Graphics.Rendering.Chart.Backend.Diagrams:calcFontMetrics from Chart-diagrams-1.5.1, A

Percentage Accurate: 88.0% → 99.9%

Time: 6.2s

Alternatives: 9

Speedup: 0.3×

Specification

Math

\[\begin{array}{l} \\ \frac{x + y}{1 - \frac{y}{z}} \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

def code(x, y, z):
	return (x + y) / (1.0 - (y / z))

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 88.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{x + y}{1 - \frac{y}{z}} \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

def code(x, y, z):
	return (x + y) / (1.0 - (y / z))

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x + y}{1 - \frac{y}{z}}\\ \mathbf{if}\;t\_0 \leq -2 \cdot 10^{-307} \lor \neg \left(t\_0 \leq 0\right):\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{\left(-x\right) - y}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ (+ x y) (- 1.0 (/ y z)))))
   (if (or (<= t_0 -2e-307) (not (<= t_0 0.0))) t_0 (* z (/ (- (- x) y) y)))))

C

double code(double x, double y, double z) {
	double t_0 = (x + y) / (1.0 - (y / z));
	double tmp;
	if ((t_0 <= -2e-307) || !(t_0 <= 0.0)) {
		tmp = t_0;
	} else {
		tmp = z * ((-x - y) / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (x + y) / (1.0d0 - (y / z))
    if ((t_0 <= (-2d-307)) .or. (.not. (t_0 <= 0.0d0))) then
        tmp = t_0
    else
        tmp = z * ((-x - y) / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = (x + y) / (1.0 - (y / z));
	double tmp;
	if ((t_0 <= -2e-307) || !(t_0 <= 0.0)) {
		tmp = t_0;
	} else {
		tmp = z * ((-x - y) / y);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (x + y) / (1.0 - (y / z))
	tmp = 0
	if (t_0 <= -2e-307) or not (t_0 <= 0.0):
		tmp = t_0
	else:
		tmp = z * ((-x - y) / y)
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(x + y) / Float64(1.0 - Float64(y / z)))
	tmp = 0.0
	if ((t_0 <= -2e-307) || !(t_0 <= 0.0))
		tmp = t_0;
	else
		tmp = Float64(z * Float64(Float64(Float64(-x) - y) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (x + y) / (1.0 - (y / z));
	tmp = 0.0;
	if ((t_0 <= -2e-307) || ~((t_0 <= 0.0)))
		tmp = t_0;
	else
		tmp = z * ((-x - y) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(x + y), $MachinePrecision] / N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$0, -2e-307], N[Not[LessEqual[t$95$0, 0.0]], $MachinePrecision]], t$95$0, N[(z * N[(N[((-x) - y), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (+.f64 x y) (-.f64 #s(literal 1 binary64) (/.f64 y z))) < -1.99999999999999982e-307 or -0.0 < (/.f64 (+.f64 x y) (-.f64 #s(literal 1 binary64) (/.f64 y z)))

   1. Initial program 99.9%

      \[\frac{x + y}{1 - \frac{y}{z}} \]
   2. Add Preprocessing

   if -1.99999999999999982e-307 < (/.f64 (+.f64 x y) (-.f64 #s(literal 1 binary64) (/.f64 y z))) < -0.0

   1. Initial program 5.8%

      \[\frac{x + y}{1 - \frac{y}{z}} \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 99.8%

