Numeric.LinearAlgebra.Util:formatSparse from hmatrix-0.16.1.5

Percentage Accurate: 100.0% → 100.0%

Time: 5.6s

Alternatives: 6

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: 74.6% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -8400000 \lor \neg \left(x \leq 1.6 \cdot 10^{-73}\right):\\ \;\;\;\;\left|\frac{x}{y}\right|\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= x -8400000.0) (not (<= x 1.6e-73))) (fabs (/ x y)) 1.0))

C

double code(double x, double y) {
	double tmp;
	if ((x <= -8400000.0) || !(x <= 1.6e-73)) {
		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 ((x <= (-8400000.0d0)) .or. (.not. (x <= 1.6d-73))) 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 ((x <= -8400000.0) || !(x <= 1.6e-73)) {
		tmp = Math.abs((x / y));
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (x <= -8400000.0) or not (x <= 1.6e-73):
		tmp = math.fabs((x / y))
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((x <= -8400000.0) || !(x <= 1.6e-73))
		tmp = abs(Float64(x / y));
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((x <= -8400000.0) || ~((x <= 1.6e-73)))
		tmp = abs((x / y));
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[x, -8400000.0], N[Not[LessEqual[x, 1.6e-73]], $MachinePrecision]], N[Abs[N[(x / y), $MachinePrecision]], $MachinePrecision], 1.0]

Derivation

1. Split input into 2 regimes

2. if x < -8.4e6 or 1.59999999999999993e-73 < x

   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 78.5%

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

   if -8.4e6 < x < 1.59999999999999993e-73

   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 18.9%

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

   8. Applied egg-rr 36.1%

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

      1. *-inverses 82.0%

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

   10. Simplified 82.0%

       \[\leadsto \color{blue}{1} \]
3. Recombined 2 regimes into one program.

4. Final simplification 79.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -8400000 \lor \neg \left(x \leq 1.6 \cdot 10^{-73}\right):\\ \;\;\;\;\left|\frac{x}{y}\right|\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 57.6% accurate, 8.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x - y}{y}\\ \mathbf{if}\;y \leq -2.8 \cdot 10^{+18}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -1.55 \cdot 10^{-54}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq -5 \cdot 10^{-157}:\\ \;\;\;\;\left(x + -1\right) \cdot \left(x + -1\right)\\ \mathbf{elif}\;y \leq 2.4 \cdot 10^{-12}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (/ (- x y) y)))
   (if (<= y -2.8e+18)
     1.0
     (if (<= y -1.55e-54)
       t_0
       (if (<= y -5e-157)
         (* (+ x -1.0) (+ x -1.0))
         (if (<= y 2.4e-12) t_0 1.0))))))

C

double code(double x, double y) {
	double t_0 = (x - y) / y;
	double tmp;
	if (y <= -2.8e+18) {
		tmp = 1.0;
	} else if (y <= -1.55e-54) {
		tmp = t_0;
	} else if (y <= -5e-157) {
		tmp = (x + -1.0) * (x + -1.0);
	} else if (y <= 2.4e-12) {
		tmp = t_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) :: t_0
    real(8) :: tmp
    t_0 = (x - y) / y
    if (y <= (-2.8d+18)) then
        tmp = 1.0d0
    else if (y <= (-1.55d-54)) then
        tmp = t_0
    else if (y <= (-5d-157)) then
        tmp = (x + (-1.0d0)) * (x + (-1.0d0))
    else if (y <= 2.4d-12) then
        tmp = t_0
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = (x - y) / y;
	double tmp;
	if (y <= -2.8e+18) {
		tmp = 1.0;
	} else if (y <= -1.55e-54) {
		tmp = t_0;
	} else if (y <= -5e-157) {
		tmp = (x + -1.0) * (x + -1.0);
	} else if (y <= 2.4e-12) {
		tmp = t_0;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = (x - y) / y
	tmp = 0
	if y <= -2.8e+18:
		tmp = 1.0
	elif y <= -1.55e-54:
		tmp = t_0
	elif y <= -5e-157:
		tmp = (x + -1.0) * (x + -1.0)
	elif y <= 2.4e-12:
		tmp = t_0
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(Float64(x - y) / y)
	tmp = 0.0
	if (y <= -2.8e+18)
		tmp = 1.0;
	elseif (y <= -1.55e-54)
		tmp = t_0;
	elseif (y <= -5e-157)
		tmp = Float64(Float64(x + -1.0) * Float64(x + -1.0));
	elseif (y <= 2.4e-12)
		tmp = t_0;
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = (x - y) / y;
	tmp = 0.0;
	if (y <= -2.8e+18)
		tmp = 1.0;
	elseif (y <= -1.55e-54)
		tmp = t_0;
	elseif (y <= -5e-157)
		tmp = (x + -1.0) * (x + -1.0);
	elseif (y <= 2.4e-12)
		tmp = t_0;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(N[(x - y), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[y, -2.8e+18], 1.0, If[LessEqual[y, -1.55e-54], t$95$0, If[LessEqual[y, -5e-157], N[(N[(x + -1.0), $MachinePrecision] * N[(x + -1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.4e-12], t$95$0, 1.0]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.8e18 or 2.39999999999999987e-12 < 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 28.5%

