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

Percentage Accurate: 87.9% → 99.9%

Time: 7.0s

Alternatives: 13

Speedup: 0.5×

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: 87.9% 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, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -0.0025 \lor \neg \left(y \leq 120000000\right):\\ \;\;\;\;\frac{z}{\frac{z - y}{y + x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{y + x}{1 - \frac{y}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -0.0025) (not (<= y 120000000.0)))
   (/ z (/ (- z y) (+ y x)))
   (/ (+ y x) (- 1.0 (/ y z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -0.0025) || !(y <= 120000000.0)) {
		tmp = z / ((z - y) / (y + x));
	} else {
		tmp = (y + x) / (1.0 - (y / 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 <= (-0.0025d0)) .or. (.not. (y <= 120000000.0d0))) then
        tmp = z / ((z - y) / (y + x))
    else
        tmp = (y + x) / (1.0d0 - (y / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -0.0025) || !(y <= 120000000.0)) {
		tmp = z / ((z - y) / (y + x));
	} else {
		tmp = (y + x) / (1.0 - (y / z));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -0.0025) or not (y <= 120000000.0):
		tmp = z / ((z - y) / (y + x))
	else:
		tmp = (y + x) / (1.0 - (y / z))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -0.0025) || !(y <= 120000000.0))
		tmp = Float64(z / Float64(Float64(z - y) / Float64(y + x)));
	else
		tmp = Float64(Float64(y + x) / Float64(1.0 - Float64(y / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -0.0025) || ~((y <= 120000000.0)))
		tmp = z / ((z - y) / (y + x));
	else
		tmp = (y + x) / (1.0 - (y / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -0.0025], N[Not[LessEqual[y, 120000000.0]], $MachinePrecision]], N[(z / N[(N[(z - y), $MachinePrecision] / N[(y + x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y + x), $MachinePrecision] / N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -0.00250000000000000005 or 1.2e8 < y

   1. Initial program 78.5%

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

   3. Taylor expanded in z around 0 78.5%

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

      1. associate-/r/ 99.9%

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

      2. add-cube-cbrt 97.7%

         \[\leadsto \frac{x + y}{z - y} \cdot \color{blue}{\left(\left(\sqrt[3]{z} \cdot \sqrt[3]{z}\right) \cdot \sqrt[3]{z}\right)} \]

      3. associate-*r* 97.6%

         \[\leadsto \color{blue}{\left(\frac{x + y}{z - y} \cdot \left(\sqrt[3]{z} \cdot \sqrt[3]{z}\right)\right) \cdot \sqrt[3]{z}} \]

      4. pow2 97.6%

         \[\leadsto \left(\frac{x + y}{z - y} \cdot \color{blue}{{\left(\sqrt[3]{z}\right)}^{2}}\right) \cdot \sqrt[3]{z} \]

   5. Applied egg-rr 97.6%

      \[\leadsto \color{blue}{\left(\frac{x + y}{z - y} \cdot {\left(\sqrt[3]{z}\right)}^{2}\right) \cdot \sqrt[3]{z}} \]
   6. Step-by-step derivation

      1. associate-*l* 97.7%

         \[\leadsto \color{blue}{\frac{x + y}{z - y} \cdot \left({\left(\sqrt[3]{z}\right)}^{2} \cdot \sqrt[3]{z}\right)} \]

      2. clear-num 97.7%

         \[\leadsto \color{blue}{\frac{1}{\frac{z - y}{x + y}}} \cdot \left({\left(\sqrt[3]{z}\right)}^{2} \cdot \sqrt[3]{z}\right) \]

      3. unpow2 97.7%

         \[\leadsto \frac{1}{\frac{z - y}{x + y}} \cdot \left(\color{blue}{\left(\sqrt[3]{z} \cdot \sqrt[3]{z}\right)} \cdot \sqrt[3]{z}\right) \]

      4. add-cube-cbrt 99.8%

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

      5. associate-*l/ 99.9%

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

      6. *-un-lft-identity 99.9%

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

   7. Applied egg-rr 99.9%

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

   if -0.00250000000000000005 < y < 1.2e8

   1. Initial program 99.9%

      \[\frac{x + y}{1 - \frac{y}{z}} \]
   2. Add Preprocessing
3. Recombined 2 regimes into one program.

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.0025 \lor \neg \left(y \leq 120000000\right):\\ \;\;\;\;\frac{z}{\frac{z - y}{y + x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{y + x}{1 - \frac{y}{z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 68.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 1 - \frac{y}{z}\\ \mathbf{if}\;y \leq -3.2 \cdot 10^{+150}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq -0.00016:\\ \;\;\;\;\frac{z}{\frac{z - y}{x}}\\ \mathbf{elif}\;y \leq 2.7 \cdot 10^{-41}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;y \leq 9 \cdot 10^{+34}:\\ \;\;\;\;\frac{x}{t\_0}\\ \mathbf{elif}\;y \leq 6 \cdot 10^{+138}:\\ \;\;\;\;\frac{y}{t\_0}\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- 1.0 (/ y z))))
   (if (<= y -3.2e+150)
     (- z)
     (if (<= y -0.00016)
       (/ z (/ (- z y) x))
       (if (<= y 2.7e-41)
         (+ y x)
         (if (<= y 9e+34) (/ x t_0) (if (<= y 6e+138) (/ y t_0) (- z))))))))

