xlohi (overflows)

Percentage Accurate: 3.1% → 21.4%

Time: 18.1s

Alternatives: 5

Speedup: 7.0×

Specification

\[lo < -1 \cdot 10^{+308} \land hi > 10^{+308}\]

Math

\[\begin{array}{l} \\ \frac{x - lo}{hi - lo} \end{array} \]

FPCore

(FPCore (lo hi x) :precision binary64 (/ (- x lo) (- hi lo)))

C

double code(double lo, double hi, double x) {
	return (x - lo) / (hi - lo);
}

Fortran

real(8) function code(lo, hi, x)
    real(8), intent (in) :: lo
    real(8), intent (in) :: hi
    real(8), intent (in) :: x
    code = (x - lo) / (hi - lo)
end function

Java

public static double code(double lo, double hi, double x) {
	return (x - lo) / (hi - lo);
}

Python

def code(lo, hi, x):
	return (x - lo) / (hi - lo)

Julia

function code(lo, hi, x)
	return Float64(Float64(x - lo) / Float64(hi - lo))
end

MATLAB

function tmp = code(lo, hi, x)
	tmp = (x - lo) / (hi - lo);
end

Wolfram

code[lo_, hi_, x_] := N[(N[(x - lo), $MachinePrecision] / N[(hi - lo), $MachinePrecision]), $MachinePrecision]

Initial Program: 3.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{x - lo}{hi - lo} \end{array} \]

FPCore

(FPCore (lo hi x) :precision binary64 (/ (- x lo) (- hi lo)))

C

double code(double lo, double hi, double x) {
	return (x - lo) / (hi - lo);
}

Fortran

real(8) function code(lo, hi, x)
    real(8), intent (in) :: lo
    real(8), intent (in) :: hi
    real(8), intent (in) :: x
    code = (x - lo) / (hi - lo)
end function

Java

public static double code(double lo, double hi, double x) {
	return (x - lo) / (hi - lo);
}

Python

def code(lo, hi, x):
	return (x - lo) / (hi - lo)

Julia

function code(lo, hi, x)
	return Float64(Float64(x - lo) / Float64(hi - lo))
end

MATLAB

function tmp = code(lo, hi, x)
	tmp = (x - lo) / (hi - lo);
end

Wolfram

code[lo_, hi_, x_] := N[(N[(x - lo), $MachinePrecision] / N[(hi - lo), $MachinePrecision]), $MachinePrecision]

Alternative 1: 21.4% accurate, 0.0× speedup

Math

\[\begin{array}{l} \\ \frac{x}{hi} - \mathsf{expm1}\left(lo \cdot \left(\left(\frac{1}{hi} + -0.5 \cdot \left(lo \cdot {\left(\frac{1}{hi} - \frac{x}{{hi}^{2}}\right)}^{2}\right)\right) - \frac{\frac{x}{hi}}{hi}\right)\right) \end{array} \]

FPCore

(FPCore (lo hi x)
 :precision binary64
 (-
  (/ x hi)
  (expm1
   (*
    lo
    (-
     (+ (/ 1.0 hi) (* -0.5 (* lo (pow (- (/ 1.0 hi) (/ x (pow hi 2.0))) 2.0))))
     (/ (/ x hi) hi))))))

C

double code(double lo, double hi, double x) {
	return (x / hi) - expm1((lo * (((1.0 / hi) + (-0.5 * (lo * pow(((1.0 / hi) - (x / pow(hi, 2.0))), 2.0)))) - ((x / hi) / hi))));
}

Java

public static double code(double lo, double hi, double x) {
	return (x / hi) - Math.expm1((lo * (((1.0 / hi) + (-0.5 * (lo * Math.pow(((1.0 / hi) - (x / Math.pow(hi, 2.0))), 2.0)))) - ((x / hi) / hi))));
}

Python

def code(lo, hi, x):
	return (x / hi) - math.expm1((lo * (((1.0 / hi) + (-0.5 * (lo * math.pow(((1.0 / hi) - (x / math.pow(hi, 2.0))), 2.0)))) - ((x / hi) / hi))))

