Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisLine from plot-0.2.3.4, A

Percentage Accurate: 97.9% → 98.0%

Time: 9.4s

Alternatives: 13

Speedup: 1.0×

Specification

Math

\[\begin{array}{l} \\ x + y \cdot \frac{z - t}{z - a} \end{array} \]

FPCore

(FPCore (x y z t a) :precision binary64 (+ x (* y (/ (- z t) (- z a)))))

C

double code(double x, double y, double z, double t, double a) {
	return x + (y * ((z - t) / (z - a)));
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    code = x + (y * ((z - t) / (z - a)))
end function

Java

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

Python

def code(x, y, z, t, a):
	return x + (y * ((z - t) / (z - a)))

Julia

function code(x, y, z, t, a)
	return Float64(x + Float64(y * Float64(Float64(z - t) / Float64(z - a))))
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = x + (y * ((z - t) / (z - a)));
end

Wolfram

code[x_, y_, z_, t_, a_] := N[(x + N[(y * N[(N[(z - t), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Initial Program: 97.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x + y \cdot \frac{z - t}{z - a} \end{array} \]

FPCore

(FPCore (x y z t a) :precision binary64 (+ x (* y (/ (- z t) (- z a)))))

C

double code(double x, double y, double z, double t, double a) {
	return x + (y * ((z - t) / (z - a)));
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    code = x + (y * ((z - t) / (z - a)))
end function

Java

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

Python

def code(x, y, z, t, a):
	return x + (y * ((z - t) / (z - a)))

Julia

function code(x, y, z, t, a)
	return Float64(x + Float64(y * Float64(Float64(z - t) / Float64(z - a))))
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = x + (y * ((z - t) / (z - a)));
end

Wolfram

code[x_, y_, z_, t_, a_] := N[(x + N[(y * N[(N[(z - t), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Alternative 1: 98.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.1%

   \[x + y \cdot \frac{z - t}{z - a} \]
2. Add Preprocessing
3. Step-by-step derivation

   1. clear-num 99.2%

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

   2. un-div-inv 99.2%

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

4. Applied egg-rr 99.2%

   \[\leadsto x + \color{blue}{\frac{y}{\frac{z - a}{z - t}}} \]
5. Add Preprocessing

Alternative 2: 76.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.9 \cdot 10^{+129}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq -4 \cdot 10^{+59}:\\ \;\;\;\;x - \frac{y}{\frac{z}{t}}\\ \mathbf{elif}\;z \leq 7.8 \cdot 10^{-47}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.9e+129)
   (+ x y)
   (if (<= z -4e+59)
     (- x (/ y (/ z t)))
     (if (<= z 7.8e-47) (+ x (/ y (/ a t))) (+ x y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.9e+129) {
		tmp = x + y;
	} else if (z <= -4e+59) {
		tmp = x - (y / (z / t));
	} else if (z <= 7.8e-47) {
		tmp = x + (y / (a / t));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-1.9d+129)) then
        tmp = x + y
    else if (z <= (-4d+59)) then
        tmp = x - (y / (z / t))
    else if (z <= 7.8d-47) then
        tmp = x + (y / (a / t))
    else
        tmp = x + y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.9e+129) {
		tmp = x + y;
	} else if (z <= -4e+59) {
		tmp = x - (y / (z / t));
	} else if (z <= 7.8e-47) {
		tmp = x + (y / (a / t));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.9e+129:
		tmp = x + y
	elif z <= -4e+59:
		tmp = x - (y / (z / t))
	elif z <= 7.8e-47:
		tmp = x + (y / (a / t))
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.9e+129)
		tmp = Float64(x + y);
	elseif (z <= -4e+59)
		tmp = Float64(x - Float64(y / Float64(z / t)));
	elseif (z <= 7.8e-47)
		tmp = Float64(x + Float64(y / Float64(a / t)));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.9e+129)
		tmp = x + y;
	elseif (z <= -4e+59)
		tmp = x - (y / (z / t));
	elseif (z <= 7.8e-47)
		tmp = x + (y / (a / t));
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.9e+129], N[(x + y), $MachinePrecision], If[LessEqual[z, -4e+59], N[(x - N[(y / N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 7.8e-47], N[(x + N[(y / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.90000000000000003e129 or 7.79999999999999956e-47 < z

