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

Percentage Accurate: 87.4% → 99.3%

Time: 6.0s

Alternatives: 11

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: 87.4% 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: 99.3% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x + y}{1 - \frac{y}{z}}\\ \mathbf{if}\;t\_0 \leq -4 \cdot 10^{-258} \lor \neg \left(t\_0 \leq 4 \cdot 10^{-278}\right):\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;\frac{z \cdot \left(x + z\right)}{-y} - z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ (+ x y) (- 1.0 (/ y z)))))
   (if (or (<= t_0 -4e-258) (not (<= t_0 4e-278)))
     t_0
     (- (/ (* z (+ 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-258) || !(t_0 <= 4e-278)) {
		tmp = t_0;
	} else {
		tmp = ((z * (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-258)) .or. (.not. (t_0 <= 4d-278))) then
        tmp = t_0
    else
        tmp = ((z * (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-258) || !(t_0 <= 4e-278)) {
		tmp = t_0;
	} else {
		tmp = ((z * (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-258) or not (t_0 <= 4e-278):
		tmp = t_0
	else:
		tmp = ((z * (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-258) || !(t_0 <= 4e-278))
		tmp = t_0;
	else
		tmp = Float64(Float64(Float64(z * Float64(x + 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-258) || ~((t_0 <= 4e-278)))
		tmp = t_0;
	else
		tmp = ((z * (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-258], N[Not[LessEqual[t$95$0, 4e-278]], $MachinePrecision]], t$95$0, N[(N[(N[(z * N[(x + z), $MachinePrecision]), $MachinePrecision] / (-y)), $MachinePrecision] - z), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (+.f64 x y) (-.f64 #s(literal 1 binary64) (/.f64 y z))) < -3.99999999999999982e-258 or 3.99999999999999975e-278 < (/.f64 (+.f64 x y) (-.f64 #s(literal 1 binary64) (/.f64 y z)))

   1. Initial program 99.8%

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

   if -3.99999999999999982e-258 < (/.f64 (+.f64 x y) (-.f64 #s(literal 1 binary64) (/.f64 y z))) < 3.99999999999999975e-278

   1. Initial program 28.7%

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

   3. Taylor expanded in y around inf 100.0%

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

      1. associate--l+ 100.0%

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

      2. associate-*r/ 100.0%

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

      3. div-sub 100.0%

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

      4. remove-double-neg 100.0%

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

      5. mul-1-neg 100.0%

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

      6. neg-mul-1 100.0%

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

      7. distribute-lft-out-- 100.0%

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

      8. mul-1-neg 100.0%

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

      9. distribute-neg-frac 100.0%

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

      10. unsub-neg 100.0%

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

      11. mul-1-neg 100.0%

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

      12. sub-neg 100.0%

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

      13. mul-1-neg 100.0%

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

      14. remove-double-neg 100.0%

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

      15. +-commutative 100.0%

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

      16. unpow2 100.0%

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

      17. distribute-rgt-out 100.0%

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

   5. Simplified 100.0%

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

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + y}{1 - \frac{y}{z}} \leq -4 \cdot 10^{-258} \lor \neg \left(\frac{x + y}{1 - \frac{y}{z}} \leq 4 \cdot 10^{-278}\right):\\ \;\;\;\;\frac{x + y}{1 - \frac{y}{z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{z \cdot \left(x + z\right)}{-y} - z\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 99.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x + y}{1 - \frac{y}{z}}\\ \mathbf{if}\;t\_0 \leq -4 \cdot 10^{-258} \lor \neg \left(t\_0 \leq 4 \cdot 10^{-278}\right):\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{x + y}{-y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ (+ x y) (- 1.0 (/ y z)))))
   (if (or (<= t_0 -4e-258) (not (<= t_0 4e-278)))
     t_0
     (* z (/ (+ x y) (- y))))))