Julia

function code(lo, hi, x)
	return Float64(Float64(x / hi) - expm1(Float64(lo * Float64(Float64(Float64(1.0 / hi) + Float64(-0.5 * Float64(lo * (Float64(Float64(1.0 / hi) - Float64(x / (hi ^ 2.0))) ^ 2.0)))) - Float64(Float64(x / hi) / hi)))))
end

Wolfram

code[lo_, hi_, x_] := N[(N[(x / hi), $MachinePrecision] - N[(Exp[N[(lo * N[(N[(N[(1.0 / hi), $MachinePrecision] + N[(-0.5 * N[(lo * N[Power[N[(N[(1.0 / hi), $MachinePrecision] - N[(x / N[Power[hi, 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(x / hi), $MachinePrecision] / hi), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]] - 1), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 3.1%

   \[\frac{x - lo}{hi - lo} \]
2. Add Preprocessing

3. Taylor expanded in lo around 0 18.8%

   \[\leadsto \color{blue}{-1 \cdot \left(lo \cdot \left(-1 \cdot \frac{x}{{hi}^{2}} + \frac{1}{hi}\right)\right) + \frac{x}{hi}} \]
4. Step-by-step derivation

   1. +-commutative 18.8%

      \[\leadsto \color{blue}{\frac{x}{hi} + -1 \cdot \left(lo \cdot \left(-1 \cdot \frac{x}{{hi}^{2}} + \frac{1}{hi}\right)\right)} \]

   2. mul-1-neg 18.8%

      \[\leadsto \frac{x}{hi} + \color{blue}{\left(-lo \cdot \left(-1 \cdot \frac{x}{{hi}^{2}} + \frac{1}{hi}\right)\right)} \]

   3. unsub-neg 18.8%

      \[\leadsto \color{blue}{\frac{x}{hi} - lo \cdot \left(-1 \cdot \frac{x}{{hi}^{2}} + \frac{1}{hi}\right)} \]

   4. +-commutative 18.8%

      \[\leadsto \frac{x}{hi} - lo \cdot \color{blue}{\left(\frac{1}{hi} + -1 \cdot \frac{x}{{hi}^{2}}\right)} \]

   5. mul-1-neg 18.8%

      \[\leadsto \frac{x}{hi} - lo \cdot \left(\frac{1}{hi} + \color{blue}{\left(-\frac{x}{{hi}^{2}}\right)}\right) \]

   6. unsub-neg 18.8%

      \[\leadsto \frac{x}{hi} - lo \cdot \color{blue}{\left(\frac{1}{hi} - \frac{x}{{hi}^{2}}\right)} \]

5. Simplified 18.8%

   \[\leadsto \color{blue}{\frac{x}{hi} - lo \cdot \left(\frac{1}{hi} - \frac{x}{{hi}^{2}}\right)} \]
6. Step-by-step derivation

   1. expm1-log1p-u 9.9%

      \[\leadsto \frac{x}{hi} - \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(lo \cdot \left(\frac{1}{hi} - \frac{x}{{hi}^{2}}\right)\right)\right)} \]

   2. expm1-undefine 9.9%

      \[\leadsto \frac{x}{hi} - \color{blue}{\left(e^{\mathsf{log1p}\left(lo \cdot \left(\frac{1}{hi} - \frac{x}{{hi}^{2}}\right)\right)} - 1\right)} \]

   3. div-inv 9.9%

      \[\leadsto \frac{x}{hi} - \left(e^{\mathsf{log1p}\left(lo \cdot \left(\frac{1}{hi} - \color{blue}{x \cdot \frac{1}{{hi}^{2}}}\right)\right)} - 1\right) \]

   4. pow-flip 9.9%

      \[\leadsto \frac{x}{hi} - \left(e^{\mathsf{log1p}\left(lo \cdot \left(\frac{1}{hi} - x \cdot \color{blue}{{hi}^{\left(-2\right)}}\right)\right)} - 1\right) \]

   5. metadata-eval 9.9%

      \[\leadsto \frac{x}{hi} - \left(e^{\mathsf{log1p}\left(lo \cdot \left(\frac{1}{hi} - x \cdot {hi}^{\color{blue}{-2}}\right)\right)} - 1\right) \]