   1. Initial program 99.9%

      \[x + y \cdot \frac{z - t}{z - a} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 77.2%

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

      1. +-commutative 77.2%

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

   5. Simplified 77.2%

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

   if -1.90000000000000003e129 < z < -3.99999999999999989e59

   1. Initial program 99.8%

      \[x + y \cdot \frac{z - t}{z - a} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 84.8%

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

      1. associate-*r/ 84.8%

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

      2. mul-1-neg 84.8%

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

      3. distribute-lft-neg-out 84.8%

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

      4. *-commutative 84.8%

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

      5. *-lft-identity 84.8%

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

      6. times-frac 89.7%

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

      7. /-rgt-identity 89.7%

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

      8. distribute-neg-frac 89.7%

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

      9. distribute-neg-frac2 89.7%

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

      10. neg-sub0 89.7%

          \[\leadsto x + y \cdot \frac{t}{\color{blue}{0 - \left(z - a\right)}} \]

      11. sub-neg 89.7%

          \[\leadsto x + y \cdot \frac{t}{0 - \color{blue}{\left(z + \left(-a\right)\right)}} \]

      12. +-commutative 89.7%

          \[\leadsto x + y \cdot \frac{t}{0 - \color{blue}{\left(\left(-a\right) + z\right)}} \]

      13. associate--r+ 89.7%

          \[\leadsto x + y \cdot \frac{t}{\color{blue}{\left(0 - \left(-a\right)\right) - z}} \]

      14. neg-sub0 89.7%

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

      15. remove-double-neg 89.7%

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

   5. Simplified 89.7%

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

   6. Taylor expanded in a around 0 89.8%

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

      1. associate-*r/ 89.8%

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

      2. neg-mul-1 89.8%

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

   8. Simplified 89.8%

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

   9. Taylor expanded in x around 0 84.9%

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

       1. mul-1-neg 84.9%

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

       2. *-commutative 84.9%

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

       3. associate-*r/ 89.8%

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

       4. sub-neg 89.8%

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

   11. Simplified 89.8%

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

       1. clear-num 89.9%

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

       2. un-div-inv 89.9%

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

   13. Applied egg-rr 89.9%

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

   if -3.99999999999999989e59 < z < 7.79999999999999956e-47

   1. Initial program 98.2%

      \[x + y \cdot \frac{z - t}{z - a} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. clear-num 98.3%

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

      2. un-div-inv 98.3%

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

   4. Applied egg-rr 98.3%

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

   5. Taylor expanded in z around 0 82.3%

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

4. Final simplification 80.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.9 \cdot 10^{+129}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq -4 \cdot 10^{+59}:\\ \;\;\;\;x - \frac{y}{\frac{z}{t}}\\ \mathbf{elif}\;z \leq 7.8 \cdot 10^{-47}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 76.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.8 \cdot 10^{+125}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq -4.2 \cdot 10^{+59}:\\ \;\;\;\;x - y \cdot \frac{t}{z}\\ \mathbf{elif}\;z \leq 10^{-49}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -4.8e+125)
   (+ x y)
   (if (<= z -4.2e+59)
     (- x (* y (/ t z)))
     (if (<= z 1e-49) (+ x (/ y (/ a t))) (+ x y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -4.8e+125) {
		tmp = x + y;
	} else if (z <= -4.2e+59) {
		tmp = x - (y * (t / z));
	} else if (z <= 1e-49) {
		tmp = x + (y / (a / t));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-4.8d+125)) then
        tmp = x + y
    else if (z <= (-4.2d+59)) then
        tmp = x - (y * (t / z))
    else if (z <= 1d-49) then
        tmp = x + (y / (a / t))
    else
        tmp = x + y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -4.8e+125) {
		tmp = x + y;
	} else if (z <= -4.2e+59) {
		tmp = x - (y * (t / z));
	} else if (z <= 1e-49) {
		tmp = x + (y / (a / t));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -4.8e+125:
		tmp = x + y
	elif z <= -4.2e+59:
		tmp = x - (y * (t / z))
	elif z <= 1e-49:
		tmp = x + (y / (a / t))
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -4.8e+125)
		tmp = Float64(x + y);
	elseif (z <= -4.2e+59)
		tmp = Float64(x - Float64(y * Float64(t / z)));
	elseif (z <= 1e-49)
		tmp = Float64(x + Float64(y / Float64(a / t)));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -4.8e+125)
		tmp = x + y;
	elseif (z <= -4.2e+59)
		tmp = x - (y * (t / z));
	elseif (z <= 1e-49)
		tmp = x + (y / (a / t));
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -4.8e+125], N[(x + y), $MachinePrecision], If[LessEqual[z, -4.2e+59], N[(x - N[(y * N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1e-49], N[(x + N[(y / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.7999999999999999e125 or 9.99999999999999936e-50 < z