C

double code(double x, double y, double z) {
	double t_0 = (x + y) / (1.0 - (y / z));
	double tmp;
	if ((t_0 <= -4e-258) || !(t_0 <= 4e-278)) {
		tmp = t_0;
	} else {
		tmp = z * ((x + y) / -y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (x + y) / (1.0d0 - (y / z))
    if ((t_0 <= (-4d-258)) .or. (.not. (t_0 <= 4d-278))) then
        tmp = t_0
    else
        tmp = z * ((x + y) / -y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = (x + y) / (1.0 - (y / z));
	double tmp;
	if ((t_0 <= -4e-258) || !(t_0 <= 4e-278)) {
		tmp = t_0;
	} else {
		tmp = z * ((x + y) / -y);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (x + y) / (1.0 - (y / z))
	tmp = 0
	if (t_0 <= -4e-258) or not (t_0 <= 4e-278):
		tmp = t_0
	else:
		tmp = z * ((x + y) / -y)
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(x + y) / Float64(1.0 - Float64(y / z)))
	tmp = 0.0
	if ((t_0 <= -4e-258) || !(t_0 <= 4e-278))
		tmp = t_0;
	else
		tmp = Float64(z * Float64(Float64(x + y) / Float64(-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-258) || ~((t_0 <= 4e-278)))
		tmp = t_0;
	else
		tmp = z * ((x + y) / -y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(x + y), $MachinePrecision] / N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$0, -4e-258], N[Not[LessEqual[t$95$0, 4e-278]], $MachinePrecision]], t$95$0, N[(z * N[(N[(x + y), $MachinePrecision] / (-y)), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (+.f64 x y) (-.f64 #s(literal 1 binary64) (/.f64 y z))) < -3.99999999999999982e-258 or 3.99999999999999975e-278 < (/.f64 (+.f64 x y) (-.f64 #s(literal 1 binary64) (/.f64 y z)))

   1. Initial program 99.8%

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

   if -3.99999999999999982e-258 < (/.f64 (+.f64 x y) (-.f64 #s(literal 1 binary64) (/.f64 y z))) < 3.99999999999999975e-278

   1. Initial program 28.7%

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

   3. Taylor expanded in z around 0 85.2%

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

      1. *-commutative 85.2%

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

      2. associate-/l* 100.0%

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

      3. associate-*r* 100.0%

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

      4. associate-*l/ 100.0%

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

      5. *-commutative 100.0%

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

      6. neg-mul-1 100.0%

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

      7. distribute-neg-in 100.0%

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

      8. unsub-neg 100.0%

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

   5. Simplified 100.0%

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

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + y}{1 - \frac{y}{z}} \leq -4 \cdot 10^{-258} \lor \neg \left(\frac{x + y}{1 - \frac{y}{z}} \leq 4 \cdot 10^{-278}\right):\\ \;\;\;\;\frac{x + y}{1 - \frac{y}{z}}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{x + y}{-y}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 68.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.55 \cdot 10^{+220}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq -0.082:\\ \;\;\;\;y \cdot \frac{z}{z - y}\\ \mathbf{elif}\;y \leq -1.45 \cdot 10^{-194}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq 3.3 \cdot 10^{+81}:\\ \;\;\;\;\frac{x}{1 - \frac{y}{z}}\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -3.55e+220)
   (- z)
   (if (<= y -0.082)
     (* y (/ z (- z y)))
     (if (<= y -1.45e-194)
       (+ x y)
       (if (<= y 3.3e+81) (/ x (- 1.0 (/ y z))) (- z))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -3.55e+220) {
		tmp = -z;
	} else if (y <= -0.082) {
		tmp = y * (z / (z - y));
	} else if (y <= -1.45e-194) {
		tmp = x + y;
	} else if (y <= 3.3e+81) {
		tmp = x / (1.0 - (y / z));
	} 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 <= (-3.55d+220)) then
        tmp = -z
    else if (y <= (-0.082d0)) then
        tmp = y * (z / (z - y))
    else if (y <= (-1.45d-194)) then
        tmp = x + y
    else if (y <= 3.3d+81) then
        tmp = x / (1.0d0 - (y / z))
    else
        tmp = -z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -3.55e+220) {
		tmp = -z;
	} else if (y <= -0.082) {
		tmp = y * (z / (z - y));
	} else if (y <= -1.45e-194) {
		tmp = x + y;
	} else if (y <= 3.3e+81) {
		tmp = x / (1.0 - (y / z));
	} else {
		tmp = -z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -3.55e+220:
		tmp = -z
	elif y <= -0.082:
		tmp = y * (z / (z - y))
	elif y <= -1.45e-194:
		tmp = x + y
	elif y <= 3.3e+81:
		tmp = x / (1.0 - (y / z))
	else:
		tmp = -z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -3.55e+220)
		tmp = Float64(-z);
	elseif (y <= -0.082)
		tmp = Float64(y * Float64(z / Float64(z - y)));
	elseif (y <= -1.45e-194)
		tmp = Float64(x + y);
	elseif (y <= 3.3e+81)
		tmp = Float64(x / Float64(1.0 - Float64(y / z)));
	else
		tmp = Float64(-z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -3.55e+220)
		tmp = -z;
	elseif (y <= -0.082)
		tmp = y * (z / (z - y));
	elseif (y <= -1.45e-194)
		tmp = x + y;
	elseif (y <= 3.3e+81)
		tmp = x / (1.0 - (y / z));
	else
		tmp = -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -3.55e+220], (-z), If[LessEqual[y, -0.082], N[(y * N[(z / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.45e-194], N[(x + y), $MachinePrecision], If[LessEqual[y, 3.3e+81], N[(x / N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], (-z)]]]]