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

      1. mul-1-neg 99.8%

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

      2. associate-/l* 100.0%

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

      3. distribute-rgt-neg-in 100.0%

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

      4. distribute-neg-frac2 100.0%

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

      5. +-commutative 100.0%

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

   5. Simplified 100.0%

      \[\leadsto \color{blue}{z \cdot \frac{y + x}{-y}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + y}{1 - \frac{y}{z}} \leq -2 \cdot 10^{-307} \lor \neg \left(\frac{x + y}{1 - \frac{y}{z}} \leq 0\right):\\ \;\;\;\;\frac{x + y}{1 - \frac{y}{z}}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{\left(-x\right) - y}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 69.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -8 \cdot 10^{+200}:\\ \;\;\;\;z \cdot \left(-1 - \frac{z}{y}\right)\\ \mathbf{elif}\;y \leq -1.9 \cdot 10^{+32}:\\ \;\;\;\;\frac{z \cdot \left(\left(-x\right) - y\right)}{y}\\ \mathbf{elif}\;y \leq 3.7 \cdot 10^{+127}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -8e+200)
   (* z (- -1.0 (/ z y)))
   (if (<= y -1.9e+32)
     (/ (* z (- (- x) y)) y)
     (if (<= y 3.7e+127) (+ x y) (- z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -8e+200) {
		tmp = z * (-1.0 - (z / y));
	} else if (y <= -1.9e+32) {
		tmp = (z * (-x - y)) / y;
	} else if (y <= 3.7e+127) {
		tmp = x + y;
	} else {
		tmp = -z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= (-8d+200)) then
        tmp = z * ((-1.0d0) - (z / y))
    else if (y <= (-1.9d+32)) then
        tmp = (z * (-x - y)) / y
    else if (y <= 3.7d+127) then
        tmp = x + y
    else
        tmp = -z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -8e+200) {
		tmp = z * (-1.0 - (z / y));
	} else if (y <= -1.9e+32) {
		tmp = (z * (-x - y)) / y;
	} else if (y <= 3.7e+127) {
		tmp = x + y;
	} else {
		tmp = -z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -8e+200:
		tmp = z * (-1.0 - (z / y))
	elif y <= -1.9e+32:
		tmp = (z * (-x - y)) / y
	elif y <= 3.7e+127:
		tmp = x + y
	else:
		tmp = -z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -8e+200)
		tmp = Float64(z * Float64(-1.0 - Float64(z / y)));
	elseif (y <= -1.9e+32)
		tmp = Float64(Float64(z * Float64(Float64(-x) - y)) / y);
	elseif (y <= 3.7e+127)
		tmp = Float64(x + y);
	else
		tmp = Float64(-z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -8e+200)
		tmp = z * (-1.0 - (z / y));
	elseif (y <= -1.9e+32)
		tmp = (z * (-x - y)) / y;
	elseif (y <= 3.7e+127)
		tmp = x + y;
	else
		tmp = -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -8e+200], N[(z * N[(-1.0 - N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.9e+32], N[(N[(z * N[((-x) - y), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[y, 3.7e+127], N[(x + y), $MachinePrecision], (-z)]]]

Derivation

1. Split input into 4 regimes

2. if y < -7.9999999999999998e200

   1. Initial program 54.5%

      \[\frac{x + y}{1 - \frac{y}{z}} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 45.7%

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

   4. Taylor expanded in z around 0 86.7%

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

   5. Taylor expanded in z around inf 50.6%

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

      1. mul-1-neg 50.6%

         \[\leadsto \color{blue}{-{z}^{2} \cdot \left(\frac{1}{y} + \frac{1}{z}\right)} \]

      2. unpow2 50.6%

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

      3. associate-*l* 86.4%

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

      4. distribute-lft-in 86.5%

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

      5. associate-*r/ 86.5%

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

      6. *-rgt-identity 86.5%

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

      7. rgt-mult-inverse 86.7%

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

      8. distribute-lft-out 86.7%

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

      9. *-rgt-identity 86.7%

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

      10. +-commutative 86.7%

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

      11. distribute-neg-out 86.7%

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

      12. unsub-neg 86.7%

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

      13. neg-mul-1 86.7%

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

      14. *-commutative 86.7%

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

      15. distribute-lft-out-- 86.7%

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

   7. Simplified 86.7%

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

   if -7.9999999999999998e200 < y < -1.9000000000000002e32

   1. Initial program 74.4%

      \[\frac{x + y}{1 - \frac{y}{z}} \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 81.2%

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

      1. mul-1-neg 81.2%

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

      2. +-commutative 81.2%

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

   5. Simplified 81.2%

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

   if -1.9000000000000002e32 < y < 3.6999999999999998e127

   1. Initial program 98.2%

      \[\frac{x + y}{1 - \frac{y}{z}} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 78.8%

      \[\leadsto \color{blue}{x + y} \]
   4. Step-by-step derivation

      1. +-commutative 78.8%

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

   5. Simplified 78.8%

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

   if 3.6999999999999998e127 < y

   1. Initial program 58.5%

      \[\frac{x + y}{1 - \frac{y}{z}} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 83.1%

      \[\leadsto \color{blue}{-1 \cdot z} \]
   4. Step-by-step derivation

      1. mul-1-neg 83.1%

         \[\leadsto \color{blue}{-z} \]

   5. Simplified 83.1%

      \[\leadsto \color{blue}{-z} \]
3. Recombined 4 regimes into one program.

