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

Percentage Accurate: 87.8% → 99.6%

Time: 6.3s

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: 87.8% 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: 99.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x + y}{1 - \frac{y}{z}}\\ \mathbf{if}\;t_0 \leq -4 \cdot 10^{-257} \lor \neg \left(t_0 \leq 5 \cdot 10^{-298}\right):\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\left(\left(-z\right) - \frac{z}{\frac{y}{x}}\right) - \frac{z}{\frac{y}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ (+ x y) (- 1.0 (/ y z)))))
   (if (or (<= t_0 -4e-257) (not (<= t_0 5e-298)))
     t_0
     (- (- (- z) (/ z (/ y x))) (/ z (/ y z))))))

C

double code(double x, double y, double z) {
	double t_0 = (x + y) / (1.0 - (y / z));
	double tmp;
	if ((t_0 <= -4e-257) || !(t_0 <= 5e-298)) {
		tmp = t_0;
	} else {
		tmp = (-z - (z / (y / x))) - (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) :: t_0
    real(8) :: tmp
    t_0 = (x + y) / (1.0d0 - (y / z))
    if ((t_0 <= (-4d-257)) .or. (.not. (t_0 <= 5d-298))) then
        tmp = t_0
    else
        tmp = (-z - (z / (y / x))) - (z / (y / z))
    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 <= -4e-257) || !(t_0 <= 5e-298)) {
		tmp = t_0;
	} else {
		tmp = (-z - (z / (y / x))) - (z / (y / z));
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (x + y) / (1.0 - (y / z))
	tmp = 0
	if (t_0 <= -4e-257) or not (t_0 <= 5e-298):
		tmp = t_0
	else:
		tmp = (-z - (z / (y / x))) - (z / (y / z))
	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 <= -4e-257) || !(t_0 <= 5e-298))
		tmp = t_0;
	else
		tmp = Float64(Float64(Float64(-z) - Float64(z / Float64(y / x))) - Float64(z / Float64(y / z)));
	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 <= -4e-257) || ~((t_0 <= 5e-298)))
		tmp = t_0;
	else
		tmp = (-z - (z / (y / x))) - (z / (y / z));
	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, -4e-257], N[Not[LessEqual[t$95$0, 5e-298]], $MachinePrecision]], t$95$0, N[(N[((-z) - N[(z / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(z / N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (+.f64 x y) (-.f64 1 (/.f64 y z))) < -3.9999999999999999e-257 or 5.0000000000000002e-298 < (/.f64 (+.f64 x y) (-.f64 1 (/.f64 y z)))

   1. Initial program 99.9%

      \[\frac{x + y}{1 - \frac{y}{z}} \]

   if -3.9999999999999999e-257 < (/.f64 (+.f64 x y) (-.f64 1 (/.f64 y z))) < 5.0000000000000002e-298

   1. Initial program 9.5%

      \[\frac{x + y}{1 - \frac{y}{z}} \]

   2. Taylor expanded in y around inf 99.9%

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

      1. mul-1-neg 99.9%

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

      2. unsub-neg 99.9%

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

      3. mul-1-neg 99.9%

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

      4. associate-/l* 100.0%

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

      5. unpow2 100.0%

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

      6. associate-/l* 100.0%

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

   4. Simplified 100.0%

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

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + y}{1 - \frac{y}{z}} \leq -4 \cdot 10^{-257} \lor \neg \left(\frac{x + y}{1 - \frac{y}{z}} \leq 5 \cdot 10^{-298}\right):\\ \;\;\;\;\frac{x + y}{1 - \frac{y}{z}}\\ \mathbf{else}:\\ \;\;\;\;\left(\left(-z\right) - \frac{z}{\frac{y}{x}}\right) - \frac{z}{\frac{y}{z}}\\ \end{array} \]

Alternative 2: 99.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x + y}{1 - \frac{y}{z}}\\ \mathbf{if}\;t_0 \leq -4 \cdot 10^{-257} \lor \neg \left(t_0 \leq 5 \cdot 10^{-298}\right):\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\left(-z\right) - z \cdot \frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ (+ x y) (- 1.0 (/ y z)))))
   (if (or (<= t_0 -4e-257) (not (<= t_0 5e-298)))
     t_0
     (- (- z) (* z (/ x y))))))