Derivation

1. Split input into 4 regimes

2. if y < -3.55000000000000002e220 or 3.3e81 < y

   1. Initial program 68.4%

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

   3. Taylor expanded in y around inf 68.6%

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

      1. mul-1-neg 68.6%

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

   5. Simplified 68.6%

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

   if -3.55000000000000002e220 < y < -0.0820000000000000034

   1. Initial program 84.5%

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

   3. Taylor expanded in z around 0 84.5%

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

   4. Taylor expanded in x around 0 59.4%

      \[\leadsto \color{blue}{\frac{y \cdot z}{z - y}} \]
   5. Step-by-step derivation

      1. associate-/l* 71.4%

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

   6. Simplified 71.4%

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

   if -0.0820000000000000034 < y < -1.44999999999999985e-194

   1. Initial program 99.8%

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

   3. Taylor expanded in z around inf 65.5%

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

      1. +-commutative 65.5%

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

   5. Simplified 65.5%

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

   if -1.44999999999999985e-194 < y < 3.3e81

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 80.9%

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

4. Final simplification 73.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.55 \cdot 10^{+220}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq -0.082:\\ \;\;\;\;y \cdot \frac{z}{z - y}\\ \mathbf{elif}\;y \leq -1.45 \cdot 10^{-194}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq 3.3 \cdot 10^{+81}:\\ \;\;\;\;\frac{x}{1 - \frac{y}{z}}\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 73.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.3 \cdot 10^{-6}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{-72}:\\ \;\;\;\;x \cdot \frac{z}{-y} - z\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{+81}:\\ \;\;\;\;\frac{x}{1 - \frac{y}{z}}\\ \mathbf{else}:\\ \;\;\;\;\left(x + y\right) \cdot \left(1 + \frac{y}{z}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -1.3e-6)
   (+ x y)
   (if (<= z 3.2e-72)
     (- (* x (/ z (- y))) z)
     (if (<= z 8.5e+81) (/ x (- 1.0 (/ y z))) (* (+ x y) (+ 1.0 (/ y z)))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.3e-6) {
		tmp = x + y;
	} else if (z <= 3.2e-72) {
		tmp = (x * (z / -y)) - z;
	} else if (z <= 8.5e+81) {
		tmp = x / (1.0 - (y / z));
	} else {
		tmp = (x + y) * (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 (z <= (-1.3d-6)) then
        tmp = x + y
    else if (z <= 3.2d-72) then
        tmp = (x * (z / -y)) - z
    else if (z <= 8.5d+81) then
        tmp = x / (1.0d0 - (y / z))
    else
        tmp = (x + y) * (1.0d0 + (y / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.3e-6) {
		tmp = x + y;
	} else if (z <= 3.2e-72) {
		tmp = (x * (z / -y)) - z;
	} else if (z <= 8.5e+81) {
		tmp = x / (1.0 - (y / z));
	} else {
		tmp = (x + y) * (1.0 + (y / z));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -1.3e-6:
		tmp = x + y
	elif z <= 3.2e-72:
		tmp = (x * (z / -y)) - z
	elif z <= 8.5e+81:
		tmp = x / (1.0 - (y / z))
	else:
		tmp = (x + y) * (1.0 + (y / z))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -1.3e-6)
		tmp = Float64(x + y);
	elseif (z <= 3.2e-72)
		tmp = Float64(Float64(x * Float64(z / Float64(-y))) - z);
	elseif (z <= 8.5e+81)
		tmp = Float64(x / Float64(1.0 - Float64(y / z)));
	else
		tmp = Float64(Float64(x + y) * Float64(1.0 + Float64(y / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -1.3e-6)
		tmp = x + y;
	elseif (z <= 3.2e-72)
		tmp = (x * (z / -y)) - z;
	elseif (z <= 8.5e+81)
		tmp = x / (1.0 - (y / z));
	else
		tmp = (x + y) * (1.0 + (y / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -1.3e-6], N[(x + y), $MachinePrecision], If[LessEqual[z, 3.2e-72], N[(N[(x * N[(z / (-y)), $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision], If[LessEqual[z, 8.5e+81], N[(x / N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x + y), $MachinePrecision] * N[(1.0 + N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.30000000000000005e-6