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

   8. Applied egg-rr 35.3%

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

      1. *-inverses 74.3%

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

   10. Simplified 74.3%

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

   if -2.8e18 < y < -1.55000000000000002e-54 or -5.0000000000000002e-157 < y < 2.39999999999999987e-12

   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. add-sqr-sqrt 46.2%

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

      6. fabs-sqr 46.2%

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

      7. add-sqr-sqrt 46.8%

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

   7. Applied egg-rr 46.8%

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

   if -1.55000000000000002e-54 < y < -5.0000000000000002e-157

   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. add-sqr-sqrt 14.2%

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

      6. fabs-sqr 14.2%

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

      7. add-sqr-sqrt 15.1%

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

   7. Applied egg-rr 15.1%

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

   9. Applied egg-rr 73.8%

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

Alternative 4: 57.5% accurate, 13.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.4 \cdot 10^{-142}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 2 \cdot 10^{-12}:\\ \;\;\;\;\frac{x - y}{y}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -1.4e-142) 1.0 (if (<= y 2e-12) (/ (- x y) y) 1.0)))

C

double code(double x, double y) {
	double tmp;
	if (y <= -1.4e-142) {
		tmp = 1.0;
	} else if (y <= 2e-12) {
		tmp = (x - y) / 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 <= (-1.4d-142)) then
        tmp = 1.0d0
    else if (y <= 2d-12) then
        tmp = (x - y) / y
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -1.4e-142) {
		tmp = 1.0;
	} else if (y <= 2e-12) {
		tmp = (x - y) / y;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -1.4e-142:
		tmp = 1.0
	elif y <= 2e-12:
		tmp = (x - y) / y
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -1.4e-142)
		tmp = 1.0;
	elseif (y <= 2e-12)
		tmp = Float64(Float64(x - y) / y);
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -1.4e-142)
		tmp = 1.0;
	elseif (y <= 2e-12)
		tmp = (x - y) / y;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -1.4e-142], 1.0, If[LessEqual[y, 2e-12], N[(N[(x - y), $MachinePrecision] / y), $MachinePrecision], 1.0]]

Derivation

1. Split input into 2 regimes

2. if y < -1.40000000000000002e-142 or 1.99999999999999996e-12 < 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 34.7%

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

   8. Applied egg-rr 32.6%

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

      1. *-inverses 67.9%

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

   10. Simplified 67.9%

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

   if -1.40000000000000002e-142 < y < 1.99999999999999996e-12

   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. add-sqr-sqrt 43.9%

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

      6. fabs-sqr 43.9%

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

      7. add-sqr-sqrt 44.3%

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

   7. Applied egg-rr 44.3%

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

Alternative 5: 57.6% accurate, 15.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.45 \cdot 10^{-142}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 4 \cdot 10^{-12}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -1.45e-142) 1.0 (if (<= y 4e-12) (/ x y) 1.0)))

C

double code(double x, double y) {
	double tmp;
	if (y <= -1.45e-142) {
		tmp = 1.0;
	} else if (y <= 4e-12) {
		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 <= (-1.45d-142)) then
        tmp = 1.0d0
    else if (y <= 4d-12) 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 <= -1.45e-142) {
		tmp = 1.0;
	} else if (y <= 4e-12) {
		tmp = x / y;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -1.45e-142:
		tmp = 1.0
	elif y <= 4e-12:
		tmp = x / y
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -1.45e-142)
		tmp = 1.0;
	elseif (y <= 4e-12)
		tmp = Float64(x / y);
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -1.45e-142)
		tmp = 1.0;
	elseif (y <= 4e-12)
		tmp = x / y;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -1.45e-142], 1.0, If[LessEqual[y, 4e-12], N[(x / y), $MachinePrecision], 1.0]]

Derivation

1. Split input into 2 regimes

2. if y < -1.44999999999999995e-142 or 3.99999999999999992e-12 < 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 34.7%

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

   8. Applied egg-rr 32.6%

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

      1. *-inverses 67.9%

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

   10. Simplified 67.9%

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

   if -1.44999999999999995e-142 < y < 3.99999999999999992e-12

   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 49.8%

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

      3. fabs-sqr 49.8%

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

      4. add-sqr-sqrt 50.2%

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

      5. *-commutative 50.2%

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

      6. add-sqr-sqrt 26.1%

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

      7. fabs-sqr 26.1%

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

      8. add-sqr-sqrt 44.2%

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

   4. Applied egg-rr 44.2%

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

   5. Taylor expanded in x around inf 44.0%

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

   6. Taylor expanded in y around 0 44.1%

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

Alternative 6: 51.2% 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 56.4%

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

8. Applied egg-rr 21.8%

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

   1. *-inverses 46.1%

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

10. Simplified 46.1%

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

Reproduce

herbie shell --seed 2024181 
(FPCore (x y)
  :name "Numeric.LinearAlgebra.Util:formatSparse from hmatrix-0.16.1.5"
  :precision binary64
  (/ (fabs (- x y)) (fabs y)))