Numeric.LinearAlgebra.Util:formatSparse from hmatrix-0.16.1.5

Percentage Accurate: 100.0% → 100.0%

Time: 5.0s

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: 72.2% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7.8 \cdot 10^{+64}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 2.45 \cdot 10^{-141}:\\ \;\;\;\;\left|\frac{x}{y}\right|\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -7.8e+64) 1.0 (if (<= y 2.45e-141) (fabs (/ x y)) 1.0)))

C

double code(double x, double y) {
	double tmp;
	if (y <= -7.8e+64) {
		tmp = 1.0;
	} else if (y <= 2.45e-141) {
		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 <= (-7.8d+64)) then
        tmp = 1.0d0
    else if (y <= 2.45d-141) 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 <= -7.8e+64) {
		tmp = 1.0;
	} else if (y <= 2.45e-141) {
		tmp = Math.abs((x / y));
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -7.8e+64:
		tmp = 1.0
	elif y <= 2.45e-141:
		tmp = math.fabs((x / y))
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -7.8e+64)
		tmp = 1.0;
	elseif (y <= 2.45e-141)
		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 <= -7.8e+64)
		tmp = 1.0;
	elseif (y <= 2.45e-141)
		tmp = abs((x / y));
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -7.8e+64], 1.0, If[LessEqual[y, 2.45e-141], N[Abs[N[(x / y), $MachinePrecision]], $MachinePrecision], 1.0]]

Derivation

1. Split input into 2 regimes

2. if y < -7.7999999999999996e64 or 2.45000000000000003e-141 < 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. Step-by-step derivation

      1. clear-num 99.9%

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

      2. inv-pow 99.9%

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

   7. Applied egg-rr 99.9%

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

   9. Applied egg-rr 77.2%

      \[\leadsto \color{blue}{\frac{x + -1}{x + -1}} \]
   10. Step-by-step derivation

       1. *-inverses 77.2%

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

   11. Simplified 77.2%

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

   if -7.7999999999999996e64 < y < 2.45000000000000003e-141

   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 81.7%

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

Alternative 3: 61.1% accurate, 11.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1260000000000:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -2.7 \cdot 10^{-236}:\\ \;\;\;\;\left(x + -1\right) \cdot \left(x + -1\right)\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{-143}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -1260000000000.0)
   1.0
   (if (<= y -2.7e-236)
     (* (+ x -1.0) (+ x -1.0))
     (if (<= y 2.6e-143) (/ x y) 1.0))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -1260000000000.0) {
		tmp = 1.0;
	} else if (y <= -2.7e-236) {
		tmp = (x + -1.0) * (x + -1.0);
	} else if (y <= 2.6e-143) {
		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 <= (-1260000000000.0d0)) then
        tmp = 1.0d0
    else if (y <= (-2.7d-236)) then
        tmp = (x + (-1.0d0)) * (x + (-1.0d0))
    else if (y <= 2.6d-143) 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 <= -1260000000000.0) {
		tmp = 1.0;
	} else if (y <= -2.7e-236) {
		tmp = (x + -1.0) * (x + -1.0);
	} else if (y <= 2.6e-143) {
		tmp = x / y;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -1260000000000.0:
		tmp = 1.0
	elif y <= -2.7e-236:
		tmp = (x + -1.0) * (x + -1.0)
	elif y <= 2.6e-143:
		tmp = x / y
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -1260000000000.0)
		tmp = 1.0;
	elseif (y <= -2.7e-236)
		tmp = Float64(Float64(x + -1.0) * Float64(x + -1.0));
	elseif (y <= 2.6e-143)
		tmp = Float64(x / y);
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -1260000000000.0)
		tmp = 1.0;
	elseif (y <= -2.7e-236)
		tmp = (x + -1.0) * (x + -1.0);
	elseif (y <= 2.6e-143)
		tmp = x / y;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -1260000000000.0], 1.0, If[LessEqual[y, -2.7e-236], N[(N[(x + -1.0), $MachinePrecision] * N[(x + -1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.6e-143], N[(x / y), $MachinePrecision], 1.0]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.26e12 or 2.59999999999999987e-143 < 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. Step-by-step derivation