7. Applied egg-rr 9.9%

   \[\leadsto \frac{x}{hi} - \color{blue}{\left(e^{\mathsf{log1p}\left(lo \cdot \left(\frac{1}{hi} - x \cdot {hi}^{-2}\right)\right)} - 1\right)} \]
8. Step-by-step derivation

   1. expm1-define 9.9%

      \[\leadsto \frac{x}{hi} - \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(lo \cdot \left(\frac{1}{hi} - x \cdot {hi}^{-2}\right)\right)\right)} \]

9. Simplified 9.9%

   \[\leadsto \frac{x}{hi} - \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(lo \cdot \left(\frac{1}{hi} - x \cdot {hi}^{-2}\right)\right)\right)} \]

10. Taylor expanded in lo around 0 21.4%

    \[\leadsto \frac{x}{hi} - \mathsf{expm1}\left(\color{blue}{lo \cdot \left(\left(-0.5 \cdot \left(lo \cdot {\left(\frac{1}{hi} - \frac{x}{{hi}^{2}}\right)}^{2}\right) + \frac{1}{hi}\right) - \frac{x}{{hi}^{2}}\right)}\right) \]
11. Step-by-step derivation

    1. *-un-lft-identity 21.4%

       \[\leadsto \frac{x}{hi} - \mathsf{expm1}\left(lo \cdot \left(\left(-0.5 \cdot \left(lo \cdot {\left(\frac{1}{hi} - \frac{x}{{hi}^{2}}\right)}^{2}\right) + \frac{1}{hi}\right) - \frac{\color{blue}{1 \cdot x}}{{hi}^{2}}\right)\right) \]

    2. unpow2 21.4%

       \[\leadsto \frac{x}{hi} - \mathsf{expm1}\left(lo \cdot \left(\left(-0.5 \cdot \left(lo \cdot {\left(\frac{1}{hi} - \frac{x}{{hi}^{2}}\right)}^{2}\right) + \frac{1}{hi}\right) - \frac{1 \cdot x}{\color{blue}{hi \cdot hi}}\right)\right) \]

    3. times-frac 21.4%

       \[\leadsto \frac{x}{hi} - \mathsf{expm1}\left(lo \cdot \left(\left(-0.5 \cdot \left(lo \cdot {\left(\frac{1}{hi} - \frac{x}{{hi}^{2}}\right)}^{2}\right) + \frac{1}{hi}\right) - \color{blue}{\frac{1}{hi} \cdot \frac{x}{hi}}\right)\right) \]

12. Applied egg-rr 21.4%

    \[\leadsto \frac{x}{hi} - \mathsf{expm1}\left(lo \cdot \left(\left(-0.5 \cdot \left(lo \cdot {\left(\frac{1}{hi} - \frac{x}{{hi}^{2}}\right)}^{2}\right) + \frac{1}{hi}\right) - \color{blue}{\frac{1}{hi} \cdot \frac{x}{hi}}\right)\right) \]
13. Step-by-step derivation

    1. associate-*l/ 21.4%

       \[\leadsto \frac{x}{hi} - \mathsf{expm1}\left(lo \cdot \left(\left(-0.5 \cdot \left(lo \cdot {\left(\frac{1}{hi} - \frac{x}{{hi}^{2}}\right)}^{2}\right) + \frac{1}{hi}\right) - \color{blue}{\frac{1 \cdot \frac{x}{hi}}{hi}}\right)\right) \]

    2. *-lft-identity 21.4%

       \[\leadsto \frac{x}{hi} - \mathsf{expm1}\left(lo \cdot \left(\left(-0.5 \cdot \left(lo \cdot {\left(\frac{1}{hi} - \frac{x}{{hi}^{2}}\right)}^{2}\right) + \frac{1}{hi}\right) - \frac{\color{blue}{\frac{x}{hi}}}{hi}\right)\right) \]

14. Simplified 21.4%

    \[\leadsto \frac{x}{hi} - \mathsf{expm1}\left(lo \cdot \left(\left(-0.5 \cdot \left(lo \cdot {\left(\frac{1}{hi} - \frac{x}{{hi}^{2}}\right)}^{2}\right) + \frac{1}{hi}\right) - \color{blue}{\frac{\frac{x}{hi}}{hi}}\right)\right) \]