C

double code(double x, double y, double z) {
	double t_0 = 1.0 - (y / z);
	double tmp;
	if (y <= -3.2e+150) {
		tmp = -z;
	} else if (y <= -0.00016) {
		tmp = z / ((z - y) / x);
	} else if (y <= 2.7e-41) {
		tmp = y + x;
	} else if (y <= 9e+34) {
		tmp = x / t_0;
	} else if (y <= 6e+138) {
		tmp = y / t_0;
	} 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) :: t_0
    real(8) :: tmp
    t_0 = 1.0d0 - (y / z)
    if (y <= (-3.2d+150)) then
        tmp = -z
    else if (y <= (-0.00016d0)) then
        tmp = z / ((z - y) / x)
    else if (y <= 2.7d-41) then
        tmp = y + x
    else if (y <= 9d+34) then
        tmp = x / t_0
    else if (y <= 6d+138) then
        tmp = y / t_0
    else
        tmp = -z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = 1.0 - (y / z);
	double tmp;
	if (y <= -3.2e+150) {
		tmp = -z;
	} else if (y <= -0.00016) {
		tmp = z / ((z - y) / x);
	} else if (y <= 2.7e-41) {
		tmp = y + x;
	} else if (y <= 9e+34) {
		tmp = x / t_0;
	} else if (y <= 6e+138) {
		tmp = y / t_0;
	} else {
		tmp = -z;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = 1.0 - (y / z)
	tmp = 0
	if y <= -3.2e+150:
		tmp = -z
	elif y <= -0.00016:
		tmp = z / ((z - y) / x)
	elif y <= 2.7e-41:
		tmp = y + x
	elif y <= 9e+34:
		tmp = x / t_0
	elif y <= 6e+138:
		tmp = y / t_0
	else:
		tmp = -z
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(1.0 - Float64(y / z))
	tmp = 0.0
	if (y <= -3.2e+150)
		tmp = Float64(-z);
	elseif (y <= -0.00016)
		tmp = Float64(z / Float64(Float64(z - y) / x));
	elseif (y <= 2.7e-41)
		tmp = Float64(y + x);
	elseif (y <= 9e+34)
		tmp = Float64(x / t_0);
	elseif (y <= 6e+138)
		tmp = Float64(y / t_0);
	else
		tmp = Float64(-z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = 1.0 - (y / z);
	tmp = 0.0;
	if (y <= -3.2e+150)
		tmp = -z;
	elseif (y <= -0.00016)
		tmp = z / ((z - y) / x);
	elseif (y <= 2.7e-41)
		tmp = y + x;
	elseif (y <= 9e+34)
		tmp = x / t_0;
	elseif (y <= 6e+138)
		tmp = y / t_0;
	else
		tmp = -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -3.2e+150], (-z), If[LessEqual[y, -0.00016], N[(z / N[(N[(z - y), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.7e-41], N[(y + x), $MachinePrecision], If[LessEqual[y, 9e+34], N[(x / t$95$0), $MachinePrecision], If[LessEqual[y, 6e+138], N[(y / t$95$0), $MachinePrecision], (-z)]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -3.20000000000000016e150 or 6.0000000000000002e138 < y

   1. Initial program 64.6%

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

   3. Taylor expanded in y around inf 76.6%

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

      1. neg-mul-1 76.6%

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

   5. Simplified 76.6%

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

   if -3.20000000000000016e150 < y < -1.60000000000000013e-4

   1. Initial program 86.8%

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

   3. Taylor expanded in z around 0 87.1%

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

      1. associate-/r/ 99.7%

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

      2. add-cube-cbrt 97.7%

         \[\leadsto \frac{x + y}{z - y} \cdot \color{blue}{\left(\left(\sqrt[3]{z} \cdot \sqrt[3]{z}\right) \cdot \sqrt[3]{z}\right)} \]

      3. associate-*r* 97.7%

         \[\leadsto \color{blue}{\left(\frac{x + y}{z - y} \cdot \left(\sqrt[3]{z} \cdot \sqrt[3]{z}\right)\right) \cdot \sqrt[3]{z}} \]

      4. pow2 97.7%

         \[\leadsto \left(\frac{x + y}{z - y} \cdot \color{blue}{{\left(\sqrt[3]{z}\right)}^{2}}\right) \cdot \sqrt[3]{z} \]

   5. Applied egg-rr 97.7%

      \[\leadsto \color{blue}{\left(\frac{x + y}{z - y} \cdot {\left(\sqrt[3]{z}\right)}^{2}\right) \cdot \sqrt[3]{z}} \]
   6. Step-by-step derivation

      1. associate-*l* 97.7%

         \[\leadsto \color{blue}{\frac{x + y}{z - y} \cdot \left({\left(\sqrt[3]{z}\right)}^{2} \cdot \sqrt[3]{z}\right)} \]

      2. clear-num 97.7%

         \[\leadsto \color{blue}{\frac{1}{\frac{z - y}{x + y}}} \cdot \left({\left(\sqrt[3]{z}\right)}^{2} \cdot \sqrt[3]{z}\right) \]

      3. unpow2 97.7%

         \[\leadsto \frac{1}{\frac{z - y}{x + y}} \cdot \left(\color{blue}{\left(\sqrt[3]{z} \cdot \sqrt[3]{z}\right)} \cdot \sqrt[3]{z}\right) \]

