binary64))) (/.f64 (fma.f64 #s(literal -2 binary64) (/.f64 x eps) (/.f64 #s(literal 1/2 binary64) x)) eps)) (.f64 eps eps))
(* -1 (* eps (+ (* -1 (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(-.f64 x (.f64 (.f64 eps (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 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64)) (/.f64 (fma.f64 (.f64 (.f64 x x) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))) (.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal -1/2 binary64)) x) (neg.f64 eps))) (neg.f64 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 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64)) (/.f64 (-.f64 x (/.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) (fma.f64 (.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))) (pow.f64 x #s(literal 4 binary64)) (.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 eps)) (.f64 x x)))) eps)) (neg.f64 eps))) (neg.f64 eps))

rewrite148.0ms (1.7%)

Memory

26.5MiB live, 217.2MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	48	313
0	74	311
1	290	309
2	2067	309
0	8172	306

Stop Event

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

Counts

21 → 604

Calls

Call 1

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

Outputs
(.f64 (pow.f64 (/.f64 (+.f64 (sqrt.f64 #s(approx (- ( x x) eps) (neg.f64 eps))) x) (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 #s(approx (- (* x x) eps) (neg.f64 eps)) #s(literal 2 binary64)))) #s(literal -1 binary64)) (pow.f64 (fma.f64 x x #s(approx (- (* x x) eps) (neg.f64 eps))) #s(literal -1 binary64)))
(.f64 (pow.f64 (/.f64 (+.f64 (sqrt.f64 #s(approx (- ( x x) eps) (neg.f64 eps))) x) (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 #s(approx (- (* x x) eps) (neg.f64 eps)) #s(literal 3 binary64)))) #s(literal -1 binary64)) (pow.f64 (fma.f64 #s(approx (- (* x x) eps) (neg.f64 eps)) (fma.f64 x x #s(approx (- (* x x) eps) (neg.f64 eps))) (pow.f64 x #s(literal 4 binary64))) #s(literal -1 binary64)))
(.f64 (/.f64 (-.f64 (.f64 x x) #s(approx (- (* x x) eps) (neg.f64 eps))) (-.f64 #s(approx (- (* x x) eps) (neg.f64 eps)) (.f64 x x))) (-.f64 (sqrt.f64 #s(approx (- ( x x) eps) (neg.f64 eps))) x))
(.f64 (/.f64 (-.f64 (.f64 x x) #s(approx (- (* x x) eps) (neg.f64 eps))) (+.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 #s(approx (- (* x x) eps) (neg.f64 eps)) #s(literal 3/2 binary64)))) (fma.f64 x (-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps)))) #s(approx (- (* x x) eps) (neg.f64 eps))))
(.f64 (pow.f64 (+.f64 (sqrt.f64 #s(approx (- ( x x) eps) (neg.f64 eps))) x) #s(literal -1 binary64)) (pow.f64 (pow.f64 (-.f64 (.f64 x x) #s(approx (- ( x x) eps) (neg.f64 eps))) #s(literal -1 binary64)) #s(literal -1 binary64)))
(.f64 (pow.f64 (+.f64 (sqrt.f64 #s(approx (- ( x x) eps) (neg.f64 eps))) x) #s(literal -1 binary64)) (-.f64 (.f64 x x) #s(approx (- ( x x) eps) (neg.f64 eps))))
(.f64 (neg.f64 (-.f64 (.f64 x x) #s(approx (- (* x x) eps) (neg.f64 eps)))) (pow.f64 (neg.f64 (+.f64 (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))) x)) #s(literal -1 binary64)))
(.f64 #s(literal 1 binary64) (/.f64 (-.f64 (.f64 x x) #s(approx (- (* x x) eps) (neg.f64 eps))) (+.f64 (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))) x)))
(.f64 (-.f64 (.f64 x x) #s(approx (- (* x x) eps) (neg.f64 eps))) (pow.f64 (+.f64 (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))) x) #s(literal -1 binary64)))
(pow.f64 (/.f64 (/.f64 (+.f64 (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))) x) (-.f64 (.f64 x x) #s(approx (- ( x x) eps) (neg.f64 eps)))) #s(literal 1 binary64)) #s(literal -1 binary64))
(pow.f64 (/.f64 (+.f64 (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))) x) (-.f64 (.f64 x x) #s(approx (- ( x x) eps) (neg.f64 eps)))) #s(literal -1 binary64))
(/.f64 (neg.f64 (.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 #s(approx (- ( x x) eps) (neg.f64 eps)) #s(literal 2 binary64))) (pow.f64 (+.f64 (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))) x) #s(literal -1 binary64)))) (neg.f64 (fma.f64 x x #s(approx (- (* x x) eps) (neg.f64 eps)))))
(/.f64 (neg.f64 (.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 #s(approx (- ( x x) eps) (neg.f64 eps)) #s(literal 3 binary64))) (pow.f64 (+.f64 (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))) x) #s(literal -1 binary64)))) (neg.f64 (fma.f64 #s(approx (- (* x x) eps) (neg.f64 eps)) (fma.f64 x x #s(approx (- (* x x) eps) (neg.f64 eps))) (pow.f64 x #s(literal 4 binary64)))))
(/.f64 (neg.f64 (.f64 (-.f64 (.f64 x x) #s(approx (- (* x x) eps) (neg.f64 eps))) #s(literal 1 binary64))) (neg.f64 (+.f64 (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))) x)))
(/.f64 (neg.f64 (-.f64 (pow.f64 (/.f64 (.f64 x x) (+.f64 (sqrt.f64 #s(approx (- ( x x) eps) (neg.f64 eps))) x)) #s(literal 2 binary64)) (pow.f64 (/.f64 #s(approx (- (* x x) eps) (neg.f64 eps)) (+.f64 (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))) x)) #s(literal 2 binary64)))) (neg.f64 (fma.f64 x (/.f64 x (+.f64 (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))) x)) (/.f64 #s(approx (- (* x x) eps) (neg.f64 eps)) (+.f64 (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))) x)))))
(/.f64 (neg.f64 (-.f64 (pow.f64 (/.f64 (.f64 x x) (+.f64 (sqrt.f64 #s(approx (- ( x x) eps) (neg.f64 eps))) x)) #s(literal 3 binary64)) (pow.f64 (/.f64 #s(approx (- (* x x) eps) (neg.f64 eps)) (+.f64 (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))) x)) #s(literal 3 binary64)))) (neg.f64 (+.f64 (pow.f64 (/.f64 (.f64 x x) (+.f64 (sqrt.f64 #s(approx (- ( x x) eps) (neg.f64 eps))) x)) #s(literal 2 binary64)) (+.f64 (pow.f64 (/.f64 #s(approx (- (* x x) eps) (neg.f64 eps)) (+.f64 (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))) x)) #s(literal 2 binary64)) (.f64 (/.f64 (.f64 x x) (+.f64 (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))) x)) (/.f64 #s(approx (- (* x x) eps) (neg.f64 eps)) (+.f64 (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))) x)))))))