15. Final simplification 21.4%

    \[\leadsto \frac{x}{hi} - \mathsf{expm1}\left(lo \cdot \left(\left(\frac{1}{hi} + -0.5 \cdot \left(lo \cdot {\left(\frac{1}{hi} - \frac{x}{{hi}^{2}}\right)}^{2}\right)\right) - \frac{\frac{x}{hi}}{hi}\right)\right) \]
16. Add Preprocessing

Alternative 2: 21.4% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \frac{x}{hi} - \mathsf{expm1}\left(\frac{lo}{hi}\right) \end{array} \]

FPCore

(FPCore (lo hi x) :precision binary64 (- (/ x hi) (expm1 (/ lo hi))))

C

double code(double lo, double hi, double x) {
	return (x / hi) - expm1((lo / hi));
}

Java

public static double code(double lo, double hi, double x) {
	return (x / hi) - Math.expm1((lo / hi));
}

Python

def code(lo, hi, x):
	return (x / hi) - math.expm1((lo / hi))

Julia

function code(lo, hi, x)
	return Float64(Float64(x / hi) - expm1(Float64(lo / hi)))
end

Wolfram

code[lo_, hi_, x_] := N[(N[(x / hi), $MachinePrecision] - N[(Exp[N[(lo / hi), $MachinePrecision]] - 1), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 3.1%

   \[\frac{x - lo}{hi - lo} \]
2. Add Preprocessing

3. Taylor expanded in lo around 0 18.8%

   \[\leadsto \color{blue}{-1 \cdot \left(lo \cdot \left(-1 \cdot \frac{x}{{hi}^{2}} + \frac{1}{hi}\right)\right) + \frac{x}{hi}} \]
4. Step-by-step derivation

   1. +-commutative 18.8%

      \[\leadsto \color{blue}{\frac{x}{hi} + -1 \cdot \left(lo \cdot \left(-1 \cdot \frac{x}{{hi}^{2}} + \frac{1}{hi}\right)\right)} \]

   2. mul-1-neg 18.8%

      \[\leadsto \frac{x}{hi} + \color{blue}{\left(-lo \cdot \left(-1 \cdot \frac{x}{{hi}^{2}} + \frac{1}{hi}\right)\right)} \]

   3. unsub-neg 18.8%

      \[\leadsto \color{blue}{\frac{x}{hi} - lo \cdot \left(-1 \cdot \frac{x}{{hi}^{2}} + \frac{1}{hi}\right)} \]

   4. +-commutative 18.8%

      \[\leadsto \frac{x}{hi} - lo \cdot \color{blue}{\left(\frac{1}{hi} + -1 \cdot \frac{x}{{hi}^{2}}\right)} \]

   5. mul-1-neg 18.8%

      \[\leadsto \frac{x}{hi} - lo \cdot \left(\frac{1}{hi} + \color{blue}{\left(-\frac{x}{{hi}^{2}}\right)}\right) \]

   6. unsub-neg 18.8%

      \[\leadsto \frac{x}{hi} - lo \cdot \color{blue}{\left(\frac{1}{hi} - \frac{x}{{hi}^{2}}\right)} \]

5. Simplified 18.8%

   \[\leadsto \color{blue}{\frac{x}{hi} - lo \cdot \left(\frac{1}{hi} - \frac{x}{{hi}^{2}}\right)} \]
6. Step-by-step derivation

   1. expm1-log1p-u 9.9%

      \[\leadsto \frac{x}{hi} - \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(lo \cdot \left(\frac{1}{hi} - \frac{x}{{hi}^{2}}\right)\right)\right)} \]

   2. expm1-undefine 9.9%

      \[\leadsto \frac{x}{hi} - \color{blue}{\left(e^{\mathsf{log1p}\left(lo \cdot \left(\frac{1}{hi} - \frac{x}{{hi}^{2}}\right)\right)} - 1\right)} \]

   3. div-inv 9.9%

      \[\leadsto \frac{x}{hi} - \left(e^{\mathsf{log1p}\left(lo \cdot \left(\frac{1}{hi} - \color{blue}{x \cdot \frac{1}{{hi}^{2}}}\right)\right)} - 1\right) \]