      4. add-cube-cbrt 99.7%

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

      5. associate-*l/ 99.9%

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

      6. *-un-lft-identity 99.9%

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

   7. Applied egg-rr 99.9%

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

   8. Taylor expanded in x around inf 58.6%

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

   if -1.60000000000000013e-4 < y < 2.7e-41

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf 83.2%

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

      1. +-commutative 83.2%

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

   5. Simplified 83.2%

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

   if 2.7e-41 < y < 9.0000000000000001e34

   1. Initial program 99.8%

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

   3. Taylor expanded in x around inf 87.1%

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

   if 9.0000000000000001e34 < y < 6.0000000000000002e138

   1. Initial program 95.9%

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

   3. Taylor expanded in x around 0 61.1%

      \[\leadsto \color{blue}{\frac{y}{1 - \frac{y}{z}}} \]
3. Recombined 5 regimes into one program.
4. Add Preprocessing

Alternative 3: 72.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{z}{\frac{z - y}{y}}\\ \mathbf{if}\;y \leq -1 \cdot 10^{+146}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq -0.001:\\ \;\;\;\;\frac{z}{\frac{z - y}{x}}\\ \mathbf{elif}\;y \leq 2.7 \cdot 10^{-41}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;y \leq 7.6 \cdot 10^{+31}:\\ \;\;\;\;\frac{x}{1 - \frac{y}{z}}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ z (/ (- z y) y))))
   (if (<= y -1e+146)
     t_0
     (if (<= y -0.001)
       (/ z (/ (- z y) x))
       (if (<= y 2.7e-41)
         (+ y x)
         (if (<= y 7.6e+31) (/ x (- 1.0 (/ y z))) t_0))))))

C

double code(double x, double y, double z) {
	double t_0 = z / ((z - y) / y);
	double tmp;
	if (y <= -1e+146) {
		tmp = t_0;
	} else if (y <= -0.001) {
		tmp = z / ((z - y) / x);
	} else if (y <= 2.7e-41) {
		tmp = y + x;
	} else if (y <= 7.6e+31) {
		tmp = x / (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 = z / ((z - y) / y)
    if (y <= (-1d+146)) then
        tmp = t_0
    else if (y <= (-0.001d0)) then
        tmp = z / ((z - y) / x)
    else if (y <= 2.7d-41) then
        tmp = y + x
    else if (y <= 7.6d+31) then
        tmp = x / (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 = z / ((z - y) / y);
	double tmp;
	if (y <= -1e+146) {
		tmp = t_0;
	} else if (y <= -0.001) {
		tmp = z / ((z - y) / x);
	} else if (y <= 2.7e-41) {
		tmp = y + x;
	} else if (y <= 7.6e+31) {
		tmp = x / (1.0 - (y / z));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = z / ((z - y) / y)
	tmp = 0
	if y <= -1e+146:
		tmp = t_0
	elif y <= -0.001:
		tmp = z / ((z - y) / x)
	elif y <= 2.7e-41:
		tmp = y + x
	elif y <= 7.6e+31:
		tmp = x / (1.0 - (y / z))
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(z / Float64(Float64(z - y) / y))
	tmp = 0.0
	if (y <= -1e+146)
		tmp = t_0;
	elseif (y <= -0.001)
		tmp = Float64(z / Float64(Float64(z - y) / x));
	elseif (y <= 2.7e-41)
		tmp = Float64(y + x);
	elseif (y <= 7.6e+31)
		tmp = Float64(x / Float64(1.0 - Float64(y / z)));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = z / ((z - y) / y);
	tmp = 0.0;
	if (y <= -1e+146)
		tmp = t_0;
	elseif (y <= -0.001)
		tmp = z / ((z - y) / x);
	elseif (y <= 2.7e-41)
		tmp = y + x;
	elseif (y <= 7.6e+31)
		tmp = x / (1.0 - (y / z));
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(z / N[(N[(z - y), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1e+146], t$95$0, If[LessEqual[y, -0.001], N[(z / N[(N[(z - y), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.7e-41], N[(y + x), $MachinePrecision], If[LessEqual[y, 7.6e+31], N[(x / N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -9.99999999999999934e145 or 7.6000000000000003e31 < y

   1. Initial program 73.2%

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

   3. Taylor expanded in z around 0 73.2%

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

      1. associate-/r/ 99.9%

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

      2. add-cube-cbrt 97.7%

         \[\leadsto \frac{x + y}{z - y} \cdot \color{blue}{\left(\left(\sqrt[3]{z} \cdot \sqrt[3]{z}\right) \cdot \sqrt[3]{z}\right)} \]

      3. associate-*r* 97.6%

         \[\leadsto \color{blue}{\left(\frac{x + y}{z - y} \cdot \left(\sqrt[3]{z} \cdot \sqrt[3]{z}\right)\right) \cdot \sqrt[3]{z}} \]

      4. pow2 97.6%

         \[\leadsto \left(\frac{x + y}{z - y} \cdot \color{blue}{{\left(\sqrt[3]{z}\right)}^{2}}\right) \cdot \sqrt[3]{z} \]

   5. Applied egg-rr 97.6%

      \[\leadsto \color{blue}{\left(\frac{x + y}{z - y} \cdot {\left(\sqrt[3]{z}\right)}^{2}\right) \cdot \sqrt[3]{z}} \]
   6. Step-by-step derivation