   1. Initial program 99.9%

      \[x + y \cdot \frac{z - t}{z - a} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 77.2%

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

      1. +-commutative 77.2%

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

   5. Simplified 77.2%

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

   if -4.7999999999999999e125 < z < -4.19999999999999968e59

   1. Initial program 99.8%

      \[x + y \cdot \frac{z - t}{z - a} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 84.8%

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

      1. associate-*r/ 84.8%

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

      2. mul-1-neg 84.8%

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

      3. distribute-lft-neg-out 84.8%

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

      4. *-commutative 84.8%

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

      5. *-lft-identity 84.8%

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

      6. times-frac 89.7%

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

      7. /-rgt-identity 89.7%

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

      8. distribute-neg-frac 89.7%

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

      9. distribute-neg-frac2 89.7%

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

      10. neg-sub0 89.7%

          \[\leadsto x + y \cdot \frac{t}{\color{blue}{0 - \left(z - a\right)}} \]

      11. sub-neg 89.7%

          \[\leadsto x + y \cdot \frac{t}{0 - \color{blue}{\left(z + \left(-a\right)\right)}} \]

      12. +-commutative 89.7%

          \[\leadsto x + y \cdot \frac{t}{0 - \color{blue}{\left(\left(-a\right) + z\right)}} \]

      13. associate--r+ 89.7%

          \[\leadsto x + y \cdot \frac{t}{\color{blue}{\left(0 - \left(-a\right)\right) - z}} \]

      14. neg-sub0 89.7%

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

      15. remove-double-neg 89.7%

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

   5. Simplified 89.7%

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

   6. Taylor expanded in a around 0 89.8%

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

      1. associate-*r/ 89.8%

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

      2. neg-mul-1 89.8%

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

   8. Simplified 89.8%

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

   9. Taylor expanded in x around 0 84.9%

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

       1. mul-1-neg 84.9%

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

       2. *-commutative 84.9%

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

       3. associate-*r/ 89.8%

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

       4. sub-neg 89.8%

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

   11. Simplified 89.8%

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

   if -4.19999999999999968e59 < z < 9.99999999999999936e-50

   1. Initial program 98.2%

      \[x + y \cdot \frac{z - t}{z - a} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. clear-num 98.3%

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

      2. un-div-inv 98.3%

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

   4. Applied egg-rr 98.3%

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

   5. Taylor expanded in z around 0 82.3%

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

4. Final simplification 80.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.8 \cdot 10^{+125}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq -4.2 \cdot 10^{+59}:\\ \;\;\;\;x - y \cdot \frac{t}{z}\\ \mathbf{elif}\;z \leq 10^{-49}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 86.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.4 \cdot 10^{+78} \lor \neg \left(t \leq 4.5 \cdot 10^{+134}\right):\\ \;\;\;\;x + t \cdot \frac{y}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{1 - \frac{a}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -2.4e+78) (not (<= t 4.5e+134)))
   (+ x (* t (/ y (- a z))))
   (+ x (/ y (- 1.0 (/ a z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -2.4e+78) || !(t <= 4.5e+134)) {
		tmp = x + (t * (y / (a - z)));
	} else {
		tmp = x + (y / (1.0 - (a / z)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-2.4d+78)) .or. (.not. (t <= 4.5d+134))) then
        tmp = x + (t * (y / (a - z)))
    else
        tmp = x + (y / (1.0d0 - (a / z)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -2.4e+78) || !(t <= 4.5e+134)) {
		tmp = x + (t * (y / (a - z)));
	} else {
		tmp = x + (y / (1.0 - (a / z)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -2.4e+78) or not (t <= 4.5e+134):
		tmp = x + (t * (y / (a - z)))
	else:
		tmp = x + (y / (1.0 - (a / z)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -2.4e+78) || !(t <= 4.5e+134))
		tmp = Float64(x + Float64(t * Float64(y / Float64(a - z))));
	else
		tmp = Float64(x + Float64(y / Float64(1.0 - Float64(a / z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -2.4e+78) || ~((t <= 4.5e+134)))
		tmp = x + (t * (y / (a - z)));
	else
		tmp = x + (y / (1.0 - (a / z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -2.4e+78], N[Not[LessEqual[t, 4.5e+134]], $MachinePrecision]], N[(x + N[(t * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y / N[(1.0 - N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -2.3999999999999999e78 or 4.4999999999999997e134 < t