      1. clear-num 99.9%

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

      2. inv-pow 99.9%

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

   7. Applied egg-rr 99.9%

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

   9. Applied egg-rr 71.5%

      \[\leadsto \color{blue}{\frac{x + -1}{x + -1}} \]
   10. Step-by-step derivation

       1. *-inverses 71.5%

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

   11. Simplified 71.5%

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

   if -1.26e12 < y < -2.7e-236

   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. Step-by-step derivation

      1. clear-num 99.7%

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

      2. inv-pow 99.7%

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

   7. Applied egg-rr 99.7%

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

   9. Applied egg-rr 46.6%

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

   if -2.7e-236 < y < 2.59999999999999987e-143

   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. Step-by-step derivation

      1. metadata-eval 100.0%

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

      2. *-inverses 100.0%

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

      3. sub-neg 100.0%

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

      4. sub-div 100.0%

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

      5. *-un-lft-identity 100.0%

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

      6. associate-*l/ 99.8%

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

      7. add-sqr-sqrt 57.8%

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

      8. fabs-sqr 57.8%

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

      9. add-sqr-sqrt 58.1%

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

      10. associate-*l/ 58.2%

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

      11. *-un-lft-identity 58.2%

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

      12. sub-div 58.2%

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

      13. frac-sub 31.1%

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

      14. associate-/r* 48.1%

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

      15. distribute-rgt-out-- 48.1%

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

   7. Applied egg-rr 48.1%

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

   8. Taylor expanded in y around 0 58.2%

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

Alternative 4: 58.4% accurate, 15.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7.2 \cdot 10^{-20}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{-143}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -7.2e-20) 1.0 (if (<= y 8.5e-143) (/ x y) 1.0)))

C

double code(double x, double y) {
	double tmp;
	if (y <= -7.2e-20) {
		tmp = 1.0;
	} else if (y <= 8.5e-143) {
		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 <= (-7.2d-20)) then
        tmp = 1.0d0
    else if (y <= 8.5d-143) 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 <= -7.2e-20) {
		tmp = 1.0;
	} else if (y <= 8.5e-143) {
		tmp = x / y;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -7.2e-20:
		tmp = 1.0
	elif y <= 8.5e-143:
		tmp = x / y
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -7.2e-20)
		tmp = 1.0;
	elseif (y <= 8.5e-143)
		tmp = Float64(x / y);
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -7.2e-20)
		tmp = 1.0;
	elseif (y <= 8.5e-143)
		tmp = x / y;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -7.2e-20], 1.0, If[LessEqual[y, 8.5e-143], N[(x / y), $MachinePrecision], 1.0]]

Derivation

1. Split input into 2 regimes

2. if y < -7.19999999999999948e-20 or 8.50000000000000072e-143 < 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. Step-by-step derivation

      1. clear-num 99.9%

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

      2. inv-pow 99.9%

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

   7. Applied egg-rr 99.9%

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

   9. Applied egg-rr 69.3%

      \[\leadsto \color{blue}{\frac{x + -1}{x + -1}} \]
   10. Step-by-step derivation

       1. *-inverses 69.3%

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

   11. Simplified 69.3%

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

   if -7.19999999999999948e-20 < y < 8.50000000000000072e-143

   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. Step-by-step derivation

      1. metadata-eval 100.0%

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

      2. *-inverses 100.0%

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

      3. sub-neg 100.0%

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

      4. sub-div 100.0%

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

      5. *-un-lft-identity 100.0%

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

      6. associate-*l/ 99.7%

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

      7. add-sqr-sqrt 45.4%

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

      8. fabs-sqr 45.4%

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

      9. add-sqr-sqrt 45.9%

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

      10. associate-*l/ 46.0%

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

      11. *-un-lft-identity 46.0%

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

      12. sub-div 46.0%

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

      13. frac-sub 28.6%

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

      14. associate-/r* 40.6%

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

      15. distribute-rgt-out-- 40.6%

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

   7. Applied egg-rr 40.6%

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

   8. Taylor expanded in y around 0 46.5%

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

Alternative 5: 51.8% 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. Step-by-step derivation

   1. clear-num 99.8%

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

   2. inv-pow 99.8%

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

7. Applied egg-rr 99.8%

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

9. Applied egg-rr 50.4%

   \[\leadsto \color{blue}{\frac{x + -1}{x + -1}} \]
10. Step-by-step derivation

    1. *-inverses 50.4%

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

11. Simplified 50.4%

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

Reproduce

herbie shell --seed 2024177 
(FPCore (x y)
  :name "Numeric.LinearAlgebra.Util:formatSparse from hmatrix-0.16.1.5"
  :precision binary64
  (/ (fabs (- x y)) (fabs y)))