Numeric.LinearAlgebra.Util:formatSparse from hmatrix-0.16.1.5

Percentage Accurate: 100.0% → 100.0%

Time: 4.5s

Alternatives: 5

Speedup: 2.0×

Specification

Math

\[\begin{array}{l} \\ \frac{\left|x - y\right|}{\left|y\right|} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (/ (fabs (- x y)) (fabs y)))

C

double code(double x, double y) {
	return fabs((x - y)) / fabs(y);
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = abs((x - y)) / abs(y)
end function

Java

public static double code(double x, double y) {
	return Math.abs((x - y)) / Math.abs(y);
}

Python

def code(x, y):
	return math.fabs((x - y)) / math.fabs(y)

Julia

function code(x, y)
	return Float64(abs(Float64(x - y)) / abs(y))
end

MATLAB

function tmp = code(x, y)
	tmp = abs((x - y)) / abs(y);
end

Wolfram

code[x_, y_] := N[(N[Abs[N[(x - y), $MachinePrecision]], $MachinePrecision] / N[Abs[y], $MachinePrecision]), $MachinePrecision]

Initial Program: 100.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{\left|x - y\right|}{\left|y\right|} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (/ (fabs (- x y)) (fabs y)))

C

double code(double x, double y) {
	return fabs((x - y)) / fabs(y);
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = abs((x - y)) / abs(y)
end function

Java

public static double code(double x, double y) {
	return Math.abs((x - y)) / Math.abs(y);
}

Python

def code(x, y):
	return math.fabs((x - y)) / math.fabs(y)

Julia

function code(x, y)
	return Float64(abs(Float64(x - y)) / abs(y))
end

MATLAB

function tmp = code(x, y)
	tmp = abs((x - y)) / abs(y);
end

Wolfram

code[x_, y_] := N[(N[Abs[N[(x - y), $MachinePrecision]], $MachinePrecision] / N[Abs[y], $MachinePrecision]), $MachinePrecision]

Alternative 1: 100.0% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \left|\frac{x}{y} + -1\right| \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (fabs (+ (/ x y) -1.0)))

C

double code(double x, double y) {
	return fabs(((x / y) + -1.0));
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = abs(((x / y) + (-1.0d0)))
end function

Java

public static double code(double x, double y) {
	return Math.abs(((x / y) + -1.0));
}

Python

def code(x, y):
	return math.fabs(((x / y) + -1.0))

Julia

function code(x, y)
	return abs(Float64(Float64(x / y) + -1.0))
end

MATLAB

function tmp = code(x, y)
	tmp = abs(((x / y) + -1.0));
end

Wolfram

code[x_, y_] := N[Abs[N[(N[(x / y), $MachinePrecision] + -1.0), $MachinePrecision]], $MachinePrecision]

Derivation

1. Initial program 100.0%

   \[\frac{\left|x - y\right|}{\left|y\right|} \]
2. Add Preprocessing

3. Taylor expanded in x around -inf 100.0%

   \[\leadsto \color{blue}{\frac{\left|-\left(y + -1 \cdot x\right)\right|}{\left|y\right|}} \]

5. Simplified 100.0%

   \[\leadsto \color{blue}{\left|\frac{x}{y} + -1\right|} \]
6. Add Preprocessing

Alternative 2: 75.2% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.9 \cdot 10^{-11}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{-71}:\\ \;\;\;\;\left|\frac{x}{y}\right|\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -2.9e-11) 1.0 (if (<= y 1.15e-71) (fabs (/ x y)) 1.0)))

C

double code(double x, double y) {
	double tmp;
	if (y <= -2.9e-11) {
		tmp = 1.0;
	} else if (y <= 1.15e-71) {
		tmp = fabs((x / y));
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (y <= (-2.9d-11)) then
        tmp = 1.0d0
    else if (y <= 1.15d-71) then
        tmp = abs((x / y))
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -2.9e-11) {
		tmp = 1.0;
	} else if (y <= 1.15e-71) {
		tmp = Math.abs((x / y));
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -2.9e-11:
		tmp = 1.0
	elif y <= 1.15e-71:
		tmp = math.fabs((x / y))
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -2.9e-11)
		tmp = 1.0;
	elseif (y <= 1.15e-71)
		tmp = abs(Float64(x / y));
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -2.9e-11)
		tmp = 1.0;
	elseif (y <= 1.15e-71)
		tmp = abs((x / y));
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -2.9e-11], 1.0, If[LessEqual[y, 1.15e-71], N[Abs[N[(x / y), $MachinePrecision]], $MachinePrecision], 1.0]]