4. Final simplification 80.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8 \cdot 10^{+200}:\\ \;\;\;\;z \cdot \left(-1 - \frac{z}{y}\right)\\ \mathbf{elif}\;y \leq -1.9 \cdot 10^{+32}:\\ \;\;\;\;\frac{z \cdot \left(\left(-x\right) - y\right)}{y}\\ \mathbf{elif}\;y \leq 3.7 \cdot 10^{+127}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 68.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.2 \cdot 10^{+118}:\\ \;\;\;\;z \cdot \left(-1 - \frac{z}{y}\right)\\ \mathbf{elif}\;y \leq -1.85 \cdot 10^{+30}:\\ \;\;\;\;\frac{y}{1 - \frac{y}{z}}\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{+126}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -5.2e+118)
   (* z (- -1.0 (/ z y)))
   (if (<= y -1.85e+30)
     (/ y (- 1.0 (/ y z)))
     (if (<= y 2.5e+126) (+ x y) (- z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -5.2e+118) {
		tmp = z * (-1.0 - (z / y));
	} else if (y <= -1.85e+30) {
		tmp = y / (1.0 - (y / z));
	} else if (y <= 2.5e+126) {
		tmp = x + y;
	} else {
		tmp = -z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= (-5.2d+118)) then
        tmp = z * ((-1.0d0) - (z / y))
    else if (y <= (-1.85d+30)) then
        tmp = y / (1.0d0 - (y / z))
    else if (y <= 2.5d+126) then
        tmp = x + y
    else
        tmp = -z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -5.2e+118) {
		tmp = z * (-1.0 - (z / y));
	} else if (y <= -1.85e+30) {
		tmp = y / (1.0 - (y / z));
	} else if (y <= 2.5e+126) {
		tmp = x + y;
	} else {
		tmp = -z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -5.2e+118:
		tmp = z * (-1.0 - (z / y))
	elif y <= -1.85e+30:
		tmp = y / (1.0 - (y / z))
	elif y <= 2.5e+126:
		tmp = x + y
	else:
		tmp = -z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -5.2e+118)
		tmp = Float64(z * Float64(-1.0 - Float64(z / y)));
	elseif (y <= -1.85e+30)
		tmp = Float64(y / Float64(1.0 - Float64(y / z)));
	elseif (y <= 2.5e+126)
		tmp = Float64(x + y);
	else
		tmp = Float64(-z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -5.2e+118)
		tmp = z * (-1.0 - (z / y));
	elseif (y <= -1.85e+30)
		tmp = y / (1.0 - (y / z));
	elseif (y <= 2.5e+126)
		tmp = x + y;
	else
		tmp = -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -5.2e+118], N[(z * N[(-1.0 - N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.85e+30], N[(y / N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.5e+126], N[(x + y), $MachinePrecision], (-z)]]]

Derivation

1. Split input into 4 regimes

2. if y < -5.20000000000000032e118

   1. Initial program 52.5%

      \[\frac{x + y}{1 - \frac{y}{z}} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 44.6%

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

   4. Taylor expanded in z around 0 84.1%

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

   5. Taylor expanded in z around inf 44.9%

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

      1. mul-1-neg 44.9%

         \[\leadsto \color{blue}{-{z}^{2} \cdot \left(\frac{1}{y} + \frac{1}{z}\right)} \]

      2. unpow2 44.9%

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

      3. associate-*l* 83.8%

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

      4. distribute-lft-in 83.9%

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

      5. associate-*r/ 83.9%

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

      6. *-rgt-identity 83.9%

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

      7. rgt-mult-inverse 84.1%

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

      8. distribute-lft-out 84.1%

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

      9. *-rgt-identity 84.1%

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

      10. +-commutative 84.1%

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

      11. distribute-neg-out 84.1%

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

      12. unsub-neg 84.1%

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

      13. neg-mul-1 84.1%

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

      14. *-commutative 84.1%

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

      15. distribute-lft-out-- 84.1%

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

   7. Simplified 84.1%

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

   if -5.20000000000000032e118 < y < -1.85000000000000008e30

   1. Initial program 91.3%

      \[\frac{x + y}{1 - \frac{y}{z}} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 67.7%