C

double code(double x, double y, double z) {
	double t_0 = (x + y) / (1.0 - (y / z));
	double tmp;
	if ((t_0 <= -4e-257) || !(t_0 <= 5e-298)) {
		tmp = t_0;
	} else {
		tmp = -z - (z * (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) :: t_0
    real(8) :: tmp
    t_0 = (x + y) / (1.0d0 - (y / z))
    if ((t_0 <= (-4d-257)) .or. (.not. (t_0 <= 5d-298))) then
        tmp = t_0
    else
        tmp = -z - (z * (x / 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 <= -4e-257) || !(t_0 <= 5e-298)) {
		tmp = t_0;
	} else {
		tmp = -z - (z * (x / y));
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (x + y) / (1.0 - (y / z))
	tmp = 0
	if (t_0 <= -4e-257) or not (t_0 <= 5e-298):
		tmp = t_0
	else:
		tmp = -z - (z * (x / 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 <= -4e-257) || !(t_0 <= 5e-298))
		tmp = t_0;
	else
		tmp = Float64(Float64(-z) - Float64(z * Float64(x / 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 <= -4e-257) || ~((t_0 <= 5e-298)))
		tmp = t_0;
	else
		tmp = -z - (z * (x / 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, -4e-257], N[Not[LessEqual[t$95$0, 5e-298]], $MachinePrecision]], t$95$0, N[((-z) - N[(z * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (+.f64 x y) (-.f64 1 (/.f64 y z))) < -3.9999999999999999e-257 or 5.0000000000000002e-298 < (/.f64 (+.f64 x y) (-.f64 1 (/.f64 y z)))

   1. Initial program 99.9%

      \[\frac{x + y}{1 - \frac{y}{z}} \]

   if -3.9999999999999999e-257 < (/.f64 (+.f64 x y) (-.f64 1 (/.f64 y z))) < 5.0000000000000002e-298

   1. Initial program 9.5%

      \[\frac{x + y}{1 - \frac{y}{z}} \]

   2. Taylor expanded in z around 0 96.5%

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

      1. mul-1-neg 96.5%

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

      2. associate-/l* 9.5%

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

      3. +-commutative 9.5%

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

      4. distribute-neg-frac 9.5%

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

      5. distribute-neg-in 9.5%

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

      6. +-commutative 9.5%

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

      7. sub-neg 9.5%

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

   4. Simplified 9.5%

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

   5. Taylor expanded in y around 0 99.9%

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

      1. distribute-lft-out 99.9%

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

      2. associate-*r/ 99.9%

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

      3. neg-mul-1 99.9%

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

   7. Simplified 99.9%

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

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + y}{1 - \frac{y}{z}} \leq -4 \cdot 10^{-257} \lor \neg \left(\frac{x + y}{1 - \frac{y}{z}} \leq 5 \cdot 10^{-298}\right):\\ \;\;\;\;\frac{x + y}{1 - \frac{y}{z}}\\ \mathbf{else}:\\ \;\;\;\;\left(-z\right) - z \cdot \frac{x}{y}\\ \end{array} \]