   1. Initial program 97.4%

      \[x + y \cdot \frac{z - t}{z - a} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 71.9%

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

      1. mul-1-neg 71.9%

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

      2. associate-/l* 86.4%

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

   5. Simplified 86.4%

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

   if -2.3999999999999999e78 < t < 4.4999999999999997e134

   1. Initial program 99.9%

      \[x + y \cdot \frac{z - t}{z - a} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. clear-num 99.9%

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

      2. un-div-inv 100.0%

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

   4. Applied egg-rr 100.0%

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

   5. Taylor expanded in t around 0 94.3%

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

      1. div-sub 94.3%

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

      2. *-inverses 94.3%

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

   7. Simplified 94.3%

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

4. Final simplification 91.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.4 \cdot 10^{+78} \lor \neg \left(t \leq 4.5 \cdot 10^{+134}\right):\\ \;\;\;\;x + t \cdot \frac{y}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{1 - \frac{a}{z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 85.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4.5 \cdot 10^{+83} \lor \neg \left(t \leq 1.22 \cdot 10^{+135}\right):\\ \;\;\;\;x + \frac{y}{\frac{a - z}{t}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{1 - \frac{a}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -4.5e+83) (not (<= t 1.22e+135)))
   (+ x (/ y (/ (- a z) t)))
   (+ x (/ y (- 1.0 (/ a z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -4.5e+83) || !(t <= 1.22e+135)) {
		tmp = x + (y / ((a - z) / t));
	} else {
		tmp = x + (y / (1.0 - (a / z)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-4.5d+83)) .or. (.not. (t <= 1.22d+135))) then
        tmp = x + (y / ((a - z) / t))
    else
        tmp = x + (y / (1.0d0 - (a / z)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -4.5e+83) || !(t <= 1.22e+135)) {
		tmp = x + (y / ((a - z) / t));
	} else {
		tmp = x + (y / (1.0 - (a / z)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -4.5e+83) or not (t <= 1.22e+135):
		tmp = x + (y / ((a - z) / t))
	else:
		tmp = x + (y / (1.0 - (a / z)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -4.5e+83) || !(t <= 1.22e+135))
		tmp = Float64(x + Float64(y / Float64(Float64(a - z) / t)));
	else
		tmp = Float64(x + Float64(y / Float64(1.0 - Float64(a / z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -4.5e+83) || ~((t <= 1.22e+135)))
		tmp = x + (y / ((a - z) / t));
	else
		tmp = x + (y / (1.0 - (a / z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -4.5e+83], N[Not[LessEqual[t, 1.22e+135]], $MachinePrecision]], N[(x + N[(y / N[(N[(a - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y / N[(1.0 - N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -4.4999999999999999e83 or 1.21999999999999996e135 < t

   1. Initial program 97.4%

      \[x + y \cdot \frac{z - t}{z - a} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. clear-num 97.5%

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

      2. un-div-inv 97.5%

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

   4. Applied egg-rr 97.5%

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

   5. Taylor expanded in t around inf 84.9%

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

      1. mul-1-neg 84.9%

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

      2. distribute-frac-neg 84.9%

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

      3. sub-neg 84.9%

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

      4. distribute-neg-in 84.9%

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

      5. remove-double-neg 84.9%

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

      6. +-commutative 84.9%

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

      7. sub-neg 84.9%

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

   7. Simplified 84.9%

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

   if -4.4999999999999999e83 < t < 1.21999999999999996e135

   1. Initial program 99.9%

      \[x + y \cdot \frac{z - t}{z - a} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. clear-num 99.9%