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 75.7%

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

      1. +-commutative 75.7%

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

   5. Simplified 75.7%

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

   if -1.30000000000000005e-6 < z < 3.19999999999999999e-72

   1. Initial program 77.5%

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

   3. Taylor expanded in y around inf 78.5%

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

      1. associate--l+ 78.5%

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

      2. associate-*r/ 78.5%

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

      3. div-sub 78.5%

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

      4. remove-double-neg 78.5%

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

      5. mul-1-neg 78.5%

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

      6. neg-mul-1 78.5%

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

      7. distribute-lft-out-- 78.5%

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

      8. mul-1-neg 78.5%

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

      9. distribute-neg-frac 78.5%

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

      10. unsub-neg 78.5%

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

      11. mul-1-neg 78.5%

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

      12. sub-neg 78.5%

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

      13. mul-1-neg 78.5%

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

      14. remove-double-neg 78.5%

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

      15. +-commutative 78.5%

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

      16. unpow2 78.5%

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

      17. distribute-rgt-out 78.5%

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

   5. Simplified 78.5%

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

   6. Taylor expanded in z around 0 78.6%

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

      1. associate-/l* 76.8%

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

   8. Simplified 76.8%

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

   if 3.19999999999999999e-72 < z < 8.49999999999999986e81

   1. Initial program 95.9%

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

   3. Taylor expanded in x around inf 80.1%

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

   if 8.49999999999999986e81 < z

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf 71.6%

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

      1. associate-+r+ 71.6%

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

      2. *-rgt-identity 71.6%

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

      3. *-commutative 71.6%

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

      4. associate-/l* 86.9%

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

      5. distribute-lft-in 86.8%

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

      6. +-commutative 86.8%

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

   5. Simplified 86.8%

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

4. Final simplification 78.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.3 \cdot 10^{-6}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{-72}:\\ \;\;\;\;x \cdot \frac{z}{-y} - z\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{+81}:\\ \;\;\;\;\frac{x}{1 - \frac{y}{z}}\\ \mathbf{else}:\\ \;\;\;\;\left(x + y\right) \cdot \left(1 + \frac{y}{z}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 66.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.5 \cdot 10^{+209}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq -1.4 \cdot 10^{+186}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq -9 \cdot 10^{+27} \lor \neg \left(y \leq 5.5 \cdot 10^{+82}\right):\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -3.5e+209)
   (- z)
   (if (<= y -1.4e+186)
     y
     (if (or (<= y -9e+27) (not (<= y 5.5e+82))) (- z) (+ x y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -3.5e+209) {
		tmp = -z;
	} else if (y <= -1.4e+186) {
		tmp = y;
	} else if ((y <= -9e+27) || !(y <= 5.5e+82)) {
		tmp = -z;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= (-3.5d+209)) then