(/.f64 (neg.f64 (neg.f64 (neg.f64 (-.f64 (.f64 x x) #s(approx (- ( x x) eps) (neg.f64 eps)))))) (neg.f64 (neg.f64 (neg.f64 (+.f64 (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))) x)))))
(/.f64 (neg.f64 (.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 #s(approx (- ( x x) eps) (neg.f64 eps)) #s(literal 2 binary64))) #s(literal 1 binary64))) (neg.f64 (.f64 (fma.f64 x x #s(approx (- ( x x) eps) (neg.f64 eps))) (+.f64 (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))) x))))
(/.f64 (neg.f64 (.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 #s(approx (- ( x x) eps) (neg.f64 eps)) #s(literal 3 binary64))) #s(literal 1 binary64))) (neg.f64 (.f64 (fma.f64 #s(approx (- ( x x) eps) (neg.f64 eps)) (fma.f64 x x #s(approx (- (* x x) eps) (neg.f64 eps))) (pow.f64 x #s(literal 4 binary64))) (+.f64 (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))) x))))
(/.f64 (neg.f64 (-.f64 (.f64 (.f64 x x) (+.f64 (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))) x)) (.f64 (+.f64 (sqrt.f64 #s(approx (- ( x x) eps) (neg.f64 eps))) x) #s(approx (- (* x x) eps) (neg.f64 eps))))) (neg.f64 (pow.f64 (+.f64 (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))) x) #s(literal 2 binary64))))
(/.f64 (-.f64 (.f64 (neg.f64 (.f64 x x)) (neg.f64 (+.f64 (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))) x))) (.f64 (neg.f64 (+.f64 (sqrt.f64 #s(approx (- ( x x) eps) (neg.f64 eps))) x)) (neg.f64 #s(approx (- (* x x) eps) (neg.f64 eps))))) (.f64 (neg.f64 (+.f64 (sqrt.f64 #s(approx (- ( x x) eps) (neg.f64 eps))) x)) (neg.f64 (+.f64 (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))) x))))
(/.f64 (-.f64 (.f64 (neg.f64 (.f64 x x)) (/.f64 (+.f64 (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))) x) #s(approx (- (* x x) eps) (neg.f64 eps)))) (.f64 (neg.f64 (+.f64 (sqrt.f64 #s(approx (- ( x x) eps) (neg.f64 eps))) x)) #s(literal 1 binary64))) (.f64 (neg.f64 (+.f64 (sqrt.f64 #s(approx (- ( x x) eps) (neg.f64 eps))) x)) (/.f64 (+.f64 (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))) x) #s(approx (- (* x x) eps) (neg.f64 eps)))))
(/.f64 (-.f64 (.f64 (neg.f64 (.f64 x x)) (+.f64 (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))) x)) (.f64 (neg.f64 (+.f64 (sqrt.f64 #s(approx (- ( x x) eps) (neg.f64 eps))) x)) #s(approx (- (* x x) eps) (neg.f64 eps)))) (.f64 (neg.f64 (+.f64 (sqrt.f64 #s(approx (- ( x x) eps) (neg.f64 eps))) x)) (+.f64 (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))) x)))
(/.f64 (-.f64 (.f64 #s(literal 1 binary64) (neg.f64 (+.f64 (sqrt.f64 #s(approx (- ( x x) eps) (neg.f64 eps))) x))) (.f64 (/.f64 (+.f64 (sqrt.f64 #s(approx (- ( x x) eps) (neg.f64 eps))) x) (.f64 x x)) (neg.f64 #s(approx (- ( x x) eps) (neg.f64 eps))))) (.f64 (/.f64 (+.f64 (sqrt.f64 #s(approx (- ( x x) eps) (neg.f64 eps))) x) (.f64 x x)) (neg.f64 (+.f64 (sqrt.f64 #s(approx (- ( x x) eps) (neg.f64 eps))) x))))
(/.f64 (-.f64 (.f64 #s(literal 1 binary64) (/.f64 (+.f64 (sqrt.f64 #s(approx (- ( x x) eps) (neg.f64 eps))) x) #s(approx (- (* x x) eps) (neg.f64 eps)))) (.f64 (/.f64 (+.f64 (sqrt.f64 #s(approx (- ( x x) eps) (neg.f64 eps))) x) (.f64 x x)) #s(literal 1 binary64))) (.f64 (/.f64 (+.f64 (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))) x) (.f64 x x)) (/.f64 (+.f64 (sqrt.f64 #s(approx (- ( x x) eps) (neg.f64 eps))) x) #s(approx (- (* x x) eps) (neg.f64 eps)))))
(/.f64 (-.f64 (.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 #s(approx (- ( x x) eps) (neg.f64 eps))) x)) (.f64 (/.f64 (+.f64 (sqrt.f64 #s(approx (- ( x x) eps) (neg.f64 eps))) x) (.f64 x x)) #s(approx (- ( x x) eps) (neg.f64 eps)))) (.f64 (/.f64 (+.f64 (sqrt.f64 #s(approx (- ( x x) eps) (neg.f64 eps))) x) (.f64 x x)) (+.f64 (sqrt.f64 #s(approx (- ( x x) eps) (neg.f64 eps))) x)))
(/.f64 (-.f64 (.f64 (.f64 x x) (neg.f64 (+.f64 (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))) x))) (.f64 (+.f64 (sqrt.f64 #s(approx (- ( x x) eps) (neg.f64 eps))) x) (neg.f64 #s(approx (- (* x x) eps) (neg.f64 eps))))) (.f64 (+.f64 (sqrt.f64 #s(approx (- ( x x) eps) (neg.f64 eps))) x) (neg.f64 (+.f64 (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))) x))))
(/.f64 (-.f64 (.f64 (.f64 x x) (/.f64 (+.f64 (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))) x) #s(approx (- (* x x) eps) (neg.f64 eps)))) (.f64 (+.f64 (sqrt.f64 #s(approx (- ( x x) eps) (neg.f64 eps))) x) #s(literal 1 binary64))) (.f64 (+.f64 (sqrt.f64 #s(approx (- ( x x) eps) (neg.f64 eps))) x) (/.f64 (+.f64 (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))) x) #s(approx (- (* x x) eps) (neg.f64 eps)))))
(/.f64 (-.f64 (neg.f64 (.f64 x x)) (neg.f64 #s(approx (- ( x x) eps) (neg.f64 eps)))) (neg.f64 (+.f64 (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))) x)))
(/.f64 (.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 #s(approx (- ( x x) eps) (neg.f64 eps)) #s(literal 2 binary64))) (pow.f64 (+.f64 (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))) x) #s(literal -1 binary64))) (fma.f64 x x #s(approx (- (* x x) eps) (neg.f64 eps))))
(/.f64 (.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 #s(approx (- ( x x) eps) (neg.f64 eps)) #s(literal 3 binary64))) (pow.f64 (+.f64 (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))) x) #s(literal -1 binary64))) (fma.f64 #s(approx (- (* x x) eps) (neg.f64 eps)) (fma.f64 x x #s(approx (- (* x x) eps) (neg.f64 eps))) (pow.f64 x #s(literal 4 binary64))))
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(/.f64 (neg.f64 (fma.f64 #s(literal 8 binary64) (pow.f64 x #s(literal 3 binary64)) (pow.f64 (.f64 (/.f64 (fma.f64 #s(literal -1/8 binary64) (/.f64 (/.f64 eps x) x) #s(literal -1/2 binary64)) x) eps) #s(literal 3 binary64)))) (neg.f64 (fma.f64 (.f64 #s(literal 2 binary64) x) (-.f64 (.f64 #s(literal 2 binary64) x) (.f64 (/.f64 (fma.f64 #s(literal -1/8 binary64) (/.f64 (/.f64 eps x) x) #s(literal -1/2 binary64)) x) eps)) (pow.f64 (*.f64 (/.f64 (fma.f64 #s(literal -1/8 binary64) (/.f64 (/.f64 eps x) x) #s(literal -1/2 binary64)) x) eps) #s(literal 2 binary64)))))