Alternative 3: 68.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.7 \cdot 10^{+116}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq -7 \cdot 10^{+69}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq -2 \cdot 10^{+64}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq -2.8 \cdot 10^{-184}:\\ \;\;\;\;\frac{x}{1 - \frac{y}{z}}\\ \mathbf{elif}\;y \leq 1.08 \cdot 10^{+89}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -2.7e+116)
   (- z)
   (if (<= y -7e+69)
     (+ x y)
     (if (<= y -2e+64)
       (- z)
       (if (<= y -2.8e-184)
         (/ x (- 1.0 (/ y z)))
         (if (<= y 1.08e+89) (+ x y) (- z)))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -2.7e+116) {
		tmp = -z;
	} else if (y <= -7e+69) {
		tmp = x + y;
	} else if (y <= -2e+64) {
		tmp = -z;
	} else if (y <= -2.8e-184) {
		tmp = x / (1.0 - (y / z));
	} else if (y <= 1.08e+89) {
		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 <= (-2.7d+116)) then
        tmp = -z
    else if (y <= (-7d+69)) then
        tmp = x + y
    else if (y <= (-2d+64)) then
        tmp = -z
    else if (y <= (-2.8d-184)) then
        tmp = x / (1.0d0 - (y / z))
    else if (y <= 1.08d+89) 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 <= -2.7e+116) {
		tmp = -z;
	} else if (y <= -7e+69) {
		tmp = x + y;
	} else if (y <= -2e+64) {
		tmp = -z;
	} else if (y <= -2.8e-184) {
		tmp = x / (1.0 - (y / z));
	} else if (y <= 1.08e+89) {
		tmp = x + y;
	} else {
		tmp = -z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -2.7e+116:
		tmp = -z
	elif y <= -7e+69:
		tmp = x + y
	elif y <= -2e+64:
		tmp = -z
	elif y <= -2.8e-184:
		tmp = x / (1.0 - (y / z))
	elif y <= 1.08e+89:
		tmp = x + y
	else:
		tmp = -z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -2.7e+116)
		tmp = Float64(-z);
	elseif (y <= -7e+69)
		tmp = Float64(x + y);
	elseif (y <= -2e+64)
		tmp = Float64(-z);
	elseif (y <= -2.8e-184)
		tmp = Float64(x / Float64(1.0 - Float64(y / z)));
	elseif (y <= 1.08e+89)
		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 <= -2.7e+116)
		tmp = -z;
	elseif (y <= -7e+69)
		tmp = x + y;
	elseif (y <= -2e+64)
		tmp = -z;
	elseif (y <= -2.8e-184)
		tmp = x / (1.0 - (y / z));
	elseif (y <= 1.08e+89)
		tmp = x + y;
	else
		tmp = -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -2.7e+116], (-z), If[LessEqual[y, -7e+69], N[(x + y), $MachinePrecision], If[LessEqual[y, -2e+64], (-z), If[LessEqual[y, -2.8e-184], N[(x / N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.08e+89], N[(x + y), $MachinePrecision], (-z)]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.7e116 or -6.99999999999999974e69 < y < -2.00000000000000004e64 or 1.08000000000000006e89 < y

   1. Initial program 72.9%

      \[\frac{x + y}{1 - \frac{y}{z}} \]

   2. Taylor expanded in y around inf 74.2%

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

      1. mul-1-neg 74.2%

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

   4. Simplified 74.2%

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

   if -2.7e116 < y < -6.99999999999999974e69 or -2.7999999999999998e-184 < y < 1.08000000000000006e89

   1. Initial program 96.4%

      \[\frac{x + y}{1 - \frac{y}{z}} \]

   2. Taylor expanded in z around inf 74.2%

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

   if -2.00000000000000004e64 < y < -2.7999999999999998e-184

   1. Initial program 99.8%

      \[\frac{x + y}{1 - \frac{y}{z}} \]

   2. Taylor expanded in x around inf 66.7%

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

4. Final simplification 72.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.7 \cdot 10^{+116}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq -7 \cdot 10^{+69}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq -2 \cdot 10^{+64}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq -2.8 \cdot 10^{-184}:\\ \;\;\;\;\frac{x}{1 - \frac{y}{z}}\\ \mathbf{elif}\;y \leq 1.08 \cdot 10^{+89}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \]

Alternative 4: 66.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 1 - \frac{y}{z}\\ t_1 := \frac{x}{t_0}\\ \mathbf{if}\;x \leq -2.15 \cdot 10^{-13}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 7.2 \cdot 10^{-102}:\\ \;\;\;\;\frac{y}{t_0}\\ \mathbf{elif}\;x \leq 7 \cdot 10^{+25}:\\ \;\;\;\;\left(-z\right) - z \cdot \frac{x}{y}\\ \mathbf{elif}\;x \leq 1.3 \cdot 10^{+47}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- 1.0 (/ y z))) (t_1 (/ x t_0)))
   (if (<= x -2.15e-13)
     t_1
     (if (<= x 7.2e-102)
       (/ y t_0)
       (if (<= x 7e+25)
         (- (- z) (* z (/ x y)))
         (if (<= x 1.3e+47) (+ x y) t_1))))))