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

   if -1.85000000000000008e30 < y < 2.49999999999999989e126

   1. Initial program 98.2%

      \[\frac{x + y}{1 - \frac{y}{z}} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 78.8%

      \[\leadsto \color{blue}{x + y} \]
   4. Step-by-step derivation

      1. +-commutative 78.8%

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

   5. Simplified 78.8%

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

   if 2.49999999999999989e126 < y

   1. Initial program 58.5%

      \[\frac{x + y}{1 - \frac{y}{z}} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 83.1%

      \[\leadsto \color{blue}{-1 \cdot z} \]
   4. Step-by-step derivation

      1. mul-1-neg 83.1%

         \[\leadsto \color{blue}{-z} \]

   5. Simplified 83.1%

      \[\leadsto \color{blue}{-z} \]
3. Recombined 4 regimes into one program.

4. Final simplification 79.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.2 \cdot 10^{+118}:\\ \;\;\;\;z \cdot \left(-1 - \frac{z}{y}\right)\\ \mathbf{elif}\;y \leq -1.85 \cdot 10^{+30}:\\ \;\;\;\;\frac{y}{1 - \frac{y}{z}}\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{+126}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 57.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.3 \cdot 10^{+31}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq 0.006:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 4.7 \cdot 10^{+126}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -4.3e+31) (- z) (if (<= y 0.006) x (if (<= y 4.7e+126) y (- z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -4.3e+31) {
		tmp = -z;
	} else if (y <= 0.006) {
		tmp = x;
	} else if (y <= 4.7e+126) {
		tmp = y;
	} else {
		tmp = -z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= (-4.3d+31)) then
        tmp = -z
    else if (y <= 0.006d0) then
        tmp = x
    else if (y <= 4.7d+126) then
        tmp = y
    else
        tmp = -z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -4.3e+31) {
		tmp = -z;
	} else if (y <= 0.006) {
		tmp = x;
	} else if (y <= 4.7e+126) {
		tmp = y;
	} else {
		tmp = -z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -4.3e+31:
		tmp = -z
	elif y <= 0.006:
		tmp = x
	elif y <= 4.7e+126:
		tmp = y
	else:
		tmp = -z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -4.3e+31)
		tmp = Float64(-z);
	elseif (y <= 0.006)
		tmp = x;
	elseif (y <= 4.7e+126)
		tmp = y;
	else
		tmp = Float64(-z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -4.3e+31)
		tmp = -z;
	elseif (y <= 0.006)
		tmp = x;
	elseif (y <= 4.7e+126)
		tmp = y;
	else
		tmp = -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -4.3e+31], (-z), If[LessEqual[y, 0.006], x, If[LessEqual[y, 4.7e+126], y, (-z)]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.29999999999999989e31 or 4.6999999999999999e126 < y

   1. Initial program 64.0%

      \[\frac{x + y}{1 - \frac{y}{z}} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 74.1%

      \[\leadsto \color{blue}{-1 \cdot z} \]
   4. Step-by-step derivation

      1. mul-1-neg 74.1%

         \[\leadsto \color{blue}{-z} \]

   5. Simplified 74.1%

      \[\leadsto \color{blue}{-z} \]

   if -4.29999999999999989e31 < y < 0.0060000000000000001

   1. Initial program 99.9%

      \[\frac{x + y}{1 - \frac{y}{z}} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 64.8%

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

   if 0.0060000000000000001 < y < 4.6999999999999999e126

   1. Initial program 89.1%

      \[\frac{x + y}{1 - \frac{y}{z}} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 59.3%

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

   4. Taylor expanded in y around 0 47.8%

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

Alternative 5: 67.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.55 \cdot 10^{+32} \lor \neg \left(y \leq 2.4 \cdot 10^{+126}\right):\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -1.55e+32) (not (<= y 2.4e+126))) (- z) (+ x y)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.55e+32) || !(y <= 2.4e+126)) {
		tmp = -z;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((y <= (-1.55d+32)) .or. (.not. (y <= 2.4d+126))) then
        tmp = -z
    else
        tmp = x + y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.55e+32) || !(y <= 2.4e+126)) {
		tmp = -z;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -1.55e+32) or not (y <= 2.4e+126):
		tmp = -z
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -1.55e+32) || !(y <= 2.4e+126))
		tmp = Float64(-z);
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -1.55e+32) || ~((y <= 2.4e+126)))
		tmp = -z;
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -1.55e+32], N[Not[LessEqual[y, 2.4e+126]], $MachinePrecision]], (-z), N[(x + y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.54999999999999997e32 or 2.40000000000000012e126 < y