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

      2. un-div-inv 100.0%

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

   4. Applied egg-rr 100.0%

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

   5. Taylor expanded in t around 0 94.3%

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

      1. div-sub 94.3%

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

      2. *-inverses 94.3%

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

   7. Simplified 94.3%

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

4. Final simplification 91.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.5 \cdot 10^{+83} \lor \neg \left(t \leq 1.22 \cdot 10^{+135}\right):\\ \;\;\;\;x + \frac{y}{\frac{a - z}{t}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{1 - \frac{a}{z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 85.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.5 \cdot 10^{+78} \lor \neg \left(t \leq 2.5 \cdot 10^{+134}\right):\\ \;\;\;\;x - y \cdot \frac{t}{z - a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{1 - \frac{a}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -3.5e+78) (not (<= t 2.5e+134)))
   (- x (* y (/ t (- z a))))
   (+ x (/ y (- 1.0 (/ a z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -3.5e+78) || !(t <= 2.5e+134)) {
		tmp = x - (y * (t / (z - a)));
	} else {
		tmp = x + (y / (1.0 - (a / z)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-3.5d+78)) .or. (.not. (t <= 2.5d+134))) then
        tmp = x - (y * (t / (z - a)))
    else
        tmp = x + (y / (1.0d0 - (a / z)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -3.5e+78) || !(t <= 2.5e+134)) {
		tmp = x - (y * (t / (z - a)));
	} else {
		tmp = x + (y / (1.0 - (a / z)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -3.5e+78) or not (t <= 2.5e+134):
		tmp = x - (y * (t / (z - a)))
	else:
		tmp = x + (y / (1.0 - (a / z)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -3.5e+78) || !(t <= 2.5e+134))
		tmp = Float64(x - Float64(y * Float64(t / Float64(z - a))));
	else
		tmp = Float64(x + Float64(y / Float64(1.0 - Float64(a / z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -3.5e+78) || ~((t <= 2.5e+134)))
		tmp = x - (y * (t / (z - a)));
	else
		tmp = x + (y / (1.0 - (a / z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -3.5e+78], N[Not[LessEqual[t, 2.5e+134]], $MachinePrecision]], N[(x - N[(y * N[(t / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y / N[(1.0 - N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -3.5000000000000001e78 or 2.4999999999999999e134 < t

   1. Initial program 97.4%

      \[x + y \cdot \frac{z - t}{z - a} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 71.9%

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

      1. associate-*r/ 71.9%

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

      2. mul-1-neg 71.9%

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

      3. distribute-lft-neg-out 71.9%

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

      4. *-commutative 71.9%

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

      5. *-lft-identity 71.9%

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

      6. times-frac 84.8%

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

      7. /-rgt-identity 84.8%

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

      8. distribute-neg-frac 84.8%

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

      9. distribute-neg-frac2 84.8%

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

      10. neg-sub0 84.8%

          \[\leadsto x + y \cdot \frac{t}{\color{blue}{0 - \left(z - a\right)}} \]

      11. sub-neg 84.8%

          \[\leadsto x + y \cdot \frac{t}{0 - \color{blue}{\left(z + \left(-a\right)\right)}} \]

      12. +-commutative 84.8%

          \[\leadsto x + y \cdot \frac{t}{0 - \color{blue}{\left(\left(-a\right) + z\right)}} \]

      13. associate--r+ 84.8%

          \[\leadsto x + y \cdot \frac{t}{\color{blue}{\left(0 - \left(-a\right)\right) - z}} \]

      14. neg-sub0 84.8%

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

      15. remove-double-neg 84.8%

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

   5. Simplified 84.8%

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

   if -3.5000000000000001e78 < t < 2.4999999999999999e134

   1. Initial program 99.9%

      \[x + y \cdot \frac{z - t}{z - a} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. clear-num 99.9%