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(/.f64 (fma.f64 #s(literal 8 binary64) (pow.f64 x #s(literal 3 binary64)) (pow.f64 (.f64 (/.f64 (fma.f64 #s(literal -1/8 binary64) (/.f64 (/.f64 eps x) x) #s(literal -1/2 binary64)) x) eps) #s(literal 3 binary64))) (fma.f64 #s(literal 4 binary64) (.f64 x x) (-.f64 (pow.f64 (.f64 (/.f64 (fma.f64 #s(literal -1/8 binary64) (/.f64 (/.f64 eps x) x) #s(literal -1/2 binary64)) x) eps) #s(literal 2 binary64)) (.f64 (.f64 (.f64 (/.f64 (fma.f64 #s(literal -1/8 binary64) (/.f64 (/.f64 eps x) x) #s(literal -1/2 binary64)) x) eps) #s(literal 2 binary64)) x))))
(/.f64 (fma.f64 #s(literal 8 binary64) (pow.f64 x #s(literal 3 binary64)) (pow.f64 (.f64 (/.f64 (fma.f64 #s(literal -1/8 binary64) (/.f64 (/.f64 eps x) x) #s(literal -1/2 binary64)) x) eps) #s(literal 3 binary64))) (fma.f64 (.f64 #s(literal 2 binary64) x) (-.f64 (.f64 #s(literal 2 binary64) x) (.f64 (/.f64 (fma.f64 #s(literal -1/8 binary64) (/.f64 (/.f64 eps x) x) #s(literal -1/2 binary64)) x) eps)) (pow.f64 (*.f64 (/.f64 (fma.f64 #s(literal -1/8 binary64) (/.f64 (/.f64 eps x) x) #s(literal -1/2 binary64)) x) eps) #s(literal 2 binary64))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (fma.f64 (/.f64 (fma.f64 #s(literal -1/8 binary64) (/.f64 (/.f64 eps x) x) #s(literal -1/2 binary64)) x) eps (.f64 #s(literal -2 binary64) x)) (-.f64 (pow.f64 (.f64 (/.f64 (fma.f64 #s(literal -1/8 binary64) (/.f64 (/.f64 eps x) x) #s(literal -1/2 binary64)) x) eps) #s(literal 2 binary64)) (.f64 #s(literal 4 binary64) (.f64 x x))))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (fma.f64 (.f64 #s(literal 2 binary64) x) (-.f64 (.f64 #s(literal 2 binary64) x) (.f64 (/.f64 (fma.f64 #s(literal -1/8 binary64) (/.f64 (/.f64 eps x) x) #s(literal -1/2 binary64)) x) eps)) (pow.f64 (.f64 (/.f64 (fma.f64 #s(literal -1/8 binary64) (/.f64 (/.f64 eps x) x) #s(literal -1/2 binary64)) x) eps) #s(literal 2 binary64))) (fma.f64 #s(literal 8 binary64) (pow.f64 x #s(literal 3 binary64)) (pow.f64 (*.f64 (/.f64 (fma.f64 #s(literal -1/8 binary64) (/.f64 (/.f64 eps x) x) #s(literal -1/2 binary64)) x) eps) #s(literal 3 binary64))))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (/.f64 (fma.f64 #s(literal -1/8 binary64) (/.f64 (/.f64 eps x) x) #s(literal -1/2 binary64)) x) eps (.f64 #s(literal -2 binary64) x)) (-.f64 (pow.f64 (.f64 (/.f64 (fma.f64 #s(literal -1/8 binary64) (/.f64 (/.f64 eps x) x) #s(literal -1/2 binary64)) x) eps) #s(literal 2 binary64)) (.f64 #s(literal 4 binary64) (.f64 x x)))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (.f64 #s(literal 2 binary64) x) (-.f64 (.f64 #s(literal 2 binary64) x) (.f64 (/.f64 (fma.f64 #s(literal -1/8 binary64) (/.f64 (/.f64 eps x) x) #s(literal -1/2 binary64)) x) eps)) (pow.f64 (.f64 (/.f64 (fma.f64 #s(literal -1/8 binary64) (/.f64 (/.f64 eps x) x) #s(literal -1/2 binary64)) x) eps) #s(literal 2 binary64))) (fma.f64 #s(literal 8 binary64) (pow.f64 x #s(literal 3 binary64)) (pow.f64 (*.f64 (/.f64 (fma.f64 #s(literal -1/8 binary64) (/.f64 (/.f64 eps x) x) #s(literal -1/2 binary64)) x) eps) #s(literal 3 binary64)))))
(fma.f64 (.f64 (fma.f64 #s(literal -1/8 binary64) (/.f64 (/.f64 eps x) x) #s(literal -1/2 binary64)) eps) (pow.f64 x #s(literal -1 binary64)) (.f64 #s(literal 2 binary64) x))
(fma.f64 (/.f64 (fma.f64 #s(literal -1/8 binary64) (/.f64 (/.f64 eps x) x) #s(literal -1/2 binary64)) x) eps (*.f64 #s(literal 2 binary64) x))
(fma.f64 (fma.f64 #s(literal -1/8 binary64) (/.f64 (/.f64 eps x) x) #s(literal -1/2 binary64)) (/.f64 eps x) (*.f64 #s(literal 2 binary64) x))
(fma.f64 #s(literal 2 binary64) x (*.f64 (/.f64 (fma.f64 #s(literal -1/8 binary64) (/.f64 (/.f64 eps x) x) #s(literal -1/2 binary64)) x) eps))
(fma.f64 eps (/.f64 (fma.f64 #s(literal -1/8 binary64) (/.f64 (/.f64 eps x) x) #s(literal -1/2 binary64)) x) (*.f64 #s(literal 2 binary64) x))
(fma.f64 x #s(literal 2 binary64) (*.f64 (/.f64 (fma.f64 #s(literal -1/8 binary64) (/.f64 (/.f64 eps x) x) #s(literal -1/2 binary64)) x) eps))
(-.f64 (/.f64 (pow.f64 (.f64 (/.f64 (fma.f64 #s(literal -1/8 binary64) (/.f64 (/.f64 eps x) x) #s(literal -1/2 binary64)) x) eps) #s(literal 2 binary64)) (fma.f64 (/.f64 (fma.f64 #s(literal -1/8 binary64) (/.f64 (/.f64 eps x) x) #s(literal -1/2 binary64)) x) eps (.f64 #s(literal -2 binary64) x))) (/.f64 (.f64 #s(literal 4 binary64) (.f64 x x)) (fma.f64 (/.f64 (fma.f64 #s(literal -1/8 binary64) (/.f64 (/.f64 eps x) x) #s(literal -1/2 binary64)) x) eps (*.f64 #s(literal -2 binary64) x))))
(+.f64 (.f64 (/.f64 (fma.f64 #s(literal -1/8 binary64) (/.f64 (/.f64 eps x) x) #s(literal -1/2 binary64)) x) eps) (.f64 #s(literal 2 binary64) x))
(+.f64 (.f64 #s(literal 2 binary64) x) (.f64 (/.f64 (fma.f64 #s(literal -1/8 binary64) (/.f64 (/.f64 eps x) x) #s(literal -1/2 binary64)) x) eps))
(.f64 (-.f64 #s(approx (- ( x x) eps) (neg.f64 eps)) (.f64 x x)) (pow.f64 (-.f64 (sqrt.f64 #s(approx (- ( x x) eps) (neg.f64 eps))) x) #s(literal -1 binary64)))
(.f64 (+.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 #s(approx (- ( x x) eps) (neg.f64 eps)) #s(literal 3/2 binary64))) (pow.f64 (fma.f64 x (-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps)))) #s(approx (- (* x x) eps) (neg.f64 eps))) #s(literal -1 binary64)))
(pow.f64 (/.f64 (-.f64 (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))) x) (-.f64 #s(approx (- (* x x) eps) (neg.f64 eps)) (*.f64 x x))) #s(literal -1 binary64))
(pow.f64 (/.f64 (fma.f64 x (-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps)))) #s(approx (- (* x x) eps) (neg.f64 eps))) (+.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 #s(approx (- (* x x) eps) (neg.f64 eps)) #s(literal 3/2 binary64)))) #s(literal -1 binary64))
(/.f64 (neg.f64 (neg.f64 (-.f64 #s(approx (- (* x x) eps) (neg.f64 eps)) (.f64 x x)))) (neg.f64 (neg.f64 (-.f64 (sqrt.f64 #s(approx (- ( x x) eps) (neg.f64 eps))) x))))