Derivation

1. Split input into 2 regimes

2. if y < -2.9e-11 or 1.1499999999999999e-71 < y

   1. Initial program 100.0%

      \[\frac{\left|x - y\right|}{\left|y\right|} \]
   2. Add Preprocessing

   3. Taylor expanded in x around -inf 100.0%

      \[\leadsto \color{blue}{\frac{\left|-\left(y + -1 \cdot x\right)\right|}{\left|y\right|}} \]

   5. Simplified 100.0%

      \[\leadsto \color{blue}{\left|\frac{x}{y} + -1\right|} \]

   6. Taylor expanded in x around inf 25.4%

      \[\leadsto \left|\color{blue}{\frac{x}{y}}\right| \]

   8. Applied egg-rr 38.4%

      \[\leadsto \color{blue}{\frac{\sqrt{x}}{\sqrt{x}}} \]
   9. Step-by-step derivation

      1. *-inverses 78.4%

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

   10. Simplified 78.4%

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

   if -2.9e-11 < y < 1.1499999999999999e-71

   1. Initial program 100.0%

      \[\frac{\left|x - y\right|}{\left|y\right|} \]
   2. Add Preprocessing

   3. Taylor expanded in x around -inf 100.0%

      \[\leadsto \color{blue}{\frac{\left|-\left(y + -1 \cdot x\right)\right|}{\left|y\right|}} \]

   5. Simplified 100.0%

      \[\leadsto \color{blue}{\left|\frac{x}{y} + -1\right|} \]

   6. Taylor expanded in x around inf 84.5%

      \[\leadsto \left|\color{blue}{\frac{x}{y}}\right| \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 3: 60.5% accurate, 9.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.5 \cdot 10^{-66}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 1.85 \cdot 10^{-212}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{+58}:\\ \;\;\;\;1 + x \cdot \left(x + -2\right)\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -1.5e-66)
   1.0
   (if (<= y 1.85e-212)
     (/ x y)
     (if (<= y 1.15e+58) (+ 1.0 (* x (+ x -2.0))) 1.0))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -1.5e-66) {
		tmp = 1.0;
	} else if (y <= 1.85e-212) {
		tmp = x / y;
	} else if (y <= 1.15e+58) {
		tmp = 1.0 + (x * (x + -2.0));
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (y <= (-1.5d-66)) then
        tmp = 1.0d0
    else if (y <= 1.85d-212) then
        tmp = x / y
    else if (y <= 1.15d+58) then
        tmp = 1.0d0 + (x * (x + (-2.0d0)))
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -1.5e-66) {
		tmp = 1.0;
	} else if (y <= 1.85e-212) {
		tmp = x / y;
	} else if (y <= 1.15e+58) {
		tmp = 1.0 + (x * (x + -2.0));
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -1.5e-66:
		tmp = 1.0
	elif y <= 1.85e-212:
		tmp = x / y
	elif y <= 1.15e+58:
		tmp = 1.0 + (x * (x + -2.0))
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -1.5e-66)
		tmp = 1.0;
	elseif (y <= 1.85e-212)
		tmp = Float64(x / y);
	elseif (y <= 1.15e+58)
		tmp = Float64(1.0 + Float64(x * Float64(x + -2.0)));
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -1.5e-66)
		tmp = 1.0;
	elseif (y <= 1.85e-212)
		tmp = x / y;
	elseif (y <= 1.15e+58)
		tmp = 1.0 + (x * (x + -2.0));
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -1.5e-66], 1.0, If[LessEqual[y, 1.85e-212], N[(x / y), $MachinePrecision], If[LessEqual[y, 1.15e+58], N[(1.0 + N[(x * N[(x + -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 1.0]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.5000000000000001e-66 or 1.15000000000000001e58 < y