      1. associate-*l* 97.7%

         \[\leadsto \color{blue}{\frac{x + y}{z - y} \cdot \left({\left(\sqrt[3]{z}\right)}^{2} \cdot \sqrt[3]{z}\right)} \]

      2. clear-num 97.7%

         \[\leadsto \color{blue}{\frac{1}{\frac{z - y}{x + y}}} \cdot \left({\left(\sqrt[3]{z}\right)}^{2} \cdot \sqrt[3]{z}\right) \]

      3. unpow2 97.7%

         \[\leadsto \frac{1}{\frac{z - y}{x + y}} \cdot \left(\color{blue}{\left(\sqrt[3]{z} \cdot \sqrt[3]{z}\right)} \cdot \sqrt[3]{z}\right) \]

      4. add-cube-cbrt 99.8%

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

      5. associate-*l/ 99.9%

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

      6. *-un-lft-identity 99.9%

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

   7. Applied egg-rr 99.9%

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

   8. Taylor expanded in x around 0 80.7%

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

   if -9.99999999999999934e145 < y < -1e-3

   1. Initial program 86.8%

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

   3. Taylor expanded in z around 0 87.1%

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

      1. associate-/r/ 99.7%

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

      2. add-cube-cbrt 97.7%

         \[\leadsto \frac{x + y}{z - y} \cdot \color{blue}{\left(\left(\sqrt[3]{z} \cdot \sqrt[3]{z}\right) \cdot \sqrt[3]{z}\right)} \]

      3. associate-*r* 97.7%

         \[\leadsto \color{blue}{\left(\frac{x + y}{z - y} \cdot \left(\sqrt[3]{z} \cdot \sqrt[3]{z}\right)\right) \cdot \sqrt[3]{z}} \]

      4. pow2 97.7%

         \[\leadsto \left(\frac{x + y}{z - y} \cdot \color{blue}{{\left(\sqrt[3]{z}\right)}^{2}}\right) \cdot \sqrt[3]{z} \]

   5. Applied egg-rr 97.7%

      \[\leadsto \color{blue}{\left(\frac{x + y}{z - y} \cdot {\left(\sqrt[3]{z}\right)}^{2}\right) \cdot \sqrt[3]{z}} \]
   6. Step-by-step derivation

      1. associate-*l* 97.7%

         \[\leadsto \color{blue}{\frac{x + y}{z - y} \cdot \left({\left(\sqrt[3]{z}\right)}^{2} \cdot \sqrt[3]{z}\right)} \]

      2. clear-num 97.7%

         \[\leadsto \color{blue}{\frac{1}{\frac{z - y}{x + y}}} \cdot \left({\left(\sqrt[3]{z}\right)}^{2} \cdot \sqrt[3]{z}\right) \]

      3. unpow2 97.7%

         \[\leadsto \frac{1}{\frac{z - y}{x + y}} \cdot \left(\color{blue}{\left(\sqrt[3]{z} \cdot \sqrt[3]{z}\right)} \cdot \sqrt[3]{z}\right) \]

      4. add-cube-cbrt 99.7%

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

      5. associate-*l/ 99.9%

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

      6. *-un-lft-identity 99.9%

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

   7. Applied egg-rr 99.9%

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

   8. Taylor expanded in x around inf 58.6%

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

   if -1e-3 < y < 2.7e-41

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf 83.2%

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

      1. +-commutative 83.2%

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

   5. Simplified 83.2%

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

   if 2.7e-41 < y < 7.6000000000000003e31

   1. Initial program 99.8%

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

   3. Taylor expanded in x around inf 87.1%

      \[\leadsto \color{blue}{\frac{x}{1 - \frac{y}{z}}} \]
3. Recombined 4 regimes into one program.
4. Add Preprocessing

Alternative 4: 94.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.5 \cdot 10^{-119} \lor \neg \left(y \leq 2.5 \cdot 10^{-185}\right):\\ \;\;\;\;\frac{z}{\frac{z - y}{y + x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 - \frac{y}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -4.5e-119) (not (<= y 2.5e-185)))
   (/ z (/ (- z y) (+ y x)))
   (/ x (- 1.0 (/ y z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -4.5e-119) || !(y <= 2.5e-185)) {
		tmp = z / ((z - y) / (y + x));
	} else {
		tmp = x / (1.0 - (y / 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 <= (-4.5d-119)) .or. (.not. (y <= 2.5d-185))) then
        tmp = z / ((z - y) / (y + x))
    else
        tmp = x / (1.0d0 - (y / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -4.5e-119) || !(y <= 2.5e-185)) {
		tmp = z / ((z - y) / (y + x));
	} else {
		tmp = x / (1.0 - (y / z));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -4.5e-119) or not (y <= 2.5e-185):
		tmp = z / ((z - y) / (y + x))
	else:
		tmp = x / (1.0 - (y / z))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -4.5e-119) || !(y <= 2.5e-185))
		tmp = Float64(z / Float64(Float64(z - y) / Float64(y + x)));
	else
		tmp = Float64(x / Float64(1.0 - Float64(y / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -4.5e-119) || ~((y <= 2.5e-185)))
		tmp = z / ((z - y) / (y + x));
	else
		tmp = x / (1.0 - (y / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -4.5e-119], N[Not[LessEqual[y, 2.5e-185]], $MachinePrecision]], N[(z / N[(N[(z - y), $MachinePrecision] / N[(y + x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -4.5000000000000003e-119 or 2.5000000000000001e-185 < y