C

double code(double x, double y, double z) {
	double t_0 = 1.0 - (y / z);
	double t_1 = x / t_0;
	double tmp;
	if (x <= -2.15e-13) {
		tmp = t_1;
	} else if (x <= 7.2e-102) {
		tmp = y / t_0;
	} else if (x <= 7e+25) {
		tmp = -z - (z * (x / y));
	} else if (x <= 1.3e+47) {
		tmp = x + y;
	} else {
		tmp = t_1;
	}
	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) :: t_1
    real(8) :: tmp
    t_0 = 1.0d0 - (y / z)
    t_1 = x / t_0
    if (x <= (-2.15d-13)) then
        tmp = t_1
    else if (x <= 7.2d-102) then
        tmp = y / t_0
    else if (x <= 7d+25) then
        tmp = -z - (z * (x / y))
    else if (x <= 1.3d+47) then
        tmp = x + y
    else
        tmp = t_1
    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 t_1 = x / t_0;
	double tmp;
	if (x <= -2.15e-13) {
		tmp = t_1;
	} else if (x <= 7.2e-102) {
		tmp = y / t_0;
	} else if (x <= 7e+25) {
		tmp = -z - (z * (x / y));
	} else if (x <= 1.3e+47) {
		tmp = x + y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = 1.0 - (y / z)
	t_1 = x / t_0
	tmp = 0
	if x <= -2.15e-13:
		tmp = t_1
	elif x <= 7.2e-102:
		tmp = y / t_0
	elif x <= 7e+25:
		tmp = -z - (z * (x / y))
	elif x <= 1.3e+47:
		tmp = x + y
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(1.0 - Float64(y / z))
	t_1 = Float64(x / t_0)
	tmp = 0.0
	if (x <= -2.15e-13)
		tmp = t_1;
	elseif (x <= 7.2e-102)
		tmp = Float64(y / t_0);
	elseif (x <= 7e+25)
		tmp = Float64(Float64(-z) - Float64(z * Float64(x / y)));
	elseif (x <= 1.3e+47)
		tmp = Float64(x + y);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = 1.0 - (y / z);
	t_1 = x / t_0;
	tmp = 0.0;
	if (x <= -2.15e-13)
		tmp = t_1;
	elseif (x <= 7.2e-102)
		tmp = y / t_0;
	elseif (x <= 7e+25)
		tmp = -z - (z * (x / y));
	elseif (x <= 1.3e+47)
		tmp = x + y;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(x / t$95$0), $MachinePrecision]}, If[LessEqual[x, -2.15e-13], t$95$1, If[LessEqual[x, 7.2e-102], N[(y / t$95$0), $MachinePrecision], If[LessEqual[x, 7e+25], N[((-z) - N[(z * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.3e+47], N[(x + y), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -2.1499999999999999e-13 or 1.30000000000000002e47 < x

   1. Initial program 88.8%

      \[\frac{x + y}{1 - \frac{y}{z}} \]

   2. Taylor expanded in x around inf 75.2%

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

   if -2.1499999999999999e-13 < x < 7.2e-102

   1. Initial program 92.8%

      \[\frac{x + y}{1 - \frac{y}{z}} \]

   2. Taylor expanded in x around 0 74.8%

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

   if 7.2e-102 < x < 6.99999999999999999e25

   1. Initial program 86.8%

      \[\frac{x + y}{1 - \frac{y}{z}} \]

   2. Taylor expanded in z around 0 61.2%

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

      1. mul-1-neg 61.2%

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

      2. associate-/l* 58.1%

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

      3. +-commutative 58.1%

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

      4. distribute-neg-frac 58.1%

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

      5. distribute-neg-in 58.1%

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

      6. +-commutative 58.1%

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

      7. sub-neg 58.1%

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

   4. Simplified 58.1%

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

   5. Taylor expanded in y around 0 67.9%

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

      1. distribute-lft-out 67.9%

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

      2. associate-*r/ 71.2%

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

      3. neg-mul-1 71.2%

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

   7. Simplified 71.2%

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

   if 6.99999999999999999e25 < x < 1.30000000000000002e47

   1. Initial program 100.0%

      \[\frac{x + y}{1 - \frac{y}{z}} \]

   2. Taylor expanded in z around inf 85.9%

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

4. Final simplification 74.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.15 \cdot 10^{-13}:\\ \;\;\;\;\frac{x}{1 - \frac{y}{z}}\\ \mathbf{elif}\;x \leq 7.2 \cdot 10^{-102}:\\ \;\;\;\;\frac{y}{1 - \frac{y}{z}}\\ \mathbf{elif}\;x \leq 7 \cdot 10^{+25}:\\ \;\;\;\;\left(-z\right) - z \cdot \frac{x}{y}\\ \mathbf{elif}\;x \leq 1.3 \cdot 10^{+47}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 - \frac{y}{z}}\\ \end{array} \]