   1. Initial program 100.0%

      \[\frac{\left|x - y\right|}{\left|y\right|} \]
   2. Add Preprocessing

   3. Taylor expanded in x around -inf 100.0%

      \[\leadsto \color{blue}{\frac{\left|-\left(y + -1 \cdot x\right)\right|}{\left|y\right|}} \]

   5. Simplified 100.0%

      \[\leadsto \color{blue}{\left|\frac{x}{y} + -1\right|} \]

   6. Taylor expanded in x around inf 25.6%

      \[\leadsto \left|\color{blue}{\frac{x}{y}}\right| \]

   8. Applied egg-rr 40.9%

      \[\leadsto \color{blue}{\frac{\sqrt{x}}{\sqrt{x}}} \]
   9. Step-by-step derivation

      1. *-inverses 78.1%

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

   10. Simplified 78.1%

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

   if -1.5000000000000001e-66 < y < 1.84999999999999995e-212

   1. Initial program 100.0%

      \[\frac{\left|x - y\right|}{\left|y\right|} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. div-inv 99.7%

         \[\leadsto \color{blue}{\left|x - y\right| \cdot \frac{1}{\left|y\right|}} \]

      2. add-sqr-sqrt 44.1%

         \[\leadsto \left|\color{blue}{\sqrt{x - y} \cdot \sqrt{x - y}}\right| \cdot \frac{1}{\left|y\right|} \]

      3. fabs-sqr 44.1%

         \[\leadsto \color{blue}{\left(\sqrt{x - y} \cdot \sqrt{x - y}\right)} \cdot \frac{1}{\left|y\right|} \]

      4. add-sqr-sqrt 44.6%

         \[\leadsto \color{blue}{\left(x - y\right)} \cdot \frac{1}{\left|y\right|} \]

      5. *-commutative 44.6%

         \[\leadsto \color{blue}{\frac{1}{\left|y\right|} \cdot \left(x - y\right)} \]

      6. add-sqr-sqrt 15.9%

         \[\leadsto \frac{1}{\left|\color{blue}{\sqrt{y} \cdot \sqrt{y}}\right|} \cdot \left(x - y\right) \]

      7. fabs-sqr 15.9%

         \[\leadsto \frac{1}{\color{blue}{\sqrt{y} \cdot \sqrt{y}}} \cdot \left(x - y\right) \]

      8. add-sqr-sqrt 58.9%

         \[\leadsto \frac{1}{\color{blue}{y}} \cdot \left(x - y\right) \]

   4. Applied egg-rr 58.9%

      \[\leadsto \color{blue}{\frac{1}{y} \cdot \left(x - y\right)} \]

   5. Taylor expanded in x around inf 59.2%

      \[\leadsto \frac{1}{y} \cdot \color{blue}{x} \]

   6. Taylor expanded in y around 0 59.3%

      \[\leadsto \color{blue}{\frac{x}{y}} \]

   if 1.84999999999999995e-212 < y < 1.15000000000000001e58

   1. Initial program 100.0%

      \[\frac{\left|x - y\right|}{\left|y\right|} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. add-sqr-sqrt 29.1%

         \[\leadsto \frac{\left|\color{blue}{\sqrt{x - y} \cdot \sqrt{x - y}}\right|}{\left|y\right|} \]

      2. fabs-sqr 29.1%

         \[\leadsto \frac{\color{blue}{\sqrt{x - y} \cdot \sqrt{x - y}}}{\left|y\right|} \]

      3. add-sqr-sqrt 28.9%

         \[\leadsto \frac{\sqrt{x - y} \cdot \sqrt{x - y}}{\left|\color{blue}{\sqrt{y} \cdot \sqrt{y}}\right|} \]

      4. fabs-sqr 28.9%

         \[\leadsto \frac{\sqrt{x - y} \cdot \sqrt{x - y}}{\color{blue}{\sqrt{y} \cdot \sqrt{y}}} \]

      5. add-sqr-sqrt 29.1%

         \[\leadsto \frac{\sqrt{x - y} \cdot \sqrt{x - y}}{\color{blue}{y}} \]

      6. add-sqr-sqrt 29.9%

         \[\leadsto \frac{\color{blue}{x - y}}{y} \]