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

      2. un-div-inv 100.0%

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

   4. Applied egg-rr 100.0%

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

   5. Taylor expanded in t around 0 94.3%

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

      1. div-sub 94.3%

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

      2. *-inverses 94.3%

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

   7. Simplified 94.3%

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

4. Final simplification 91.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.5 \cdot 10^{+78} \lor \neg \left(t \leq 2.5 \cdot 10^{+134}\right):\\ \;\;\;\;x - y \cdot \frac{t}{z - a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{1 - \frac{a}{z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 86.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.35 \cdot 10^{+125} \lor \neg \left(z \leq 2.8 \cdot 10^{+60}\right):\\ \;\;\;\;x + y \cdot \left(1 - \frac{t}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot \frac{t}{z - a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.35e+125) (not (<= z 2.8e+60)))
   (+ x (* y (- 1.0 (/ t z))))
   (- x (* y (/ t (- z a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.35e+125) || !(z <= 2.8e+60)) {
		tmp = x + (y * (1.0 - (t / z)));
	} else {
		tmp = x - (y * (t / (z - a)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-1.35d+125)) .or. (.not. (z <= 2.8d+60))) then
        tmp = x + (y * (1.0d0 - (t / z)))
    else
        tmp = x - (y * (t / (z - a)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.35e+125) || !(z <= 2.8e+60)) {
		tmp = x + (y * (1.0 - (t / z)));
	} else {
		tmp = x - (y * (t / (z - a)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.35e+125) or not (z <= 2.8e+60):
		tmp = x + (y * (1.0 - (t / z)))
	else:
		tmp = x - (y * (t / (z - a)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.35e+125) || !(z <= 2.8e+60))
		tmp = Float64(x + Float64(y * Float64(1.0 - Float64(t / z))));
	else
		tmp = Float64(x - Float64(y * Float64(t / Float64(z - a))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -1.35e+125) || ~((z <= 2.8e+60)))
		tmp = x + (y * (1.0 - (t / z)));
	else
		tmp = x - (y * (t / (z - a)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.35e+125], N[Not[LessEqual[z, 2.8e+60]], $MachinePrecision]], N[(x + N[(y * N[(1.0 - N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(y * N[(t / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.3499999999999999e125 or 2.8e60 < z

   1. Initial program 99.9%

      \[x + y \cdot \frac{z - t}{z - a} \]
   2. Add Preprocessing

   3. Taylor expanded in a around 0 52.7%

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

      1. associate-/l* 89.4%

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

      2. div-sub 89.4%

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

      3. *-inverses 89.4%

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

   5. Simplified 89.4%

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

   if -1.3499999999999999e125 < z < 2.8e60

   1. Initial program 98.7%

      \[x + y \cdot \frac{z - t}{z - a} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 83.9%

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

      1. associate-*r/ 83.9%

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

      2. mul-1-neg 83.9%

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

      3. distribute-lft-neg-out 83.9%

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

      4. *-commutative 83.9%

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

      5. *-lft-identity 83.9%

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

      6. times-frac 87.4%

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

      7. /-rgt-identity 87.4%

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

      8. distribute-neg-frac 87.4%

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

      9. distribute-neg-frac2 87.4%

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

      10. neg-sub0 87.4%

          \[\leadsto x + y \cdot \frac{t}{\color{blue}{0 - \left(z - a\right)}} \]

      11. sub-neg 87.4%

          \[\leadsto x + y \cdot \frac{t}{0 - \color{blue}{\left(z + \left(-a\right)\right)}} \]

      12. +-commutative 87.4%

          \[\leadsto x + y \cdot \frac{t}{0 - \color{blue}{\left(\left(-a\right) + z\right)}} \]

      13. associate--r+ 87.4%

          \[\leadsto x + y \cdot \frac{t}{\color{blue}{\left(0 - \left(-a\right)\right) - z}} \]