(/.f64 (neg.f64 (neg.f64 (+.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 #s(approx (- (* x x) eps) (neg.f64 eps)) #s(literal 3/2 binary64))))) (neg.f64 (neg.f64 (fma.f64 x (-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps)))) #s(approx (- (* x x) eps) (neg.f64 eps))))))
(/.f64 (-.f64 (.f64 #s(approx (- ( x x) eps) (neg.f64 eps)) (-.f64 (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))) x)) (.f64 (-.f64 (sqrt.f64 #s(approx (- ( x x) eps) (neg.f64 eps))) x) (.f64 x x))) (.f64 (-.f64 (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))) x) (-.f64 (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))) x)))
(/.f64 (neg.f64 (-.f64 #s(approx (- (* x x) eps) (neg.f64 eps)) (.f64 x x))) (neg.f64 (-.f64 (sqrt.f64 #s(approx (- ( x x) eps) (neg.f64 eps))) x)))
(/.f64 (neg.f64 (+.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 #s(approx (- (* x x) eps) (neg.f64 eps)) #s(literal 3/2 binary64)))) (neg.f64 (fma.f64 x x (-.f64 #s(approx (- (* x x) eps) (neg.f64 eps)) (.f64 (sqrt.f64 #s(approx (- ( x x) eps) (neg.f64 eps))) x)))))
(/.f64 (neg.f64 (+.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 #s(approx (- (* x x) eps) (neg.f64 eps)) #s(literal 3/2 binary64)))) (neg.f64 (fma.f64 x (-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps)))) #s(approx (- (* x x) eps) (neg.f64 eps)))))
(/.f64 (-.f64 #s(approx (- (* x x) eps) (neg.f64 eps)) (.f64 x x)) (-.f64 (sqrt.f64 #s(approx (- ( x x) eps) (neg.f64 eps))) x))
(/.f64 (+.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 #s(approx (- (* x x) eps) (neg.f64 eps)) #s(literal 3/2 binary64))) (fma.f64 x x (-.f64 #s(approx (- (* x x) eps) (neg.f64 eps)) (.f64 (sqrt.f64 #s(approx (- ( x x) eps) (neg.f64 eps))) x))))
(/.f64 (+.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 #s(approx (- (* x x) eps) (neg.f64 eps)) #s(literal 3/2 binary64))) (fma.f64 x (-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps)))) #s(approx (- (* x x) eps) (neg.f64 eps))))
(/.f64 (neg.f64 (-.f64 (.f64 x x) #s(approx (- ( x x) eps) (neg.f64 eps)))) (neg.f64 (-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (-.f64 (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))) x) (-.f64 #s(approx (- (* x x) eps) (neg.f64 eps)) (*.f64 x x)))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (fma.f64 x (-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps)))) #s(approx (- (* x x) eps) (neg.f64 eps))) (+.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 #s(approx (- (* x x) eps) (neg.f64 eps)) #s(literal 3/2 binary64))))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))) x) (-.f64 #s(approx (- (* x x) eps) (neg.f64 eps)) (*.f64 x x))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 x (-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps)))) #s(approx (- (* x x) eps) (neg.f64 eps))) (+.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 #s(approx (- (* x x) eps) (neg.f64 eps)) #s(literal 3/2 binary64)))))
(/.f64 (-.f64 (.f64 x x) #s(approx (- ( x x) eps) (neg.f64 eps))) (-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps)))))
(fma.f64 (sqrt.f64 (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps)))) (sqrt.f64 (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps)))) x)
(fma.f64 (pow.f64 #s(approx (- (* x x) eps) (neg.f64 eps)) #s(literal 1/4 binary64)) (pow.f64 #s(approx (- (* x x) eps) (neg.f64 eps)) #s(literal 1/4 binary64)) x)
(-.f64 (/.f64 #s(approx (- (* x x) eps) (neg.f64 eps)) (-.f64 (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))) x)) (/.f64 (.f64 x x) (-.f64 (sqrt.f64 #s(approx (- ( x x) eps) (neg.f64 eps))) x)))
(+.f64 (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))) x)
(+.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))))
(*.f64 (pow.f64 (/.f64 x (neg.f64 eps)) #s(literal -1 binary64)) (pow.f64 (neg.f64 x) #s(literal -1 binary64)))
(*.f64 (pow.f64 x #s(literal -1 binary64)) (/.f64 eps x))
(*.f64 (/.f64 (neg.f64 eps) x) (pow.f64 (neg.f64 x) #s(literal -1 binary64)))
(*.f64 (/.f64 eps x) (pow.f64 x #s(literal -1 binary64)))
(*.f64 #s(literal 1 binary64) (/.f64 (/.f64 eps x) x))
(*.f64 eps (pow.f64 x #s(literal -2 binary64)))
(*.f64 eps (/.f64 (pow.f64 x #s(literal -1 binary64)) x))
(pow.f64 (/.f64 (*.f64 (/.f64 x eps) x) #s(literal 1 binary64)) #s(literal -1 binary64))
(pow.f64 (/.f64 (*.f64 x x) eps) #s(literal -1 binary64))
(pow.f64 (*.f64 (/.f64 x eps) x) #s(literal -1 binary64))
(/.f64 (neg.f64 (*.f64 (/.f64 eps x) #s(literal 1 binary64))) (neg.f64 x))
(/.f64 (neg.f64 (.f64 (neg.f64 eps) #s(literal 1 binary64))) (neg.f64 (.f64 (neg.f64 x) x)))
(/.f64 (neg.f64 (.f64 eps #s(literal 1 binary64))) (neg.f64 (.f64 x x)))
(/.f64 (*.f64 (/.f64 eps x) #s(literal 1 binary64)) x)
(/.f64 (neg.f64 (pow.f64 x #s(literal -1 binary64))) (neg.f64 (/.f64 x eps)))
(/.f64 (neg.f64 (neg.f64 eps)) (neg.f64 (*.f64 x (neg.f64 x))))
(/.f64 (neg.f64 (neg.f64 eps)) (neg.f64 (neg.f64 (*.f64 x x))))
(/.f64 (.f64 (neg.f64 eps) #s(literal 1 binary64)) (.f64 (neg.f64 x) x))
(/.f64 (.f64 eps #s(literal 1 binary64)) (.f64 x x))
(/.f64 (pow.f64 x #s(literal -1 binary64)) (/.f64 x eps))
(/.f64 (/.f64 (neg.f64 eps) x) (neg.f64 (neg.f64 (neg.f64 x))))
(/.f64 (/.f64 (neg.f64 eps) x) (neg.f64 x))
(/.f64 (/.f64 eps x) (neg.f64 (neg.f64 x)))
(/.f64 (/.f64 eps x) x)
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (*.f64 (/.f64 x eps) x) #s(literal 1 binary64))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (*.f64 x x) eps)))
(/.f64 #s(literal -1 binary64) (neg.f64 (*.f64 (/.f64 x eps) x)))
(/.f64 #s(literal 1 binary64) (neg.f64 (neg.f64 (*.f64 (/.f64 x eps) x))))
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 (/.f64 x eps) x) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 x x) eps))
(/.f64 #s(literal 1 binary64) (*.f64 (/.f64 x eps) x))
(/.f64 (neg.f64 eps) (neg.f64 (*.f64 x x)))
(/.f64 (neg.f64 eps) (*.f64 x (neg.f64 x)))
(/.f64 eps (*.f64 x x))
(neg.f64 (/.f64 (/.f64 (neg.f64 eps) x) x))
(exp.f64 (.f64 (log.f64 (.f64 (/.f64 x eps) x)) #s(literal -1 binary64)))