      7. div-sub 29.9%

         \[\leadsto \color{blue}{\frac{x}{y} - \frac{y}{y}} \]

   4. Applied egg-rr 29.9%

      \[\leadsto \color{blue}{\frac{x}{y} - \frac{y}{y}} \]

   5. Taylor expanded in y around 0 29.9%

      \[\leadsto \frac{x}{y} - \color{blue}{1} \]

   7. Applied egg-rr 51.3%

      \[\leadsto \color{blue}{\left(x + -1\right) \cdot \left(x + -1\right)} \]
   8. Step-by-step derivation

      1. distribute-lft-in 51.3%

         \[\leadsto \color{blue}{\left(x + -1\right) \cdot x + \left(x + -1\right) \cdot -1} \]

      2. *-commutative 51.3%

         \[\leadsto \left(x + -1\right) \cdot x + \color{blue}{-1 \cdot \left(x + -1\right)} \]

      3. neg-mul-1 51.3%

         \[\leadsto \left(x + -1\right) \cdot x + \color{blue}{\left(-\left(x + -1\right)\right)} \]

      4. distribute-neg-in 51.3%

         \[\leadsto \left(x + -1\right) \cdot x + \color{blue}{\left(\left(-x\right) + \left(--1\right)\right)} \]

      5. metadata-eval 51.3%

         \[\leadsto \left(x + -1\right) \cdot x + \left(\left(-x\right) + \color{blue}{1}\right) \]

      6. associate-+r+ 51.3%

         \[\leadsto \color{blue}{\left(\left(x + -1\right) \cdot x + \left(-x\right)\right) + 1} \]

      7. +-commutative 51.3%

         \[\leadsto \color{blue}{1 + \left(\left(x + -1\right) \cdot x + \left(-x\right)\right)} \]

      8. neg-mul-1 51.3%

         \[\leadsto 1 + \left(\left(x + -1\right) \cdot x + \color{blue}{-1 \cdot x}\right) \]

      9. distribute-rgt-out 51.3%

         \[\leadsto 1 + \color{blue}{x \cdot \left(\left(x + -1\right) + -1\right)} \]

      10. metadata-eval 51.3%

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

      11. associate-+l+ 51.3%

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

      12. associate-+l+ 51.3%

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

      13. metadata-eval 51.3%

          \[\leadsto 1 + x \cdot \left(\left(x + \color{blue}{0}\right) + -2\right) \]

      14. +-rgt-identity 51.3%

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

   9. Simplified 51.3%

      \[\leadsto \color{blue}{1 + x \cdot \left(x + -2\right)} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 4: 59.0% accurate, 15.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.8 \cdot 10^{-64}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 1.0885 \cdot 10^{-89}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -2.8e-64) 1.0 (if (<= y 1.0885e-89) (/ x y) 1.0)))

C

double code(double x, double y) {
	double tmp;
	if (y <= -2.8e-64) {
		tmp = 1.0;
	} else if (y <= 1.0885e-89) {
		tmp = x / y;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (y <= (-2.8d-64)) then
        tmp = 1.0d0
    else if (y <= 1.0885d-89) then
        tmp = x / y
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -2.8e-64) {
		tmp = 1.0;
	} else if (y <= 1.0885e-89) {
		tmp = x / y;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -2.8e-64:
		tmp = 1.0
	elif y <= 1.0885e-89:
		tmp = x / y
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -2.8e-64)
		tmp = 1.0;
	elseif (y <= 1.0885e-89)
		tmp = Float64(x / y);
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -2.8e-64)
		tmp = 1.0;
	elseif (y <= 1.0885e-89)
		tmp = x / y;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -2.8e-64], 1.0, If[LessEqual[y, 1.0885e-89], N[(x / y), $MachinePrecision], 1.0]]

Derivation

1. Split input into 2 regimes

2. if y < -2.80000000000000004e-64 or 1.0885e-89 < y

   1. Initial program 100.0%

      \[\frac{\left|x - y\right|}{\left|y\right|} \]
   2. Add Preprocessing

   3. Taylor expanded in x around -inf 100.0%

      \[\leadsto \color{blue}{\frac{\left|-\left(y + -1 \cdot x\right)\right|}{\left|y\right|}} \]