      14. neg-sub0 87.4%

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

      15. remove-double-neg 87.4%

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

   5. Simplified 87.4%

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

4. Final simplification 88.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.35 \cdot 10^{+125} \lor \neg \left(z \leq 2.8 \cdot 10^{+60}\right):\\ \;\;\;\;x + y \cdot \left(1 - \frac{t}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot \frac{t}{z - a}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 82.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5 \cdot 10^{-14} \lor \neg \left(z \leq 2.3 \cdot 10^{-82}\right):\\ \;\;\;\;x + y \cdot \left(1 - \frac{t}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -5e-14) (not (<= z 2.3e-82)))
   (+ x (* y (- 1.0 (/ t z))))
   (+ x (/ y (/ a t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -5e-14) || !(z <= 2.3e-82)) {
		tmp = x + (y * (1.0 - (t / z)));
	} else {
		tmp = x + (y / (a / t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-5d-14)) .or. (.not. (z <= 2.3d-82))) then
        tmp = x + (y * (1.0d0 - (t / z)))
    else
        tmp = x + (y / (a / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -5e-14) || !(z <= 2.3e-82)) {
		tmp = x + (y * (1.0 - (t / z)));
	} else {
		tmp = x + (y / (a / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -5e-14) or not (z <= 2.3e-82):
		tmp = x + (y * (1.0 - (t / z)))
	else:
		tmp = x + (y / (a / t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -5e-14) || !(z <= 2.3e-82))
		tmp = Float64(x + Float64(y * Float64(1.0 - Float64(t / z))));
	else
		tmp = Float64(x + Float64(y / Float64(a / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -5e-14) || ~((z <= 2.3e-82)))
		tmp = x + (y * (1.0 - (t / z)));
	else
		tmp = x + (y / (a / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -5e-14], N[Not[LessEqual[z, 2.3e-82]], $MachinePrecision]], N[(x + N[(y * N[(1.0 - N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -5.0000000000000002e-14 or 2.29999999999999997e-82 < z

   1. Initial program 99.9%

      \[x + y \cdot \frac{z - t}{z - a} \]
   2. Add Preprocessing

   3. Taylor expanded in a around 0 62.2%

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

      1. associate-/l* 84.1%

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

      2. div-sub 84.1%

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

      3. *-inverses 84.1%

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

   5. Simplified 84.1%

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

   if -5.0000000000000002e-14 < z < 2.29999999999999997e-82

   1. Initial program 97.8%

      \[x + y \cdot \frac{z - t}{z - a} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. clear-num 97.8%

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

      2. un-div-inv 97.8%

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

   4. Applied egg-rr 97.8%

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

   5. Taylor expanded in z around 0 87.1%

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

4. Final simplification 85.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5 \cdot 10^{-14} \lor \neg \left(z \leq 2.3 \cdot 10^{-82}\right):\\ \;\;\;\;x + y \cdot \left(1 - \frac{t}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 77.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.65 \cdot 10^{-12} \lor \neg \left(z \leq 2.8 \cdot 10^{-48}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -2.65e-12) (not (<= z 2.8e-48))) (+ x y) (+ x (/ y (/ a t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -2.65e-12) || !(z <= 2.8e-48)) {
		tmp = x + y;
	} else {
		tmp = x + (y / (a / t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-2.65d-12)) .or. (.not. (z <= 2.8d-48))) then
        tmp = x + y
    else
        tmp = x + (y / (a / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -2.65e-12) || !(z <= 2.8e-48)) {
		tmp = x + y;
	} else {
		tmp = x + (y / (a / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -2.65e-12) or not (z <= 2.8e-48):
		tmp = x + y
	else:
		tmp = x + (y / (a / t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -2.65e-12) || !(z <= 2.8e-48))
		tmp = Float64(x + y);
	else
		tmp = Float64(x + Float64(y / Float64(a / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -2.65e-12) || ~((z <= 2.8e-48)))
		tmp = x + y;
	else
		tmp = x + (y / (a / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -2.65e-12], N[Not[LessEqual[z, 2.8e-48]], $MachinePrecision]], N[(x + y), $MachinePrecision], N[(x + N[(y / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.64999999999999982e-12 or 2.80000000000000005e-48 < z

   1. Initial program 99.9%

      \[x + y \cdot \frac{z - t}{z - a} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 74.0%

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

      1. +-commutative 74.0%

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

   5. Simplified 74.0%

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

   if -2.64999999999999982e-12 < z < 2.80000000000000005e-48

   1. Initial program 97.8%

      \[x + y \cdot \frac{z - t}{z - a} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. clear-num 97.9%