   1. Initial program 84.6%

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

   3. Taylor expanded in z around 0 84.7%

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

      1. associate-/r/ 98.4%

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

      2. add-cube-cbrt 96.2%

         \[\leadsto \frac{x + y}{z - y} \cdot \color{blue}{\left(\left(\sqrt[3]{z} \cdot \sqrt[3]{z}\right) \cdot \sqrt[3]{z}\right)} \]

      3. associate-*r* 96.2%

         \[\leadsto \color{blue}{\left(\frac{x + y}{z - y} \cdot \left(\sqrt[3]{z} \cdot \sqrt[3]{z}\right)\right) \cdot \sqrt[3]{z}} \]

      4. pow2 96.2%

         \[\leadsto \left(\frac{x + y}{z - y} \cdot \color{blue}{{\left(\sqrt[3]{z}\right)}^{2}}\right) \cdot \sqrt[3]{z} \]

   5. Applied egg-rr 96.2%

      \[\leadsto \color{blue}{\left(\frac{x + y}{z - y} \cdot {\left(\sqrt[3]{z}\right)}^{2}\right) \cdot \sqrt[3]{z}} \]
   6. Step-by-step derivation

      1. associate-*l* 96.2%

         \[\leadsto \color{blue}{\frac{x + y}{z - y} \cdot \left({\left(\sqrt[3]{z}\right)}^{2} \cdot \sqrt[3]{z}\right)} \]

      2. clear-num 96.2%

         \[\leadsto \color{blue}{\frac{1}{\frac{z - y}{x + y}}} \cdot \left({\left(\sqrt[3]{z}\right)}^{2} \cdot \sqrt[3]{z}\right) \]

      3. unpow2 96.2%

         \[\leadsto \frac{1}{\frac{z - y}{x + y}} \cdot \left(\color{blue}{\left(\sqrt[3]{z} \cdot \sqrt[3]{z}\right)} \cdot \sqrt[3]{z}\right) \]

      4. add-cube-cbrt 98.2%

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

      5. associate-*l/ 98.4%

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

      6. *-un-lft-identity 98.4%

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

   7. Applied egg-rr 98.4%

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

   if -4.5000000000000003e-119 < y < 2.5000000000000001e-185

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 92.5%

      \[\leadsto \color{blue}{\frac{x}{1 - \frac{y}{z}}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 96.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.5 \cdot 10^{-119} \lor \neg \left(y \leq 2.5 \cdot 10^{-185}\right):\\ \;\;\;\;\frac{z}{\frac{z - y}{y + x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 - \frac{y}{z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 75.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -0.02 \lor \neg \left(y \leq 9.2 \cdot 10^{+35}\right):\\ \;\;\;\;z \cdot \frac{y + x}{-y}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -0.02) (not (<= y 9.2e+35))) (* z (/ (+ y x) (- y))) (+ y x)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -0.02) || !(y <= 9.2e+35)) {
		tmp = z * ((y + x) / -y);
	} else {
		tmp = y + 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 ((y <= (-0.02d0)) .or. (.not. (y <= 9.2d+35))) then
        tmp = z * ((y + x) / -y)
    else
        tmp = y + x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -0.02) || !(y <= 9.2e+35)) {
		tmp = z * ((y + x) / -y);
	} else {
		tmp = y + x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -0.02) or not (y <= 9.2e+35):
		tmp = z * ((y + x) / -y)
	else:
		tmp = y + x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -0.02) || !(y <= 9.2e+35))
		tmp = Float64(z * Float64(Float64(y + x) / Float64(-y)));
	else
		tmp = Float64(y + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -0.02) || ~((y <= 9.2e+35)))
		tmp = z * ((y + x) / -y);
	else
		tmp = y + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -0.02], N[Not[LessEqual[y, 9.2e+35]], $MachinePrecision]], N[(z * N[(N[(y + x), $MachinePrecision] / (-y)), $MachinePrecision]), $MachinePrecision], N[(y + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -0.0200000000000000004 or 9.1999999999999993e35 < y