   5. Simplified 100.0%

      \[\leadsto \color{blue}{\left|\frac{x}{y} + -1\right|} \]

   6. Taylor expanded in x around inf 30.7%

      \[\leadsto \left|\color{blue}{\frac{x}{y}}\right| \]

   8. Applied egg-rr 37.2%

      \[\leadsto \color{blue}{\frac{\sqrt{x}}{\sqrt{x}}} \]
   9. Step-by-step derivation

      1. *-inverses 73.3%

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

   10. Simplified 73.3%

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

   if -2.80000000000000004e-64 < y < 1.0885e-89

   1. Initial program 100.0%

      \[\frac{\left|x - y\right|}{\left|y\right|} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. div-inv 99.8%

         \[\leadsto \color{blue}{\left|x - y\right| \cdot \frac{1}{\left|y\right|}} \]

      2. add-sqr-sqrt 40.5%

         \[\leadsto \left|\color{blue}{\sqrt{x - y} \cdot \sqrt{x - y}}\right| \cdot \frac{1}{\left|y\right|} \]

      3. fabs-sqr 40.5%

         \[\leadsto \color{blue}{\left(\sqrt{x - y} \cdot \sqrt{x - y}\right)} \cdot \frac{1}{\left|y\right|} \]

      4. add-sqr-sqrt 41.0%

         \[\leadsto \color{blue}{\left(x - y\right)} \cdot \frac{1}{\left|y\right|} \]

      5. *-commutative 41.0%

         \[\leadsto \color{blue}{\frac{1}{\left|y\right|} \cdot \left(x - y\right)} \]

      6. add-sqr-sqrt 22.5%

         \[\leadsto \frac{1}{\left|\color{blue}{\sqrt{y} \cdot \sqrt{y}}\right|} \cdot \left(x - y\right) \]

      7. fabs-sqr 22.5%

         \[\leadsto \frac{1}{\color{blue}{\sqrt{y} \cdot \sqrt{y}}} \cdot \left(x - y\right) \]

      8. add-sqr-sqrt 50.3%

         \[\leadsto \frac{1}{\color{blue}{y}} \cdot \left(x - y\right) \]

   4. Applied egg-rr 50.3%

      \[\leadsto \color{blue}{\frac{1}{y} \cdot \left(x - y\right)} \]

   5. Taylor expanded in x around inf 50.6%

      \[\leadsto \frac{1}{y} \cdot \color{blue}{x} \]

   6. Taylor expanded in y around 0 50.7%

      \[\leadsto \color{blue}{\frac{x}{y}} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 5: 51.0% accurate, 205.0× speedup

Math

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

FPCore

(FPCore (x y) :precision binary64 1.0)

C

double code(double x, double y) {
	return 1.0;
}

Fortran

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

Java

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

Python

def code(x, y):
	return 1.0

Julia

function code(x, y)
	return 1.0
end

MATLAB

function tmp = code(x, y)
	tmp = 1.0;
end

Wolfram

code[x_, y_] := 1.0

Derivation

1. Initial program 100.0%

   \[\frac{\left|x - y\right|}{\left|y\right|} \]
2. Add Preprocessing

3. Taylor expanded in x around -inf 100.0%

   \[\leadsto \color{blue}{\frac{\left|-\left(y + -1 \cdot x\right)\right|}{\left|y\right|}} \]

5. Simplified 100.0%

   \[\leadsto \color{blue}{\left|\frac{x}{y} + -1\right|} \]

6. Taylor expanded in x around inf 53.6%

   \[\leadsto \left|\color{blue}{\frac{x}{y}}\right| \]

8. Applied egg-rr 26.3%

   \[\leadsto \color{blue}{\frac{\sqrt{x}}{\sqrt{x}}} \]
9. Step-by-step derivation

   1. *-inverses 50.6%

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

10. Simplified 50.6%

    \[\leadsto \color{blue}{1} \]
11. Add Preprocessing

Reproduce

herbie shell --seed 2024180 
(FPCore (x y)
  :name "Numeric.LinearAlgebra.Util:formatSparse from hmatrix-0.16.1.5"
  :precision binary64
  (/ (fabs (- x y)) (fabs y)))