        tmp = -z
    else if (y <= (-1.4d+186)) then
        tmp = y
    else if ((y <= (-9d+27)) .or. (.not. (y <= 5.5d+82))) then
        tmp = -z
    else
        tmp = x + y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -3.5e+209) {
		tmp = -z;
	} else if (y <= -1.4e+186) {
		tmp = y;
	} else if ((y <= -9e+27) || !(y <= 5.5e+82)) {
		tmp = -z;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -3.5e+209:
		tmp = -z
	elif y <= -1.4e+186:
		tmp = y
	elif (y <= -9e+27) or not (y <= 5.5e+82):
		tmp = -z
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -3.5e+209)
		tmp = Float64(-z);
	elseif (y <= -1.4e+186)
		tmp = y;
	elseif ((y <= -9e+27) || !(y <= 5.5e+82))
		tmp = Float64(-z);
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -3.5e+209)
		tmp = -z;
	elseif (y <= -1.4e+186)
		tmp = y;
	elseif ((y <= -9e+27) || ~((y <= 5.5e+82)))
		tmp = -z;
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -3.5e+209], (-z), If[LessEqual[y, -1.4e+186], y, If[Or[LessEqual[y, -9e+27], N[Not[LessEqual[y, 5.5e+82]], $MachinePrecision]], (-z), N[(x + y), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.5000000000000003e209 or -1.40000000000000009e186 < y < -8.9999999999999998e27 or 5.49999999999999997e82 < y

   1. Initial program 72.9%

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

   3. Taylor expanded in y around inf 63.6%

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

      1. mul-1-neg 63.6%

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

   5. Simplified 63.6%

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

   if -3.5000000000000003e209 < y < -1.40000000000000009e186

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 100.0%

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

   4. Taylor expanded in y around 0 86.0%

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

   if -8.9999999999999998e27 < y < 5.49999999999999997e82

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf 72.0%

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

      1. +-commutative 72.0%

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

   5. Simplified 72.0%

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

4. Final simplification 69.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.5 \cdot 10^{+209}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq -1.4 \cdot 10^{+186}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq -9 \cdot 10^{+27} \lor \neg \left(y \leq 5.5 \cdot 10^{+82}\right):\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 57.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.5 \cdot 10^{+209}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq -1.4 \cdot 10^{+186}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq -0.215 \lor \neg \left(y \leq 6.5 \cdot 10^{-8}\right):\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -3.5e+209)
   (- z)
   (if (<= y -1.4e+186)
     y
     (if (or (<= y -0.215) (not (<= y 6.5e-8))) (- z) x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -3.5e+209) {
		tmp = -z;
	} else if (y <= -1.4e+186) {
		tmp = y;
	} else if ((y <= -0.215) || !(y <= 6.5e-8)) {
		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 <= (-3.5d+209)) then
        tmp = -z
    else if (y <= (-1.4d+186)) then
        tmp = y
    else if ((y <= (-0.215d0)) .or. (.not. (y <= 6.5d-8))) 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 <= -3.5e+209) {
		tmp = -z;
	} else if (y <= -1.4e+186) {
		tmp = y;
	} else if ((y <= -0.215) || !(y <= 6.5e-8)) {
		tmp = -z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -3.5e+209:
		tmp = -z
	elif y <= -1.4e+186:
		tmp = y
	elif (y <= -0.215) or not (y <= 6.5e-8):
		tmp = -z
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -3.5e+209)
		tmp = Float64(-z);
	elseif (y <= -1.4e+186)
		tmp = y;
	elseif ((y <= -0.215) || !(y <= 6.5e-8))
		tmp = Float64(-z);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -3.5e+209)
		tmp = -z;
	elseif (y <= -1.4e+186)
		tmp = y;
	elseif ((y <= -0.215) || ~((y <= 6.5e-8)))
		tmp = -z;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -3.5e+209], (-z), If[LessEqual[y, -1.4e+186], y, If[Or[LessEqual[y, -0.215], N[Not[LessEqual[y, 6.5e-8]], $MachinePrecision]], (-z), x]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.5000000000000003e209 or -1.40000000000000009e186 < y < -0.214999999999999997 or 6.49999999999999997e-8 < y