   4. pow-flip 9.9%

      \[\leadsto \frac{x}{hi} - \left(e^{\mathsf{log1p}\left(lo \cdot \left(\frac{1}{hi} - x \cdot \color{blue}{{hi}^{\left(-2\right)}}\right)\right)} - 1\right) \]

   5. metadata-eval 9.9%

      \[\leadsto \frac{x}{hi} - \left(e^{\mathsf{log1p}\left(lo \cdot \left(\frac{1}{hi} - x \cdot {hi}^{\color{blue}{-2}}\right)\right)} - 1\right) \]

7. Applied egg-rr 9.9%

   \[\leadsto \frac{x}{hi} - \color{blue}{\left(e^{\mathsf{log1p}\left(lo \cdot \left(\frac{1}{hi} - x \cdot {hi}^{-2}\right)\right)} - 1\right)} \]
8. Step-by-step derivation

   1. expm1-define 9.9%

      \[\leadsto \frac{x}{hi} - \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(lo \cdot \left(\frac{1}{hi} - x \cdot {hi}^{-2}\right)\right)\right)} \]

9. Simplified 9.9%

   \[\leadsto \frac{x}{hi} - \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(lo \cdot \left(\frac{1}{hi} - x \cdot {hi}^{-2}\right)\right)\right)} \]

10. Taylor expanded in lo around 0 21.4%

    \[\leadsto \frac{x}{hi} - \mathsf{expm1}\left(\color{blue}{lo \cdot \left(\left(-0.5 \cdot \left(lo \cdot {\left(\frac{1}{hi} - \frac{x}{{hi}^{2}}\right)}^{2}\right) + \frac{1}{hi}\right) - \frac{x}{{hi}^{2}}\right)}\right) \]

11. Taylor expanded in hi around inf 21.4%

    \[\leadsto \frac{x}{hi} - \mathsf{expm1}\left(\color{blue}{\frac{lo}{hi}}\right) \]

12. Final simplification 21.4%

    \[\leadsto \frac{x}{hi} - \mathsf{expm1}\left(\frac{lo}{hi}\right) \]
13. Add Preprocessing

Alternative 3: 18.8% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \frac{x - lo}{hi} \end{array} \]

FPCore

(FPCore (lo hi x) :precision binary64 (/ (- x lo) hi))

C

double code(double lo, double hi, double x) {
	return (x - lo) / hi;
}

Fortran

real(8) function code(lo, hi, x)
    real(8), intent (in) :: lo
    real(8), intent (in) :: hi
    real(8), intent (in) :: x
    code = (x - lo) / hi
end function

Java

public static double code(double lo, double hi, double x) {
	return (x - lo) / hi;
}

Python

def code(lo, hi, x):
	return (x - lo) / hi

Julia

function code(lo, hi, x)
	return Float64(Float64(x - lo) / hi)
end

MATLAB

function tmp = code(lo, hi, x)
	tmp = (x - lo) / hi;
end

Wolfram

code[lo_, hi_, x_] := N[(N[(x - lo), $MachinePrecision] / hi), $MachinePrecision]

Derivation

1. Initial program 3.1%

   \[\frac{x - lo}{hi - lo} \]
2. Add Preprocessing

3. Taylor expanded in hi around inf 18.8%

   \[\leadsto \color{blue}{\frac{x - lo}{hi}} \]

4. Final simplification 18.8%

   \[\leadsto \frac{x - lo}{hi} \]
5. Add Preprocessing

Alternative 4: 18.8% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \frac{lo}{-hi} \end{array} \]

FPCore

(FPCore (lo hi x) :precision binary64 (/ lo (- hi)))

C

double code(double lo, double hi, double x) {
	return lo / -hi;
}

Fortran

real(8) function code(lo, hi, x)
    real(8), intent (in) :: lo
    real(8), intent (in) :: hi
    real(8), intent (in) :: x
    code = lo / -hi
end function

Java

public static double code(double lo, double hi, double x) {
	return lo / -hi;
}

Python

def code(lo, hi, x):
	return lo / -hi

Julia

function code(lo, hi, x)
	return Float64(lo / Float64(-hi))
end

MATLAB

function tmp = code(lo, hi, x)
	tmp = lo / -hi;
end

Wolfram

code[lo_, hi_, x_] := N[(lo / (-hi)), $MachinePrecision]