Alternative 5: 67.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 1 - \frac{y}{z}\\ \mathbf{if}\;x \leq -9 \cdot 10^{-14} \lor \neg \left(x \leq 9.5 \cdot 10^{-42}\right):\\ \;\;\;\;\frac{x}{t_0}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{t_0}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- 1.0 (/ y z))))
   (if (or (<= x -9e-14) (not (<= x 9.5e-42))) (/ 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 <= -9e-14) || !(x <= 9.5e-42)) {
		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 <= (-9d-14)) .or. (.not. (x <= 9.5d-42))) 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 <= -9e-14) || !(x <= 9.5e-42)) {
		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 <= -9e-14) or not (x <= 9.5e-42):
		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 <= -9e-14) || !(x <= 9.5e-42))
		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 <= -9e-14) || ~((x <= 9.5e-42)))
		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, -9e-14], N[Not[LessEqual[x, 9.5e-42]], $MachinePrecision]], N[(x / t$95$0), $MachinePrecision], N[(y / t$95$0), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -8.9999999999999995e-14 or 9.49999999999999948e-42 < x

   1. Initial program 88.9%

      \[\frac{x + y}{1 - \frac{y}{z}} \]

   2. Taylor expanded in x around inf 71.8%

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

   if -8.9999999999999995e-14 < x < 9.49999999999999948e-42

   1. Initial program 92.5%

      \[\frac{x + y}{1 - \frac{y}{z}} \]

   2. Taylor expanded in x around 0 75.1%

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

4. Final simplification 73.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -9 \cdot 10^{-14} \lor \neg \left(x \leq 9.5 \cdot 10^{-42}\right):\\ \;\;\;\;\frac{x}{1 - \frac{y}{z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{1 - \frac{y}{z}}\\ \end{array} \]

Alternative 6: 58.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.2 \cdot 10^{+115}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq -5.2 \cdot 10^{+70}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq -2 \cdot 10^{+54}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq 1.05 \cdot 10^{-40}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -6.2e+115)
   (- z)
   (if (<= y -5.2e+70)
     y
     (if (<= y -2e+54) (- z) (if (<= y 1.05e-40) x (- z))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -6.2e+115) {
		tmp = -z;
	} else if (y <= -5.2e+70) {
		tmp = y;
	} else if (y <= -2e+54) {
		tmp = -z;
	} else if (y <= 1.05e-40) {
		tmp = x;
	} 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 <= (-6.2d+115)) then
        tmp = -z
    else if (y <= (-5.2d+70)) then
        tmp = y
    else if (y <= (-2d+54)) then
        tmp = -z
    else if (y <= 1.05d-40) then
        tmp = x
    else
        tmp = -z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -6.2e+115) {
		tmp = -z;
	} else if (y <= -5.2e+70) {
		tmp = y;
	} else if (y <= -2e+54) {
		tmp = -z;
	} else if (y <= 1.05e-40) {
		tmp = x;
	} else {
		tmp = -z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -6.2e+115:
		tmp = -z
	elif y <= -5.2e+70:
		tmp = y
	elif y <= -2e+54:
		tmp = -z
	elif y <= 1.05e-40:
		tmp = x
	else:
		tmp = -z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -6.2e+115)
		tmp = Float64(-z);
	elseif (y <= -5.2e+70)
		tmp = y;
	elseif (y <= -2e+54)
		tmp = Float64(-z);
	elseif (y <= 1.05e-40)
		tmp = x;
	else
		tmp = Float64(-z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -6.2e+115)
		tmp = -z;
	elseif (y <= -5.2e+70)
		tmp = y;
	elseif (y <= -2e+54)
		tmp = -z;
	elseif (y <= 1.05e-40)
		tmp = x;
	else
		tmp = -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -6.2e+115], (-z), If[LessEqual[y, -5.2e+70], y, If[LessEqual[y, -2e+54], (-z), If[LessEqual[y, 1.05e-40], x, (-z)]]]]

Derivation

1. Split input into 3 regimes

2. if y < -6.2000000000000001e115 or -5.2000000000000001e70 < y < -2.0000000000000002e54 or 1.05000000000000009e-40 < y

   1. Initial program 80.0%

      \[\frac{x + y}{1 - \frac{y}{z}} \]

   2. Taylor expanded in y around inf 60.5%

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

      1. mul-1-neg 60.5%

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

   4. Simplified 60.5%

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

   if -6.2000000000000001e115 < y < -5.2000000000000001e70

   1. Initial program 68.4%

      \[\frac{x + y}{1 - \frac{y}{z}} \]