   1. Initial program 76.7%

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

   3. Taylor expanded in y around inf 58.7%

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

      1. mul-1-neg 58.7%

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

   5. Simplified 58.7%

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

   if -3.5000000000000003e209 < y < -1.40000000000000009e186

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 100.0%

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

   4. Taylor expanded in y around 0 86.0%

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

   if -0.214999999999999997 < y < 6.49999999999999997e-8

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 60.5%

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

4. Final simplification 60.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.5 \cdot 10^{+209}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq -1.4 \cdot 10^{+186}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq -0.215 \lor \neg \left(y \leq 6.5 \cdot 10^{-8}\right):\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 73.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.1 \cdot 10^{-7}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 5 \cdot 10^{-72}:\\ \;\;\;\;z \cdot \frac{x + y}{-y}\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{+81}:\\ \;\;\;\;\frac{x}{1 - \frac{y}{z}}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -2.1e-7)
   (+ x y)
   (if (<= z 5e-72)
     (* z (/ (+ x y) (- y)))
     (if (<= z 6.2e+81) (/ x (- 1.0 (/ y z))) (+ x y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -2.1e-7) {
		tmp = x + y;
	} else if (z <= 5e-72) {
		tmp = z * ((x + y) / -y);
	} else if (z <= 6.2e+81) {
		tmp = x / (1.0 - (y / z));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z <= (-2.1d-7)) then
        tmp = x + y
    else if (z <= 5d-72) then
        tmp = z * ((x + y) / -y)
    else if (z <= 6.2d+81) then
        tmp = x / (1.0d0 - (y / z))
    else
        tmp = x + y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -2.1e-7) {
		tmp = x + y;
	} else if (z <= 5e-72) {
		tmp = z * ((x + y) / -y);
	} else if (z <= 6.2e+81) {
		tmp = x / (1.0 - (y / z));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -2.1e-7:
		tmp = x + y
	elif z <= 5e-72:
		tmp = z * ((x + y) / -y)
	elif z <= 6.2e+81:
		tmp = x / (1.0 - (y / z))
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -2.1e-7)
		tmp = Float64(x + y);
	elseif (z <= 5e-72)
		tmp = Float64(z * Float64(Float64(x + y) / Float64(-y)));
	elseif (z <= 6.2e+81)
		tmp = Float64(x / Float64(1.0 - Float64(y / z)));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -2.1e-7)
		tmp = x + y;
	elseif (z <= 5e-72)
		tmp = z * ((x + y) / -y);
	elseif (z <= 6.2e+81)
		tmp = x / (1.0 - (y / z));
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -2.1e-7], N[(x + y), $MachinePrecision], If[LessEqual[z, 5e-72], N[(z * N[(N[(x + y), $MachinePrecision] / (-y)), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6.2e+81], N[(x / N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.1e-7 or 6.2e81 < z