   1. Initial program 77.0%

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

   3. Taylor expanded in z around 0 64.5%

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

      1. mul-1-neg 64.5%

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

      2. associate-/l* 78.9%

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

      3. distribute-rgt-neg-in 78.9%

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

      4. distribute-neg-frac2 78.9%

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

      5. +-commutative 78.9%

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

   5. Simplified 78.9%

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

   if -0.0200000000000000004 < y < 9.1999999999999993e35

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf 80.0%

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

      1. +-commutative 80.0%

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

   5. Simplified 80.0%

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

4. Final simplification 79.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.02 \lor \neg \left(y \leq 9.2 \cdot 10^{+35}\right):\\ \;\;\;\;z \cdot \frac{y + x}{-y}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 75.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -0.7:\\ \;\;\;\;\frac{-z}{\frac{y}{y + x}}\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{+35}:\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{y + x}{-y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -0.7)
   (/ (- z) (/ y (+ y x)))
   (if (<= y 1.9e+35) (+ y x) (* z (/ (+ y x) (- y))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -0.7) {
		tmp = -z / (y / (y + x));
	} else if (y <= 1.9e+35) {
		tmp = y + x;
	} else {
		tmp = z * ((y + 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 <= (-0.7d0)) then
        tmp = -z / (y / (y + x))
    else if (y <= 1.9d+35) then
        tmp = y + x
    else
        tmp = z * ((y + x) / -y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -0.7) {
		tmp = -z / (y / (y + x));
	} else if (y <= 1.9e+35) {
		tmp = y + x;
	} else {
		tmp = z * ((y + x) / -y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -0.7:
		tmp = -z / (y / (y + x))
	elif y <= 1.9e+35:
		tmp = y + x
	else:
		tmp = z * ((y + x) / -y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -0.7)
		tmp = Float64(Float64(-z) / Float64(y / Float64(y + x)));
	elseif (y <= 1.9e+35)
		tmp = Float64(y + x);
	else
		tmp = Float64(z * Float64(Float64(y + x) / Float64(-y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -0.7)
		tmp = -z / (y / (y + x));
	elseif (y <= 1.9e+35)
		tmp = y + x;
	else
		tmp = z * ((y + x) / -y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -0.7], N[((-z) / N[(y / N[(y + x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.9e+35], N[(y + x), $MachinePrecision], N[(z * N[(N[(y + x), $MachinePrecision] / (-y)), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -0.69999999999999996

   1. Initial program 78.1%

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

   3. Taylor expanded in z around 0 78.2%

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

      1. associate-/r/ 99.8%

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

      2. add-cube-cbrt 97.6%

         \[\leadsto \frac{x + y}{z - y} \cdot \color{blue}{\left(\left(\sqrt[3]{z} \cdot \sqrt[3]{z}\right) \cdot \sqrt[3]{z}\right)} \]

      3. associate-*r* 97.6%

         \[\leadsto \color{blue}{\left(\frac{x + y}{z - y} \cdot \left(\sqrt[3]{z} \cdot \sqrt[3]{z}\right)\right) \cdot \sqrt[3]{z}} \]

      4. pow2 97.6%

         \[\leadsto \left(\frac{x + y}{z - y} \cdot \color{blue}{{\left(\sqrt[3]{z}\right)}^{2}}\right) \cdot \sqrt[3]{z} \]

   5. Applied egg-rr 97.6%

      \[\leadsto \color{blue}{\left(\frac{x + y}{z - y} \cdot {\left(\sqrt[3]{z}\right)}^{2}\right) \cdot \sqrt[3]{z}} \]
   6. Step-by-step derivation

      1. associate-*l* 97.6%

         \[\leadsto \color{blue}{\frac{x + y}{z - y} \cdot \left({\left(\sqrt[3]{z}\right)}^{2} \cdot \sqrt[3]{z}\right)} \]

      2. clear-num 97.6%

         \[\leadsto \color{blue}{\frac{1}{\frac{z - y}{x + y}}} \cdot \left({\left(\sqrt[3]{z}\right)}^{2} \cdot \sqrt[3]{z}\right) \]

      3. unpow2 97.6%

         \[\leadsto \frac{1}{\frac{z - y}{x + y}} \cdot \left(\color{blue}{\left(\sqrt[3]{z} \cdot \sqrt[3]{z}\right)} \cdot \sqrt[3]{z}\right) \]

      4. add-cube-cbrt 99.8%

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

      5. associate-*l/ 99.9%

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

      6. *-un-lft-identity 99.9%

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

   7. Applied egg-rr 99.9%

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

   8. Taylor expanded in z around 0 81.7%

      \[\leadsto \frac{z}{\frac{\color{blue}{-1 \cdot y}}{x + y}} \]
   9. Step-by-step derivation

      1. neg-mul-1 81.7%

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

   10. Simplified 81.7%

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

   if -0.69999999999999996 < y < 1.9e35

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf 80.0%

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

      1. +-commutative 80.0%

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

   5. Simplified 80.0%

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

   if 1.9e35 < y

   1. Initial program 75.6%

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

   3. Taylor expanded in z around 0 65.3%

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

      1. mul-1-neg 65.3%

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

      2. associate-/l* 75.5%

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

      3. distribute-rgt-neg-in 75.5%

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

      4. distribute-neg-frac2 75.5%

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

      5. +-commutative 75.5%

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

   5. Simplified 75.5%

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

4. Final simplification 79.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.7:\\ \;\;\;\;\frac{-z}{\frac{y}{y + x}}\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{+35}:\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{y + x}{-y}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 66.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -9.5 \cdot 10^{+42} \lor \neg \left(x \leq 380000000000\right):\\ \;\;\;\;\frac{x}{1 - \frac{y}{z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{z - y}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -9.5e+42) (not (<= x 380000000000.0)))
   (/ x (- 1.0 (/ y z)))
   (/ y (/ (- z y) z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -9.5e+42) || !(x <= 380000000000.0)) {
		tmp = x / (1.0 - (y / z));
	} else {
		tmp = y / ((z - y) / 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 ((x <= (-9.5d+42)) .or. (.not. (x <= 380000000000.0d0))) then
        tmp = x / (1.0d0 - (y / z))
    else
        tmp = y / ((z - y) / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -9.5e+42) || !(x <= 380000000000.0)) {
		tmp = x / (1.0 - (y / z));
	} else {
		tmp = y / ((z - y) / z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -9.5e+42) or not (x <= 380000000000.0):
		tmp = x / (1.0 - (y / z))
	else:
		tmp = y / ((z - y) / z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -9.5e+42) || !(x <= 380000000000.0))
		tmp = Float64(x / Float64(1.0 - Float64(y / z)));
	else
		tmp = Float64(y / Float64(Float64(z - y) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -9.5e+42) || ~((x <= 380000000000.0)))
		tmp = x / (1.0 - (y / z));
	else
		tmp = y / ((z - y) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -9.5e+42], N[Not[LessEqual[x, 380000000000.0]], $MachinePrecision]], N[(x / N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y / N[(N[(z - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -9.50000000000000019e42 or 3.8e11 < x