   1. Initial program 64.0%

      \[\frac{x + y}{1 - \frac{y}{z}} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 74.1%

      \[\leadsto \color{blue}{-1 \cdot z} \]
   4. Step-by-step derivation

      1. mul-1-neg 74.1%

         \[\leadsto \color{blue}{-z} \]

   5. Simplified 74.1%

      \[\leadsto \color{blue}{-z} \]

   if -1.54999999999999997e32 < y < 2.40000000000000012e126

   1. Initial program 98.2%

      \[\frac{x + y}{1 - \frac{y}{z}} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 78.8%

      \[\leadsto \color{blue}{x + y} \]
   4. Step-by-step derivation

      1. +-commutative 78.8%

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

   5. Simplified 78.8%

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

4. Final simplification 77.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.55 \cdot 10^{+32} \lor \neg \left(y \leq 2.4 \cdot 10^{+126}\right):\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 70.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -8.5 \cdot 10^{+30}:\\ \;\;\;\;z \cdot \frac{\left(-x\right) - y}{y}\\ \mathbf{elif}\;y \leq 2.4 \cdot 10^{+126}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -8.5e+30)
   (* z (/ (- (- x) y) y))
   (if (<= y 2.4e+126) (+ x y) (- z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -8.5e+30) {
		tmp = z * ((-x - y) / y);
	} else if (y <= 2.4e+126) {
		tmp = x + y;
	} else {
		tmp = -z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= (-8.5d+30)) then
        tmp = z * ((-x - y) / y)
    else if (y <= 2.4d+126) then
        tmp = x + y
    else
        tmp = -z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -8.5e+30) {
		tmp = z * ((-x - y) / y);
	} else if (y <= 2.4e+126) {
		tmp = x + y;
	} else {
		tmp = -z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -8.5e+30:
		tmp = z * ((-x - y) / y)
	elif y <= 2.4e+126:
		tmp = x + y
	else:
		tmp = -z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -8.5e+30)
		tmp = Float64(z * Float64(Float64(Float64(-x) - y) / y));
	elseif (y <= 2.4e+126)
		tmp = Float64(x + y);
	else
		tmp = Float64(-z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -8.5e+30)
		tmp = z * ((-x - y) / y);
	elseif (y <= 2.4e+126)
		tmp = x + y;
	else
		tmp = -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -8.5e+30], N[(z * N[(N[((-x) - y), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.4e+126], N[(x + y), $MachinePrecision], (-z)]]

Derivation

1. Split input into 3 regimes

2. if y < -8.4999999999999995e30

   1. Initial program 67.2%

      \[\frac{x + y}{1 - \frac{y}{z}} \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 74.8%

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

      1. mul-1-neg 74.8%

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

      2. associate-/l* 87.4%

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

      3. distribute-rgt-neg-in 87.4%

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

      4. distribute-neg-frac2 87.4%

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

      5. +-commutative 87.4%

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

   5. Simplified 87.4%

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

   if -8.4999999999999995e30 < y < 2.40000000000000012e126

   1. Initial program 98.2%

      \[\frac{x + y}{1 - \frac{y}{z}} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 78.8%

      \[\leadsto \color{blue}{x + y} \]
   4. Step-by-step derivation

      1. +-commutative 78.8%

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

   5. Simplified 78.8%

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

   if 2.40000000000000012e126 < y

   1. Initial program 58.5%

      \[\frac{x + y}{1 - \frac{y}{z}} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 83.1%

      \[\leadsto \color{blue}{-1 \cdot z} \]
   4. Step-by-step derivation

      1. mul-1-neg 83.1%

         \[\leadsto \color{blue}{-z} \]

   5. Simplified 83.1%

      \[\leadsto \color{blue}{-z} \]
3. Recombined 3 regimes into one program.