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf 80.5%

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

      1. +-commutative 80.5%

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

   5. Simplified 80.5%

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

   if -2.1e-7 < z < 4.9999999999999996e-72

   1. Initial program 77.5%

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

   3. Taylor expanded in z around 0 71.1%

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

      1. *-commutative 71.1%

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

      2. associate-/l* 76.1%

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

      3. associate-*r* 76.1%

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

      4. associate-*l/ 76.1%

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

      5. *-commutative 76.1%

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

      6. neg-mul-1 76.1%

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

      7. distribute-neg-in 76.1%

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

      8. unsub-neg 76.1%

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

   5. Simplified 76.1%

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

   if 4.9999999999999996e-72 < z < 6.2e81

   1. Initial program 95.9%

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

   3. Taylor expanded in x around inf 80.1%

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

4. Final simplification 78.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.1 \cdot 10^{-7}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 5 \cdot 10^{-72}:\\ \;\;\;\;z \cdot \frac{x + y}{-y}\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{+81}:\\ \;\;\;\;\frac{x}{1 - \frac{y}{z}}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 73.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.6 \cdot 10^{-10}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 4.3 \cdot 10^{-73}:\\ \;\;\;\;x \cdot \frac{z}{-y} - z\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{+81}:\\ \;\;\;\;\frac{x}{1 - \frac{y}{z}}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -5.6e-10)
   (+ x y)
   (if (<= z 4.3e-73)
     (- (* x (/ z (- y))) z)
     (if (<= z 6.2e+81) (/ x (- 1.0 (/ y z))) (+ x y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -5.6e-10) {
		tmp = x + y;
	} else if (z <= 4.3e-73) {
		tmp = (x * (z / -y)) - z;
	} else if (z <= 6.2e+81) {
		tmp = x / (1.0 - (y / z));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z <= (-5.6d-10)) then
        tmp = x + y
    else if (z <= 4.3d-73) then
        tmp = (x * (z / -y)) - z
    else if (z <= 6.2d+81) then
        tmp = x / (1.0d0 - (y / z))
    else
        tmp = x + y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -5.6e-10) {
		tmp = x + y;
	} else if (z <= 4.3e-73) {
		tmp = (x * (z / -y)) - z;
	} else if (z <= 6.2e+81) {
		tmp = x / (1.0 - (y / z));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -5.6e-10:
		tmp = x + y
	elif z <= 4.3e-73:
		tmp = (x * (z / -y)) - z
	elif z <= 6.2e+81:
		tmp = x / (1.0 - (y / z))
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -5.6e-10)
		tmp = Float64(x + y);
	elseif (z <= 4.3e-73)
		tmp = Float64(Float64(x * Float64(z / Float64(-y))) - z);
	elseif (z <= 6.2e+81)
		tmp = Float64(x / Float64(1.0 - Float64(y / z)));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -5.6e-10)
		tmp = x + y;
	elseif (z <= 4.3e-73)
		tmp = (x * (z / -y)) - z;
	elseif (z <= 6.2e+81)
		tmp = x / (1.0 - (y / z));
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -5.6e-10], N[(x + y), $MachinePrecision], If[LessEqual[z, 4.3e-73], N[(N[(x * N[(z / (-y)), $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision], If[LessEqual[z, 6.2e+81], N[(x / N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.60000000000000031e-10 or 6.2e81 < z