   2. Taylor expanded in x around 0 54.2%

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

   3. Taylor expanded in y around 0 48.0%

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

   if -2.0000000000000002e54 < y < 1.05000000000000009e-40

   1. Initial program 99.9%

      \[\frac{x + y}{1 - \frac{y}{z}} \]

   2. Taylor expanded in y around 0 58.1%

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

4. Final simplification 58.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.2 \cdot 10^{+115}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq -5.2 \cdot 10^{+70}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq -2 \cdot 10^{+54}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq 1.05 \cdot 10^{-40}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \]

Alternative 7: 68.7% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -9 \cdot 10^{+115}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq 9.2 \cdot 10^{+88}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -9e+115) (- z) (if (<= y 9.2e+88) (+ x y) (- z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -9e+115) {
		tmp = -z;
	} else if (y <= 9.2e+88) {
		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 <= (-9d+115)) then
        tmp = -z
    else if (y <= 9.2d+88) 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 <= -9e+115) {
		tmp = -z;
	} else if (y <= 9.2e+88) {
		tmp = x + y;
	} else {
		tmp = -z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -9e+115:
		tmp = -z
	elif y <= 9.2e+88:
		tmp = x + y
	else:
		tmp = -z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -9e+115)
		tmp = Float64(-z);
	elseif (y <= 9.2e+88)
		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 <= -9e+115)
		tmp = -z;
	elseif (y <= 9.2e+88)
		tmp = x + y;
	else
		tmp = -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -9e+115], (-z), If[LessEqual[y, 9.2e+88], N[(x + y), $MachinePrecision], (-z)]]

Derivation

1. Split input into 2 regimes

2. if y < -8.99999999999999927e115 or 9.2000000000000007e88 < y

   1. Initial program 73.4%

      \[\frac{x + y}{1 - \frac{y}{z}} \]

   2. Taylor expanded in y around inf 74.2%

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

      1. mul-1-neg 74.2%

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

   4. Simplified 74.2%

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

   if -8.99999999999999927e115 < y < 9.2000000000000007e88

   1. Initial program 96.8%

      \[\frac{x + y}{1 - \frac{y}{z}} \]

   2. Taylor expanded in z around inf 67.9%

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

4. Final simplification 69.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9 \cdot 10^{+115}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq 9.2 \cdot 10^{+88}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \]

Alternative 8: 39.7% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5.4 \cdot 10^{-13}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 2.65 \cdot 10^{-45}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -5.4e-13) x (if (<= x 2.65e-45) y x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -5.4e-13) {
		tmp = x;
	} else if (x <= 2.65e-45) {
		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 <= (-5.4d-13)) then
        tmp = x
    else if (x <= 2.65d-45) 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 <= -5.4e-13) {
		tmp = x;
	} else if (x <= 2.65e-45) {
		tmp = y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -5.4e-13:
		tmp = x
	elif x <= 2.65e-45:
		tmp = y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -5.4e-13)
		tmp = x;
	elseif (x <= 2.65e-45)
		tmp = y;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -5.4e-13)
		tmp = x;
	elseif (x <= 2.65e-45)
		tmp = y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -5.4e-13], x, If[LessEqual[x, 2.65e-45], y, x]]

Derivation

1. Split input into 2 regimes

2. if x < -5.40000000000000021e-13 or 2.6499999999999999e-45 < x

   1. Initial program 88.9%

      \[\frac{x + y}{1 - \frac{y}{z}} \]

   2. Taylor expanded in y around 0 52.2%

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

   if -5.40000000000000021e-13 < x < 2.6499999999999999e-45

   1. Initial program 92.5%

      \[\frac{x + y}{1 - \frac{y}{z}} \]

   2. Taylor expanded in x around 0 74.2%

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

   3. Taylor expanded in y around 0 40.2%

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

4. Final simplification 47.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.4 \cdot 10^{-13}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 2.65 \cdot 10^{-45}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 9: 35.4% 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 90.3%

   \[\frac{x + y}{1 - \frac{y}{z}} \]

2. Taylor expanded in y around 0 37.0%

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

3. Final simplification 37.0%

   \[\leadsto x \]

Developer target: 93.5% accurate, 0.7× 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 2023240 
(FPCore (x y z)
  :name "Graphics.Rendering.Chart.Backend.Diagrams:calcFontMetrics from Chart-diagrams-1.5.1, A"
  :precision binary64

  :herbie-target
  (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))))