eval114.0ms (1.3%)

Memory: 0.1MiB live, 191.2MiB allocated
Compiler: Compiled 27 798 to 3 309 computations (88.1% saved)

prune44.0ms (0.5%)

Memory

0.4MiB live, 84.5MiB allocated

Pruning

17 alts after pruning (8 fresh and 9 done)

	Pruned	Kept	Total
New	712	6	718
Fresh	2	2	4
Picked	1	4	5
Done	0	5	5
Total	715	17	732

Accuracy

100.0%

Counts

732 → 17

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	55.9%	(/.f64 (-.f64 (.f64 x x) #s(approx (- ( x x) eps) (neg.f64 eps))) (+.f64 (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))) x))
	45.1%	(/.f64 #s(literal 1 binary64) #s(approx (pow (- x (sqrt (- (* x x) eps))) -1) (/.f64 (fma.f64 (/.f64 (fma.f64 (/.f64 eps (.f64 x x)) #s(literal -1/8 binary64) #s(literal -1/2 binary64)) x) eps (.f64 #s(literal 2 binary64) x)) eps)))
✓	46.3%	(/.f64 #s(literal 1 binary64) #s(approx (pow (- x (sqrt (- (* x x) eps))) -1) (/.f64 (fma.f64 #s(literal 2 binary64) x (*.f64 (/.f64 eps x) #s(literal -1/2 binary64))) eps)))
	45.1%	(/.f64 #s(literal 1 binary64) #s(approx (pow (- x (sqrt (- (* x x) eps))) -1) (/.f64 (/.f64 (fma.f64 x (/.f64 x (fma.f64 #s(literal -1/8 binary64) (/.f64 (/.f64 eps x) x) #s(literal -1/2 binary64))) (.f64 #s(literal 1/2 binary64) eps)) (.f64 #s(literal 1/2 binary64) (/.f64 x (fma.f64 #s(literal -1/8 binary64) (/.f64 (/.f64 eps x) x) #s(literal -1/2 binary64))))) eps)))
	46.3%	(/.f64 #s(literal 1 binary64) #s(approx (pow (- x (sqrt (- (* x x) eps))) -1) (/.f64 #s(approx (+ (* 2 x) (* (/ eps x) -1/2)) (/.f64 (fma.f64 (.f64 x x) #s(literal 2 binary64) (.f64 #s(literal -1/2 binary64) eps)) x)) eps)))
	45.2%	(/.f64 #s(literal 1 binary64) #s(approx (pow (- x (sqrt (- (* x x) eps))) -1) (/.f64 #s(literal 2 binary64) (/.f64 eps x))))
✓	45.1%	(/.f64 #s(literal 1 binary64) #s(approx (pow (- x (sqrt (- (* x x) eps))) -1) (*.f64 x (/.f64 #s(literal 2 binary64) eps))))
✓	46.3%	(/.f64 #s(literal 1 binary64) #s(approx (pow (- x (sqrt (- (* x x) eps))) -1) #s(approx (/ (+ (* 2 x) (* (/ eps x) -1/2)) eps) (fma.f64 (/.f64 x eps) #s(literal 2 binary64) (/.f64 #s(literal -1/2 binary64) x)))))
	46.3%	(/.f64 #s(literal 1 binary64) #s(approx (pow (- x (sqrt (- (* x x) eps))) -1) #s(approx (/ (+ (* 2 x) (* (/ eps x) -1/2)) eps) (fma.f64 (/.f64 #s(literal 2 binary64) eps) x (/.f64 #s(literal -1/2 binary64) x)))))
	35.2%	(/.f64 #s(literal 1 binary64) #s(approx (pow (- x (sqrt (- (* x x) eps))) -1) #s(approx (/ (+ (* 2 x) (* (/ eps x) -1/2)) eps) (/.f64 (fma.f64 (.f64 #s(literal 2 binary64) x) x (.f64 #s(literal -1/2 binary64) eps)) (*.f64 eps x)))))
✓	61.2%	(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
✓	56.3%	(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))))
✓	7.6%	(-.f64 x #s(approx (sqrt (- (* x x) eps)) (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) x)))
✓	3.5%	(-.f64 x #s(approx (sqrt (- (* x x) eps)) (neg.f64 x)))
	33.5%	#s(approx (/ (- (* x x) (- (* x x) eps)) (+ (sqrt (- (* x x) eps)) x)) (/.f64 (fma.f64 (/.f64 (.f64 eps eps) x) (/.f64 #s(literal 1/8 binary64) x) (fma.f64 (/.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 4 binary64))) #s(literal 1/16 binary64) (.f64 #s(literal 1/2 binary64) eps))) x))
	45.3%	#s(approx (/ 1 (pow (- x (sqrt (- (* x x) eps))) -1)) (/.f64 (*.f64 #s(literal 1/2 binary64) eps) x))
✓	45.1%	#s(approx (/ 1 (pow (- x (sqrt (- (* x x) eps))) -1)) (*.f64 (/.f64 #s(literal 1/2 binary64) x) eps))