4. Final simplification 81.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8.5 \cdot 10^{+30}:\\ \;\;\;\;z \cdot \frac{\left(-x\right) - y}{y}\\ \mathbf{elif}\;y \leq 2.4 \cdot 10^{+126}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 67.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.5 \cdot 10^{+30}:\\ \;\;\;\;z \cdot \left(-1 - \frac{z}{y}\right)\\ \mathbf{elif}\;y \leq 7 \cdot 10^{+129}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -6.5e+30) (* z (- -1.0 (/ z y))) (if (<= y 7e+129) (+ x y) (- z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -6.5e+30) {
		tmp = z * (-1.0 - (z / y));
	} else if (y <= 7e+129) {
		tmp = x + y;
	} else {
		tmp = -z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= (-6.5d+30)) then
        tmp = z * ((-1.0d0) - (z / y))
    else if (y <= 7d+129) then
        tmp = x + y
    else
        tmp = -z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -6.5e+30) {
		tmp = z * (-1.0 - (z / y));
	} else if (y <= 7e+129) {
		tmp = x + y;
	} else {
		tmp = -z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -6.5e+30:
		tmp = z * (-1.0 - (z / y))
	elif y <= 7e+129:
		tmp = x + y
	else:
		tmp = -z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -6.5e+30)
		tmp = Float64(z * Float64(-1.0 - Float64(z / y)));
	elseif (y <= 7e+129)
		tmp = Float64(x + y);
	else
		tmp = Float64(-z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -6.5e+30)
		tmp = z * (-1.0 - (z / y));
	elseif (y <= 7e+129)
		tmp = x + y;
	else
		tmp = -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -6.5e+30], N[(z * N[(-1.0 - N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 7e+129], N[(x + y), $MachinePrecision], (-z)]]

Derivation

1. Split input into 3 regimes

2. if y < -6.5e30

   1. Initial program 67.2%

      \[\frac{x + y}{1 - \frac{y}{z}} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 53.4%

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

   4. Taylor expanded in z around 0 69.3%

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

   5. Taylor expanded in z around inf 37.6%

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

      1. mul-1-neg 37.6%

         \[\leadsto \color{blue}{-{z}^{2} \cdot \left(\frac{1}{y} + \frac{1}{z}\right)} \]

      2. unpow2 37.6%

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

      3. associate-*l* 69.1%

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

      4. distribute-lft-in 69.2%

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

      5. associate-*r/ 69.2%

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

      6. *-rgt-identity 69.2%

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

      7. rgt-mult-inverse 69.3%

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

      8. distribute-lft-out 69.3%

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

      9. *-rgt-identity 69.3%

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

      10. +-commutative 69.3%

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

      11. distribute-neg-out 69.3%

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

      12. unsub-neg 69.3%

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

      13. neg-mul-1 69.3%

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

      14. *-commutative 69.3%

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

      15. distribute-lft-out-- 69.3%

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

   7. Simplified 69.3%

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

   if -6.5e30 < y < 6.9999999999999997e129

   1. Initial program 98.2%

      \[\frac{x + y}{1 - \frac{y}{z}} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 78.8%

      \[\leadsto \color{blue}{x + y} \]
   4. Step-by-step derivation

      1. +-commutative 78.8%

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

   5. Simplified 78.8%

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

   if 6.9999999999999997e129 < y

   1. Initial program 58.5%

      \[\frac{x + y}{1 - \frac{y}{z}} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 83.1%

      \[\leadsto \color{blue}{-1 \cdot z} \]
   4. Step-by-step derivation

      1. mul-1-neg 83.1%

         \[\leadsto \color{blue}{-z} \]

   5. Simplified 83.1%

      \[\leadsto \color{blue}{-z} \]
3. Recombined 3 regimes into one program.

4. Final simplification 77.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.5 \cdot 10^{+30}:\\ \;\;\;\;z \cdot \left(-1 - \frac{z}{y}\right)\\ \mathbf{elif}\;y \leq 7 \cdot 10^{+129}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 41.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.5 \cdot 10^{-139}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 3.4 \cdot 10^{-134}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -1.5e-139) x (if (<= x 3.4e-134) y x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.5e-139) {
		tmp = x;
	} else if (x <= 3.4e-134) {
		tmp = y;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (x <= (-1.5d-139)) then
        tmp = x
    else if (x <= 3.4d-134) then
        tmp = y
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.5e-139) {
		tmp = x;
	} else if (x <= 3.4e-134) {
		tmp = y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -1.5e-139:
		tmp = x
	elif x <= 3.4e-134:
		tmp = y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -1.5e-139)
		tmp = x;
	elseif (x <= 3.4e-134)
		tmp = y;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -1.5e-139)
		tmp = x;
	elseif (x <= 3.4e-134)
		tmp = y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -1.5e-139], x, If[LessEqual[x, 3.4e-134], y, x]]