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

      2. un-div-inv 97.9%

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

   4. Applied egg-rr 97.9%

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

   5. Taylor expanded in z around 0 86.5%

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

4. Final simplification 78.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.65 \cdot 10^{-12} \lor \neg \left(z \leq 2.8 \cdot 10^{-48}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 76.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.7 \cdot 10^{-12} \lor \neg \left(z \leq 3.6 \cdot 10^{-47}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -2.7e-12) (not (<= z 3.6e-47))) (+ x y) (+ x (* y (/ t a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -2.7e-12) || !(z <= 3.6e-47)) {
		tmp = x + y;
	} else {
		tmp = x + (y * (t / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-2.7d-12)) .or. (.not. (z <= 3.6d-47))) then
        tmp = x + y
    else
        tmp = x + (y * (t / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -2.7e-12) || !(z <= 3.6e-47)) {
		tmp = x + y;
	} else {
		tmp = x + (y * (t / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -2.7e-12) or not (z <= 3.6e-47):
		tmp = x + y
	else:
		tmp = x + (y * (t / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -2.7e-12) || !(z <= 3.6e-47))
		tmp = Float64(x + y);
	else
		tmp = Float64(x + Float64(y * Float64(t / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -2.7e-12) || ~((z <= 3.6e-47)))
		tmp = x + y;
	else
		tmp = x + (y * (t / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -2.7e-12], N[Not[LessEqual[z, 3.6e-47]], $MachinePrecision]], N[(x + y), $MachinePrecision], N[(x + N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.6999999999999998e-12 or 3.59999999999999991e-47 < z

   1. Initial program 99.9%

      \[x + y \cdot \frac{z - t}{z - a} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 74.0%

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

      1. +-commutative 74.0%

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

   5. Simplified 74.0%

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

   if -2.6999999999999998e-12 < z < 3.59999999999999991e-47

   1. Initial program 97.8%

      \[x + y \cdot \frac{z - t}{z - a} \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 85.5%

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

4. Final simplification 78.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.7 \cdot 10^{-12} \lor \neg \left(z \leq 3.6 \cdot 10^{-47}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 63.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1 \cdot 10^{+148}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.6 \cdot 10^{+201}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -1e+148) x (if (<= a 1.6e+201) (+ x y) x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1e+148) {
		tmp = x;
	} else if (a <= 1.6e+201) {
		tmp = x + y;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-1d+148)) then
        tmp = x
    else if (a <= 1.6d+201) then
        tmp = x + y
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1e+148) {
		tmp = x;
	} else if (a <= 1.6e+201) {
		tmp = x + y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -1e+148:
		tmp = x
	elif a <= 1.6e+201:
		tmp = x + y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -1e+148)
		tmp = x;
	elseif (a <= 1.6e+201)
		tmp = Float64(x + y);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -1e+148)
		tmp = x;
	elseif (a <= 1.6e+201)
		tmp = x + y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -1e+148], x, If[LessEqual[a, 1.6e+201], N[(x + y), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if a < -1e148 or 1.6e201 < a

   1. Initial program 99.9%

      \[x + y \cdot \frac{z - t}{z - a} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 82.0%

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

   if -1e148 < a < 1.6e201

   1. Initial program 98.9%

      \[x + y \cdot \frac{z - t}{z - a} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 66.8%

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

      1. +-commutative 66.8%

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

   5. Simplified 66.8%

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

4. Final simplification 70.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1 \cdot 10^{+148}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.6 \cdot 10^{+201}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 97.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x + y \cdot \frac{z - t}{z - a} \end{array} \]

FPCore

(FPCore (x y z t a) :precision binary64 (+ x (* y (/ (- z t) (- z a)))))

C

double code(double x, double y, double z, double t, double a) {
	return x + (y * ((z - t) / (z - a)));
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    code = x + (y * ((z - t) / (z - a)))
end function

Java

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

Python

def code(x, y, z, t, a):
	return x + (y * ((z - t) / (z - a)))

Julia

function code(x, y, z, t, a)
	return Float64(x + Float64(y * Float64(Float64(z - t) / Float64(z - a))))
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = x + (y * ((z - t) / (z - a)));
end

Wolfram

code[x_, y_, z_, t_, a_] := N[(x + N[(y * N[(N[(z - t), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.1%

   \[x + y \cdot \frac{z - t}{z - a} \]
2. Add Preprocessing
3. Add Preprocessing

Alternative 13: 50.3% accurate, 11.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_] := x

Derivation

1. Initial program 99.1%

   \[x + y \cdot \frac{z - t}{z - a} \]
2. Add Preprocessing

3. Taylor expanded in x around inf 54.0%

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

Developer Target 1: 98.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024185 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisLine from plot-0.2.3.4, A"
  :precision binary64

  :alt
  (! :herbie-platform default (+ x (/ y (/ (- z a) (- z t)))))

  (+ x (* y (/ (- z t) (- z a)))))