Compiler

Compiled 1 318 to 502 computations (61.9% saved)

regimes63.0ms (0.7%)

Memory

-3.2MiB live, 69.1MiB allocated

Counts

36 → 2

Calls

Call 1

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

Outputs

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

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

Calls

3 calls:

22.0ms	x
20.0ms	(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
17.0ms	eps

Results

Accuracy	Segments	Branch
91.1%	2	`x`
80.3%	2	`eps`
98.1%	2	`(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))`

Compiler

Compiled 10 to 10 computations (0% saved)

regimes14.0ms (0.2%)

Memory

17.9MiB live, 17.9MiB allocated

Counts

24 → 2

Calls

Call 1

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

Outputs

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

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

Calls

1 calls:

11.0ms

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

Results

Accuracy	Segments	Branch
98.1%	2	`(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))`

Compiler

Compiled 8 to 6 computations (25% saved)

regimes33.0ms (0.4%)

Memory

-19.6MiB live, 25.7MiB allocated

Counts

17 → 2

Calls

Call 1

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

Outputs

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

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

Calls

1 calls:

31.0ms

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

Results

Accuracy	Segments	Branch
98.1%	2	`(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))`

Compiler

Compiled 8 to 6 computations (25% saved)

regimes8.0ms (0.1%)

Memory

11.5MiB live, 11.5MiB allocated

Counts

13 → 2

Calls

Call 1

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

Outputs

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

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

Calls

1 calls:

7.0ms

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

Results

Accuracy	Segments	Branch
98.0%	2	`(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))`

Compiler

Compiled 8 to 6 computations (25% saved)

regimes13.0ms (0.1%)

Memory

-26.3MiB live, 10.8MiB allocated

Counts

12 → 2

Calls

Call 1

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

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

Calls

1 calls:

12.0ms

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

Results

Accuracy	Segments	Branch
97.8%	2	`(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))`

Compiler

Compiled 8 to 6 computations (25% saved)

regimes5.0ms (0.1%)

Memory

7.7MiB live, 7.7MiB allocated

Counts

7 → 2

Calls

Call 1

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

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

Calls

1 calls:

5.0ms

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

Results

Accuracy	Segments	Branch
95.3%	2	`(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))`

Compiler

Compiled 8 to 6 computations (25% saved)

regimes4.0ms (0%)

Memory

6.0MiB live, 6.0MiB allocated

Counts

4 → 2

Calls

Call 1

Inputs
(-.f64 x #s(approx (sqrt (- (* x x) eps)) (neg.f64 x)))
(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))))
#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (/.f64 #s(literal 1/2 binary64) x) eps))
#s(approx (/ 1 (pow (- x (sqrt (- (* x x) eps))) -1)) (*.f64 (/.f64 #s(literal 1/2 binary64) x) eps))

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

Calls

1 calls:

3.0ms

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

Results

Accuracy	Segments	Branch
95.1%	2	`(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))`

Compiler

Compiled 8 to 6 computations (25% saved)

regimes8.0ms (0.1%)

Memory

12.6MiB live, 12.6MiB allocated

Counts

2 → 1

Calls

Call 1

Inputs
(-.f64 x #s(approx (sqrt (- (* x x) eps)) (neg.f64 x)))
(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))))

Outputs
(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))))

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
56.3%	1	`eps`
56.3%	1	`x`
56.3%	1	`(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))`

Compiler

Compiled 10 to 10 computations (0% saved)

regimes11.0ms (0.1%)

Memory

-26.9MiB live, 11.1MiB allocated

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts

1 → 1

Calls

Call 1

Inputs
(-.f64 x #s(approx (sqrt (- (* x x) eps)) (neg.f64 x)))

Outputs
(-.f64 x #s(approx (sqrt (- (* x x) eps)) (neg.f64 x)))

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
3.5%	1	`eps`
3.5%	1	`x`
3.5%	1	`(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))`

Compiler

Compiled 10 to 10 computations (0% saved)

bsearch1.0ms (0%)

Memory

1.1MiB live, 1.1MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	-5.601400324460028e-153	0.0

Compiler

Compiled 11 to 11 computations (0% saved)

bsearch1.0ms (0%)

Memory

0.8MiB live, 0.8MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	-5.601400324460028e-153	0.0

Compiler

Compiled 11 to 11 computations (0% saved)

bsearch1.0ms (0%)

Memory

0.9MiB live, 0.9MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	-5.601400324460028e-153	0.0

Compiler

Compiled 11 to 11 computations (0% saved)

bsearch1.0ms (0%)

Memory

0.7MiB live, 0.7MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	-5.601400324460028e-153	0.0

Compiler

Compiled 11 to 11 computations (0% saved)

bsearch1.0ms (0%)

Memory

0.8MiB live, 0.8MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	-5.601400324460028e-153	0.0

Compiler

Compiled 11 to 11 computations (0% saved)

bsearch1.0ms (0%)

Memory

0.7MiB live, 0.7MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	-5.601400324460028e-153	0.0

Compiler

Compiled 11 to 11 computations (0% saved)

bsearch1.0ms (0%)

Memory

0.7MiB live, 0.7MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	-5.601400324460028e-153	0.0

Compiler

Compiled 11 to 11 computations (0% saved)

simplify78.0ms (0.9%)

Memory

10.2MiB live, 48.1MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	70	330
1	98	322
2	124	322
3	166	322
4	221	322
5	348	322
6	501	322
7	2073	322
8	5962	322