Derivation

1. Split input into 2 regimes

2. if x < -1.5e-139 or 3.39999999999999977e-134 < x

   1. Initial program 86.2%

      \[\frac{x + y}{1 - \frac{y}{z}} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 50.8%

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

   if -1.5e-139 < x < 3.39999999999999977e-134

   1. Initial program 85.3%

      \[\frac{x + y}{1 - \frac{y}{z}} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 73.1%

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

   4. Taylor expanded in y around 0 40.6%

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

Alternative 9: 35.1% accurate, 9.0× speedup

Math

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

FPCore

(FPCore (x y z) :precision binary64 x)

C

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

Fortran

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

Java

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

Python

def code(x, y, z):
	return x

Julia

function code(x, y, z)
	return x
end

MATLAB

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

Wolfram

code[x_, y_, z_] := x

Derivation

1. Initial program 85.9%

   \[\frac{x + y}{1 - \frac{y}{z}} \]
2. Add Preprocessing

3. Taylor expanded in y around 0 39.2%

   \[\leadsto \color{blue}{x} \]
4. Add Preprocessing

Developer target: 93.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{y + x}{-y} \cdot z\\ \mathbf{if}\;y < -3.7429310762689856 \cdot 10^{+171}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y < 3.5534662456086734 \cdot 10^{+168}:\\ \;\;\;\;\frac{x + y}{1 - \frac{y}{z}}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (/ (+ y x) (- y)) z)))
   (if (< y -3.7429310762689856e+171)
     t_0
     (if (< y 3.5534662456086734e+168) (/ (+ x y) (- 1.0 (/ y z))) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = ((y + x) / -y) * z;
	double tmp;
	if (y < -3.7429310762689856e+171) {
		tmp = t_0;
	} else if (y < 3.5534662456086734e+168) {
		tmp = (x + y) / (1.0 - (y / z));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = ((y + x) / -y) * z
    if (y < (-3.7429310762689856d+171)) then
        tmp = t_0
    else if (y < 3.5534662456086734d+168) then
        tmp = (x + y) / (1.0d0 - (y / z))
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = ((y + x) / -y) * z;
	double tmp;
	if (y < -3.7429310762689856e+171) {
		tmp = t_0;
	} else if (y < 3.5534662456086734e+168) {
		tmp = (x + y) / (1.0 - (y / z));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = ((y + x) / -y) * z
	tmp = 0
	if y < -3.7429310762689856e+171:
		tmp = t_0
	elif y < 3.5534662456086734e+168:
		tmp = (x + y) / (1.0 - (y / z))
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(Float64(y + x) / Float64(-y)) * z)
	tmp = 0.0
	if (y < -3.7429310762689856e+171)
		tmp = t_0;
	elseif (y < 3.5534662456086734e+168)
		tmp = Float64(Float64(x + y) / Float64(1.0 - Float64(y / z)));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = ((y + x) / -y) * z;
	tmp = 0.0;
	if (y < -3.7429310762689856e+171)
		tmp = t_0;
	elseif (y < 3.5534662456086734e+168)
		tmp = (x + y) / (1.0 - (y / z));
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(N[(y + x), $MachinePrecision] / (-y)), $MachinePrecision] * z), $MachinePrecision]}, If[Less[y, -3.7429310762689856e+171], t$95$0, If[Less[y, 3.5534662456086734e+168], N[(N[(x + y), $MachinePrecision] / N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Reproduce

herbie shell --seed 2024089 
(FPCore (x y z)
  :name "Graphics.Rendering.Chart.Backend.Diagrams:calcFontMetrics from Chart-diagrams-1.5.1, A"
  :precision binary64

  :alt
  (if (< y -3.7429310762689856e+171) (* (/ (+ y x) (- y)) z) (if (< y 3.5534662456086734e+168) (/ (+ x y) (- 1.0 (/ y z))) (* (/ (+ y x) (- y)) z)))

  (/ (+ x y) (- 1.0 (/ y z))))