   1. Initial program 89.1%

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

   3. Taylor expanded in x around inf 75.6%

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

   if -9.50000000000000019e42 < x < 3.8e11

   1. Initial program 87.8%

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

   3. Taylor expanded in z around 0 87.9%

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

   4. Taylor expanded in x around 0 64.0%

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

4. Final simplification 70.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -9.5 \cdot 10^{+42} \lor \neg \left(x \leq 380000000000\right):\\ \;\;\;\;\frac{x}{1 - \frac{y}{z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{z - y}{z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 66.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 1 - \frac{y}{z}\\ \mathbf{if}\;x \leq -1.8 \cdot 10^{+40} \lor \neg \left(x \leq 520000000000\right):\\ \;\;\;\;\frac{x}{t\_0}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{t\_0}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- 1.0 (/ y z))))
   (if (or (<= x -1.8e+40) (not (<= x 520000000000.0))) (/ x t_0) (/ y t_0))))

C

double code(double x, double y, double z) {
	double t_0 = 1.0 - (y / z);
	double tmp;
	if ((x <= -1.8e+40) || !(x <= 520000000000.0)) {
		tmp = x / t_0;
	} else {
		tmp = y / 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 = 1.0d0 - (y / z)
    if ((x <= (-1.8d+40)) .or. (.not. (x <= 520000000000.0d0))) then
        tmp = x / t_0
    else
        tmp = y / t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = 1.0 - (y / z);
	double tmp;
	if ((x <= -1.8e+40) || !(x <= 520000000000.0)) {
		tmp = x / t_0;
	} else {
		tmp = y / t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = 1.0 - (y / z)
	tmp = 0
	if (x <= -1.8e+40) or not (x <= 520000000000.0):
		tmp = x / t_0
	else:
		tmp = y / t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(1.0 - Float64(y / z))
	tmp = 0.0
	if ((x <= -1.8e+40) || !(x <= 520000000000.0))
		tmp = Float64(x / t_0);
	else
		tmp = Float64(y / t_0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = 1.0 - (y / z);
	tmp = 0.0;
	if ((x <= -1.8e+40) || ~((x <= 520000000000.0)))
		tmp = x / t_0;
	else
		tmp = y / t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[x, -1.8e+40], N[Not[LessEqual[x, 520000000000.0]], $MachinePrecision]], N[(x / t$95$0), $MachinePrecision], N[(y / t$95$0), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -1.79999999999999998e40 or 5.2e11 < x

   1. Initial program 89.1%

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

   3. Taylor expanded in x around inf 75.6%

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

   if -1.79999999999999998e40 < x < 5.2e11

   1. Initial program 87.8%

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

   3. Taylor expanded in x around 0 64.0%

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

4. Final simplification 70.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.8 \cdot 10^{+40} \lor \neg \left(x \leq 520000000000\right):\\ \;\;\;\;\frac{x}{1 - \frac{y}{z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{1 - \frac{y}{z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 68.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.9 \cdot 10^{+84} \lor \neg \left(y \leq 9 \cdot 10^{+36}\right):\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 - \frac{y}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -5.9e+84) (not (<= y 9e+36))) (- z) (/ x (- 1.0 (/ y z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -5.9e+84) || !(y <= 9e+36)) {
		tmp = -z;
	} else {
		tmp = x / (1.0 - (y / 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 <= (-5.9d+84)) .or. (.not. (y <= 9d+36))) then
        tmp = -z
    else
        tmp = x / (1.0d0 - (y / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -5.9e+84) || !(y <= 9e+36)) {
		tmp = -z;
	} else {
		tmp = x / (1.0 - (y / z));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -5.9e+84) or not (y <= 9e+36):
		tmp = -z
	else:
		tmp = x / (1.0 - (y / z))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -5.9e+84) || !(y <= 9e+36))
		tmp = Float64(-z);
	else
		tmp = Float64(x / Float64(1.0 - Float64(y / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -5.9e+84) || ~((y <= 9e+36)))
		tmp = -z;
	else
		tmp = x / (1.0 - (y / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -5.9e+84], N[Not[LessEqual[y, 9e+36]], $MachinePrecision]], (-z), N[(x / N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -5.89999999999999984e84 or 8.99999999999999994e36 < y