Stop Event

1×	node limit

Calls

Call 1

Inputs
(if (<=.f64 (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) #s(literal -4717453031026927/943490606205385338060388645247067222729230305104110107094051575061406040598037213021531681294414691885367093757690961224942646157481198158140358562858174010912348831744 binary64)) (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) (/.f64 #s(literal 1 binary64) #s(approx (pow (- x (sqrt (- (* x x) eps))) -1) (/.f64 (fma.f64 (/.f64 (fma.f64 (/.f64 eps (.f64 x x)) #s(literal -1/8 binary64) #s(literal -1/2 binary64)) x) eps (.f64 #s(literal 2 binary64) x)) eps))))
(if (<=.f64 (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) #s(literal -4717453031026927/943490606205385338060388645247067222729230305104110107094051575061406040598037213021531681294414691885367093757690961224942646157481198158140358562858174010912348831744 binary64)) (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) (/.f64 #s(literal 1 binary64) #s(approx (pow (- x (sqrt (- (* x x) eps))) -1) (/.f64 (fma.f64 #s(literal 2 binary64) x (*.f64 (/.f64 eps x) #s(literal -1/2 binary64))) eps))))
(if (<=.f64 (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) #s(literal -4717453031026927/943490606205385338060388645247067222729230305104110107094051575061406040598037213021531681294414691885367093757690961224942646157481198158140358562858174010912348831744 binary64)) (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) (/.f64 #s(literal 1 binary64) #s(approx (pow (- x (sqrt (- (* x x) eps))) -1) #s(approx (/ (+ (* 2 x) (* (/ eps x) -1/2)) eps) (fma.f64 (/.f64 x eps) #s(literal 2 binary64) (/.f64 #s(literal -1/2 binary64) x))))))
(if (<=.f64 (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) #s(literal -4717453031026927/943490606205385338060388645247067222729230305104110107094051575061406040598037213021531681294414691885367093757690961224942646157481198158140358562858174010912348831744 binary64)) (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) (/.f64 #s(literal 1 binary64) #s(approx (pow (- x (sqrt (- (* x x) eps))) -1) #s(approx (/ (+ (* 2 x) (* (/ eps x) -1/2)) eps) (fma.f64 (/.f64 #s(literal 2 binary64) eps) x (/.f64 #s(literal -1/2 binary64) x))))))
(if (<=.f64 (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) #s(literal -4717453031026927/943490606205385338060388645247067222729230305104110107094051575061406040598037213021531681294414691885367093757690961224942646157481198158140358562858174010912348831744 binary64)) (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) #s(approx (/ 1 (pow (- x (sqrt (- (* x x) eps))) -1)) (/.f64 (*.f64 #s(literal 1/2 binary64) eps) x)))
(if (<=.f64 (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) #s(literal -4717453031026927/943490606205385338060388645247067222729230305104110107094051575061406040598037213021531681294414691885367093757690961224942646157481198158140358562858174010912348831744 binary64)) (-.f64 x (sqrt.f64 #s(approx (- ( x x) eps) (neg.f64 eps)))) #s(approx (/ 1 (pow (- x (sqrt (- (* x x) eps))) -1)) (/.f64 (*.f64 #s(literal 1/2 binary64) eps) x)))
(if (<=.f64 (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) #s(literal -4717453031026927/943490606205385338060388645247067222729230305104110107094051575061406040598037213021531681294414691885367093757690961224942646157481198158140358562858174010912348831744 binary64)) (-.f64 x (sqrt.f64 #s(approx (- ( x x) eps) (neg.f64 eps)))) #s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (/.f64 #s(literal 1/2 binary64) x) eps)))
(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))))
(-.f64 x #s(approx (sqrt (- (* x x) eps)) (neg.f64 x)))

Outputs
(if (<=.f64 (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) #s(literal -4717453031026927/943490606205385338060388645247067222729230305104110107094051575061406040598037213021531681294414691885367093757690961224942646157481198158140358562858174010912348831744 binary64)) (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) (/.f64 #s(literal 1 binary64) #s(approx (pow (- x (sqrt (- (* x x) eps))) -1) (/.f64 (fma.f64 (/.f64 (fma.f64 (/.f64 eps (.f64 x x)) #s(literal -1/8 binary64) #s(literal -1/2 binary64)) x) eps (.f64 #s(literal 2 binary64) x)) eps))))
(if (<=.f64 (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) #s(literal -4717453031026927/943490606205385338060388645247067222729230305104110107094051575061406040598037213021531681294414691885367093757690961224942646157481198158140358562858174010912348831744 binary64)) (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) (pow.f64 #s(approx (pow (- x (sqrt (- (* x x) eps))) -1) (/.f64 (fma.f64 (/.f64 (fma.f64 (/.f64 eps (.f64 x x)) #s(literal -1/8 binary64) #s(literal -1/2 binary64)) x) eps (.f64 #s(literal 2 binary64) x)) eps)) #s(literal -1 binary64)))
(if (<=.f64 (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) #s(literal -4717453031026927/943490606205385338060388645247067222729230305104110107094051575061406040598037213021531681294414691885367093757690961224942646157481198158140358562858174010912348831744 binary64)) (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) (/.f64 #s(literal 1 binary64) #s(approx (pow (- x (sqrt (- (* x x) eps))) -1) (/.f64 (fma.f64 #s(literal 2 binary64) x (*.f64 (/.f64 eps x) #s(literal -1/2 binary64))) eps))))
(if (<=.f64 (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) #s(literal -4717453031026927/943490606205385338060388645247067222729230305104110107094051575061406040598037213021531681294414691885367093757690961224942646157481198158140358562858174010912348831744 binary64)) (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) (pow.f64 #s(approx (pow (- x (sqrt (- (* x x) eps))) -1) (/.f64 (fma.f64 #s(literal 2 binary64) x (*.f64 (/.f64 eps x) #s(literal -1/2 binary64))) eps)) #s(literal -1 binary64)))
(if (<=.f64 (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) #s(literal -4717453031026927/943490606205385338060388645247067222729230305104110107094051575061406040598037213021531681294414691885367093757690961224942646157481198158140358562858174010912348831744 binary64)) (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) (/.f64 #s(literal 1 binary64) #s(approx (pow (- x (sqrt (- (* x x) eps))) -1) #s(approx (/ (+ (* 2 x) (* (/ eps x) -1/2)) eps) (fma.f64 (/.f64 x eps) #s(literal 2 binary64) (/.f64 #s(literal -1/2 binary64) x))))))
(if (<=.f64 (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) #s(literal -4717453031026927/943490606205385338060388645247067222729230305104110107094051575061406040598037213021531681294414691885367093757690961224942646157481198158140358562858174010912348831744 binary64)) (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) (pow.f64 #s(approx (pow (- x (sqrt (- (* x x) eps))) -1) #s(approx (/ (+ (* 2 x) (* (/ eps x) -1/2)) eps) (fma.f64 (/.f64 x eps) #s(literal 2 binary64) (/.f64 #s(literal -1/2 binary64) x)))) #s(literal -1 binary64)))
(if (<=.f64 (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) #s(literal -4717453031026927/943490606205385338060388645247067222729230305104110107094051575061406040598037213021531681294414691885367093757690961224942646157481198158140358562858174010912348831744 binary64)) (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) (/.f64 #s(literal 1 binary64) #s(approx (pow (- x (sqrt (- (* x x) eps))) -1) #s(approx (/ (+ (* 2 x) (* (/ eps x) -1/2)) eps) (fma.f64 (/.f64 #s(literal 2 binary64) eps) x (/.f64 #s(literal -1/2 binary64) x))))))
(if (<=.f64 (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) #s(literal -4717453031026927/943490606205385338060388645247067222729230305104110107094051575061406040598037213021531681294414691885367093757690961224942646157481198158140358562858174010912348831744 binary64)) (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) (pow.f64 #s(approx (pow (- x (sqrt (- (* x x) eps))) -1) #s(approx (/ (+ (* 2 x) (* (/ eps x) -1/2)) eps) (fma.f64 (/.f64 #s(literal 2 binary64) eps) x (/.f64 #s(literal -1/2 binary64) x)))) #s(literal -1 binary64)))
(if (<=.f64 (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) #s(literal -4717453031026927/943490606205385338060388645247067222729230305104110107094051575061406040598037213021531681294414691885367093757690961224942646157481198158140358562858174010912348831744 binary64)) (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) #s(approx (/ 1 (pow (- x (sqrt (- (* x x) eps))) -1)) (/.f64 (*.f64 #s(literal 1/2 binary64) eps) x)))
(if (<=.f64 (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) #s(literal -4717453031026927/943490606205385338060388645247067222729230305104110107094051575061406040598037213021531681294414691885367093757690961224942646157481198158140358562858174010912348831744 binary64)) (-.f64 x (sqrt.f64 #s(approx (- ( x x) eps) (neg.f64 eps)))) #s(approx (/ 1 (pow (- x (sqrt (- (* x x) eps))) -1)) (/.f64 (*.f64 #s(literal 1/2 binary64) eps) x)))
(if (<=.f64 (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) #s(literal -4717453031026927/943490606205385338060388645247067222729230305104110107094051575061406040598037213021531681294414691885367093757690961224942646157481198158140358562858174010912348831744 binary64)) (-.f64 x (sqrt.f64 #s(approx (- ( x x) eps) (neg.f64 eps)))) #s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (/.f64 #s(literal 1/2 binary64) x) eps)))
(if (<=.f64 (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) #s(literal -4717453031026927/943490606205385338060388645247067222729230305104110107094051575061406040598037213021531681294414691885367093757690961224942646157481198158140358562858174010912348831744 binary64)) (-.f64 x (sqrt.f64 #s(approx (- ( x x) eps) (neg.f64 eps)))) #s(approx (/ 1 (pow (- x (sqrt (- (* x x) eps))) -1)) (*.f64 (/.f64 #s(literal 1/2 binary64) x) eps)))
(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))))
(-.f64 x #s(approx (sqrt (- (* x x) eps)) (neg.f64 x)))