Derivation

1. Initial program 3.1%

   \[\frac{x - lo}{hi - lo} \]
2. Add Preprocessing

3. Taylor expanded in lo around 0 18.8%

   \[\leadsto \color{blue}{-1 \cdot \left(lo \cdot \left(-1 \cdot \frac{x}{{hi}^{2}} + \frac{1}{hi}\right)\right) + \frac{x}{hi}} \]
4. Step-by-step derivation

   1. +-commutative 18.8%

      \[\leadsto \color{blue}{\frac{x}{hi} + -1 \cdot \left(lo \cdot \left(-1 \cdot \frac{x}{{hi}^{2}} + \frac{1}{hi}\right)\right)} \]

   2. mul-1-neg 18.8%

      \[\leadsto \frac{x}{hi} + \color{blue}{\left(-lo \cdot \left(-1 \cdot \frac{x}{{hi}^{2}} + \frac{1}{hi}\right)\right)} \]

   3. unsub-neg 18.8%

      \[\leadsto \color{blue}{\frac{x}{hi} - lo \cdot \left(-1 \cdot \frac{x}{{hi}^{2}} + \frac{1}{hi}\right)} \]

   4. +-commutative 18.8%

      \[\leadsto \frac{x}{hi} - lo \cdot \color{blue}{\left(\frac{1}{hi} + -1 \cdot \frac{x}{{hi}^{2}}\right)} \]

   5. mul-1-neg 18.8%

      \[\leadsto \frac{x}{hi} - lo \cdot \left(\frac{1}{hi} + \color{blue}{\left(-\frac{x}{{hi}^{2}}\right)}\right) \]

   6. unsub-neg 18.8%

      \[\leadsto \frac{x}{hi} - lo \cdot \color{blue}{\left(\frac{1}{hi} - \frac{x}{{hi}^{2}}\right)} \]

5. Simplified 18.8%

   \[\leadsto \color{blue}{\frac{x}{hi} - lo \cdot \left(\frac{1}{hi} - \frac{x}{{hi}^{2}}\right)} \]

6. Taylor expanded in x around 0 18.7%

   \[\leadsto \color{blue}{-1 \cdot \frac{lo}{hi}} \]
7. Step-by-step derivation

   1. neg-mul-1 18.7%

      \[\leadsto \color{blue}{-\frac{lo}{hi}} \]

   2. distribute-neg-frac2 18.7%

      \[\leadsto \color{blue}{\frac{lo}{-hi}} \]

8. Simplified 18.7%

   \[\leadsto \color{blue}{\frac{lo}{-hi}} \]

9. Final simplification 18.7%

   \[\leadsto \frac{lo}{-hi} \]
10. Add Preprocessing

Alternative 5: 18.7% accurate, 7.0× speedup

Math

\[\begin{array}{l} \\ 1 \end{array} \]

FPCore

(FPCore (lo hi x) :precision binary64 1.0)

C

double code(double lo, double hi, double x) {
	return 1.0;
}

Fortran

real(8) function code(lo, hi, x)
    real(8), intent (in) :: lo
    real(8), intent (in) :: hi
    real(8), intent (in) :: x
    code = 1.0d0
end function

Java

public static double code(double lo, double hi, double x) {
	return 1.0;
}

Python

def code(lo, hi, x):
	return 1.0

Julia

function code(lo, hi, x)
	return 1.0
end

MATLAB

function tmp = code(lo, hi, x)
	tmp = 1.0;
end

Wolfram

code[lo_, hi_, x_] := 1.0

Derivation

1. Initial program 3.1%

   \[\frac{x - lo}{hi - lo} \]
2. Add Preprocessing

3. Taylor expanded in lo around inf 18.6%

   \[\leadsto \color{blue}{1} \]

4. Final simplification 18.6%

   \[\leadsto 1 \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2024130 
(FPCore (lo hi x)
  :name "xlohi (overflows)"
  :precision binary64
  :pre (and (< lo -1e+308) (> hi 1e+308))
  (/ (- x lo) (- hi lo)))