   1. Initial program 72.4%

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

   3. Taylor expanded in y around inf 64.2%

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

      1. neg-mul-1 64.2%

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

   5. Simplified 64.2%

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

   if -5.89999999999999984e84 < y < 8.99999999999999994e36

   1. Initial program 99.2%

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

   3. Taylor expanded in x around inf 73.5%

      \[\leadsto \color{blue}{\frac{x}{1 - \frac{y}{z}}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 69.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.9 \cdot 10^{+84} \lor \neg \left(y \leq 9 \cdot 10^{+36}\right):\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 - \frac{y}{z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 68.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.8 \cdot 10^{+51} \lor \neg \left(y \leq 9.6 \cdot 10^{+36}\right):\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -5.8e+51) (not (<= y 9.6e+36))) (- z) (+ y x)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -5.8e+51) || !(y <= 9.6e+36)) {
		tmp = -z;
	} else {
		tmp = y + 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 ((y <= (-5.8d+51)) .or. (.not. (y <= 9.6d+36))) then
        tmp = -z
    else
        tmp = y + x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -5.8e+51) || !(y <= 9.6e+36)) {
		tmp = -z;
	} else {
		tmp = y + x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -5.8e+51) or not (y <= 9.6e+36):
		tmp = -z
	else:
		tmp = y + x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -5.8e+51) || !(y <= 9.6e+36))
		tmp = Float64(-z);
	else
		tmp = Float64(y + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -5.8e+51) || ~((y <= 9.6e+36)))
		tmp = -z;
	else
		tmp = y + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -5.8e+51], N[Not[LessEqual[y, 9.6e+36]], $MachinePrecision]], (-z), N[(y + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -5.7999999999999997e51 or 9.5999999999999997e36 < y

   1. Initial program 75.2%

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

   3. Taylor expanded in y around inf 61.3%

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

      1. neg-mul-1 61.3%

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

   5. Simplified 61.3%

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

   if -5.7999999999999997e51 < y < 9.5999999999999997e36

   1. Initial program 99.2%

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

   3. Taylor expanded in z around inf 76.3%

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

      1. +-commutative 76.3%

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

   5. Simplified 76.3%

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

4. Final simplification 69.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.8 \cdot 10^{+51} \lor \neg \left(y \leq 9.6 \cdot 10^{+36}\right):\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 59.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.65 \cdot 10^{+47} \lor \neg \left(y \leq 3.1 \cdot 10^{+35}\right):\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -1.65e+47) (not (<= y 3.1e+35))) (- z) x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.65e+47) || !(y <= 3.1e+35)) {
		tmp = -z;
	} 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 ((y <= (-1.65d+47)) .or. (.not. (y <= 3.1d+35))) then
        tmp = -z
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.65e+47) || !(y <= 3.1e+35)) {
		tmp = -z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -1.65e+47) or not (y <= 3.1e+35):
		tmp = -z
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -1.65e+47) || !(y <= 3.1e+35))
		tmp = Float64(-z);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -1.65e+47) || ~((y <= 3.1e+35)))
		tmp = -z;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -1.65e+47], N[Not[LessEqual[y, 3.1e+35]], $MachinePrecision]], (-z), x]

Derivation

1. Split input into 2 regimes

2. if y < -1.65e47 or 3.09999999999999987e35 < y

   1. Initial program 75.2%

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

   3. Taylor expanded in y around inf 61.3%

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

      1. neg-mul-1 61.3%

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

   5. Simplified 61.3%

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

   if -1.65e47 < y < 3.09999999999999987e35

   1. Initial program 99.2%

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

   3. Taylor expanded in y around 0 61.2%

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

4. Final simplification 61.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.65 \cdot 10^{+47} \lor \neg \left(y \leq 3.1 \cdot 10^{+35}\right):\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 40.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.7 \cdot 10^{-29}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 10^{-179}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -4.7e-29) x (if (<= x 1e-179) y x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -4.7e-29) {
		tmp = x;
	} else if (x <= 1e-179) {
		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 <= (-4.7d-29)) then
        tmp = x
    else if (x <= 1d-179) 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 <= -4.7e-29) {
		tmp = x;
	} else if (x <= 1e-179) {
		tmp = y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -4.7e-29:
		tmp = x
	elif x <= 1e-179:
		tmp = y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -4.7e-29)
		tmp = x;
	elseif (x <= 1e-179)
		tmp = y;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -4.7e-29)
		tmp = x;
	elseif (x <= 1e-179)
		tmp = y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -4.7e-29], x, If[LessEqual[x, 1e-179], y, x]]

Derivation

1. Split input into 2 regimes

2. if x < -4.6999999999999998e-29 or 1e-179 < x

   1. Initial program 88.3%

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

   3. Taylor expanded in y around 0 46.7%

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

   if -4.6999999999999998e-29 < x < 1e-179

   1. Initial program 89.2%

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

   3. Taylor expanded in z around inf 48.0%

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

      1. +-commutative 48.0%

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

   5. Simplified 48.0%

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

   6. Taylor expanded in y around inf 35.0%

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

Alternative 13: 35.2% 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 88.5%

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

3. Taylor expanded in y around 0 37.6%

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

Developer Target 1: 93.9% 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 2024191 
(FPCore (x y z)
  :name "Graphics.Rendering.Chart.Backend.Diagrams:calcFontMetrics from Chart-diagrams-1.5.1, A"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< y -3742931076268985600000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (* (/ (+ y x) (- y)) z) (if (< y 3553466245608673400000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (/ (+ x y) (- 1 (/ y z))) (* (/ (+ y x) (- y)) z))))

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