soundness901.0ms (10.2%)

Memory

-42.7MiB live, 587.8MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	48	313
0	74	311
1	290	309
2	2067	309
0	8172	306
0	257	1067
1	784	1053
2	2629	1015
3	7085	1012
0	8084	948
0	462	1990
1	1420	1882
2	4872	1853
0	8120	1750
0	508	2547
1	1559	2433
2	5439	2399
0	8389	2273
0	6	22
0	10	22
1	42	22
2	310	22
3	3602	22
0	8540	22

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

Compiler

Compiled 630 to 283 computations (55.1% saved)

preprocess184.0ms (2.1%)

Memory: 30.1MiB live, 68.2MiB allocated
Compiler: Compiled 704 to 172 computations (75.6% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

Iter	Nodes	Cost
0	18	46
1	43	44
2	118	41
3	280	41
4	498	41
5	572	41
6	586	41
0	6	8
0	10	8
1	14	8
2	22	8
3	34	8
4	52	8
5	96	8
6	163	8
7	213	8
8	301	8
9	333	8
10	349	8
0	349	8

Iter	Nodes	Cost
0	6	24
0	10	24
1	14	24
2	22	24
3	34	24
4	52	24
5	96	24
6	163	24
7	213	24
8	301	24
9	333	24
10	349	24
0	349	24

Iter	Nodes	Cost
0	18	46
1	43	44
2	118	41
3	280	41
4	498	41
5	572	41
6	586	41
0	6	8
0	10	8
1	14	8
2	22	8
3	34	8
4	52	8
5	96	8
6	163	8
7	213	8
8	301	8
9	333	8
10	349	8
0	349	8

Iter	Nodes	Cost
0	6	24
0	10	24
1	14	24
2	22	24
3	34	24
4	52	24
5	96	24
6	163	24
7	213	24
8	301	24
9	333	24
10	349	24
0	349	24

start0.0ms (0%)

analyze43.0ms (0.5%)

sample1.7s (19.2%)

explain110.0ms (1.2%)

preprocess40.0ms (0.5%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify9.0ms (0.1%)

localize28.0ms (0.3%)

series8.0ms (0.1%)

simplify245.0ms (2.8%)

rewrite203.0ms (2.3%)

eval56.0ms (0.6%)

prune34.0ms (0.4%)

simplify109.0ms (1.2%)

localize149.0ms (1.7%)

series48.0ms (0.5%)

simplify161.0ms (1.8%)

rewrite240.0ms (2.7%)

eval173.0ms (1.9%)

prune22.0ms (0.2%)

simplify290.0ms (3.3%)

localize173.0ms (1.9%)

series372.0ms (4.2%)

simplify951.0ms (10.7%)

rewrite973.0ms (11%)

eval267.0ms (3%)

prune19.0ms (0.2%)

simplify339.0ms (3.8%)

localize267.0ms (3%)

series32.0ms (0.4%)

simplify176.0ms (2%)

rewrite148.0ms (1.7%)

eval114.0ms (1.3%)

prune44.0ms (0.5%)

regimes63.0ms (0.7%)

regimes14.0ms (0.2%)

regimes33.0ms (0.4%)

regimes8.0ms (0.1%)

regimes13.0ms (0.1%)

regimes5.0ms (0.1%)

regimes4.0ms (0%)

regimes8.0ms (0.1%)

regimes11.0ms (0.1%)

bsearch1.0ms (0%)

bsearch1.0ms (0%)

bsearch1.0ms (0%)

bsearch1.0ms (0%)

bsearch1.0ms (0%)

bsearch1.0ms (0%)

bsearch1.0ms (0%)

simplify78.0ms (0.9%)

soundness901.0ms (10.2%)

preprocess184.0ms (2.1%)

end0.0ms (0%)

Profiling

Iter	Nodes	Cost
0	18	46
1	43	44
2	118	41
3	280	41
4	498	41
5	572	41
6	586	41
0	6	8
0	10	8
1	14	8
2	22	8
3	34	8
4	52	8
5	96	8
6	163	8
7	213	8
8	301	8
9	333	8
10	349	8
0	349	8

Iter	Nodes	Cost
0	6	24
0	10	24
1	14	24
2	22	24
3	34	24
4	52	24
5	96	24
6	163	24
7	213	24
8	301	24
9	333	24
10	349	24
0	349	24