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf 80.5%

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

      1. +-commutative 80.5%

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

   5. Simplified 80.5%

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

   if -5.60000000000000031e-10 < z < 4.2999999999999999e-73

   1. Initial program 77.5%

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

   3. Taylor expanded in y around inf 78.5%

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

      1. associate--l+ 78.5%

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

      2. associate-*r/ 78.5%

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

      3. div-sub 78.5%

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

      4. remove-double-neg 78.5%

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

      5. mul-1-neg 78.5%

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

      6. neg-mul-1 78.5%

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

      7. distribute-lft-out-- 78.5%

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

      8. mul-1-neg 78.5%

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

      9. distribute-neg-frac 78.5%

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

      10. unsub-neg 78.5%

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

      11. mul-1-neg 78.5%

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

      12. sub-neg 78.5%

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

      13. mul-1-neg 78.5%

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

      14. remove-double-neg 78.5%

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

      15. +-commutative 78.5%

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

      16. unpow2 78.5%

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

      17. distribute-rgt-out 78.5%

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

   5. Simplified 78.5%

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

   6. Taylor expanded in z around 0 78.6%

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

      1. associate-/l* 76.8%

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

   8. Simplified 76.8%

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

   if 4.2999999999999999e-73 < z < 6.2e81

   1. Initial program 95.9%

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

   3. Taylor expanded in x around inf 80.1%

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

4. Final simplification 78.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.6 \cdot 10^{-10}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 4.3 \cdot 10^{-73}:\\ \;\;\;\;x \cdot \frac{z}{-y} - z\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{+81}:\\ \;\;\;\;\frac{x}{1 - \frac{y}{z}}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 67.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.55 \cdot 10^{+220}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq -4.5 \cdot 10^{-11}:\\ \;\;\;\;y \cdot \frac{z}{z - y}\\ \mathbf{elif}\;y \leq 3.7 \cdot 10^{+80}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -3.55e+220)
   (- z)
   (if (<= y -4.5e-11) (* y (/ z (- z y))) (if (<= y 3.7e+80) (+ x y) (- z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -3.55e+220) {
		tmp = -z;
	} else if (y <= -4.5e-11) {
		tmp = y * (z / (z - y));
	} else if (y <= 3.7e+80) {
		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 <= (-3.55d+220)) then
        tmp = -z
    else if (y <= (-4.5d-11)) then
        tmp = y * (z / (z - y))
    else if (y <= 3.7d+80) 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 <= -3.55e+220) {
		tmp = -z;
	} else if (y <= -4.5e-11) {
		tmp = y * (z / (z - y));
	} else if (y <= 3.7e+80) {
		tmp = x + y;
	} else {
		tmp = -z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -3.55e+220:
		tmp = -z
	elif y <= -4.5e-11:
		tmp = y * (z / (z - y))
	elif y <= 3.7e+80:
		tmp = x + y
	else:
		tmp = -z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -3.55e+220)
		tmp = Float64(-z);
	elseif (y <= -4.5e-11)
		tmp = Float64(y * Float64(z / Float64(z - y)));
	elseif (y <= 3.7e+80)
		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 <= -3.55e+220)
		tmp = -z;
	elseif (y <= -4.5e-11)
		tmp = y * (z / (z - y));
	elseif (y <= 3.7e+80)
		tmp = x + y;
	else
		tmp = -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -3.55e+220], (-z), If[LessEqual[y, -4.5e-11], N[(y * N[(z / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.7e+80], N[(x + y), $MachinePrecision], (-z)]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.55000000000000002e220 or 3.69999999999999996e80 < y

   1. Initial program 68.4%

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

   3. Taylor expanded in y around inf 68.6%

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

      1. mul-1-neg 68.6%

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

   5. Simplified 68.6%

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

   if -3.55000000000000002e220 < y < -4.5e-11

   1. Initial program 84.5%

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

   3. Taylor expanded in z around 0 84.5%

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

   4. Taylor expanded in x around 0 59.4%

      \[\leadsto \color{blue}{\frac{y \cdot z}{z - y}} \]
   5. Step-by-step derivation

      1. associate-/l* 71.4%

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

   6. Simplified 71.4%

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

   if -4.5e-11 < y < 3.69999999999999996e80

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf 72.6%

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

      1. +-commutative 72.6%

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

   5. Simplified 72.6%

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

4. Final simplification 71.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.55 \cdot 10^{+220}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq -4.5 \cdot 10^{-11}:\\ \;\;\;\;y \cdot \frac{z}{z - y}\\ \mathbf{elif}\;y \leq 3.7 \cdot 10^{+80}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 40.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.08 \cdot 10^{-162}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 4.5 \cdot 10^{-134}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -1.08e-162) x (if (<= x 4.5e-134) y x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.08e-162) {
		tmp = x;
	} else if (x <= 4.5e-134) {
		tmp = y;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (x <= (-1.08d-162)) then
        tmp = x
    else if (x <= 4.5d-134) then
        tmp = y
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.08e-162) {
		tmp = x;
	} else if (x <= 4.5e-134) {
		tmp = y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -1.08e-162:
		tmp = x
	elif x <= 4.5e-134:
		tmp = y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -1.08e-162)
		tmp = x;
	elseif (x <= 4.5e-134)
		tmp = y;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -1.08e-162)
		tmp = x;
	elseif (x <= 4.5e-134)
		tmp = y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -1.08e-162], x, If[LessEqual[x, 4.5e-134], y, x]]

Derivation

1. Split input into 2 regimes

2. if x < -1.08000000000000006e-162 or 4.5000000000000005e-134 < x

   1. Initial program 88.3%

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

   3. Taylor expanded in y around 0 44.1%

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

   if -1.08000000000000006e-162 < x < 4.5000000000000005e-134

   1. Initial program 93.6%

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

   3. Taylor expanded in x around 0 84.9%

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

   4. Taylor expanded in y around 0 50.0%

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

4. Final simplification 45.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.08 \cdot 10^{-162}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 4.5 \cdot 10^{-134}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 34.3% 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 89.6%

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

3. Taylor expanded in y around 0 35.8%

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

4. Final simplification 35.8%

   \[\leadsto x \]
5. Add Preprocessing

Developer target: 93.3% 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 2024095 
(FPCore (x y z)
  :name "Graphics.Rendering.Chart.Backend.Diagrams:calcFontMetrics from Chart-diagrams-1.5.1, A"
  :precision binary64

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

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