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

Percentage Accurate: 85.9% → 98.4%

Time: 11.9s

Alternatives: 15

Speedup: 1.0×

Specification

Math

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

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(Float64(y * 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[(N[(y * N[(z - t), $MachinePrecision]), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Initial Program: 85.9% accurate, 1.0× speedup

Math

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

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(Float64(y * 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[(N[(y * N[(z - t), $MachinePrecision]), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Alternative 1: 98.4% 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 83.7%

   \[x + \frac{y \cdot \left(z - t\right)}{z - a} \]
2. Step-by-step derivation

   1. associate-*l/ 93.8%

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

3. Simplified 93.8%

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

   1. associate-/r/ 99.1%

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

5. Applied egg-rr 99.1%

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

6. Final simplification 99.1%

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

Alternative 2: 74.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.4 \cdot 10^{+170}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq -3750:\\ \;\;\;\;x - y \cdot \frac{t}{z}\\ \mathbf{elif}\;z \leq -6.2 \cdot 10^{-79}:\\ \;\;\;\;x - z \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq -1.46 \cdot 10^{-94}:\\ \;\;\;\;y \cdot \left(1 - \frac{t}{z}\right)\\ \mathbf{elif}\;z \leq 3.05 \cdot 10^{+71}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -2.4e+170)
   (+ x y)
   (if (<= z -3750.0)
     (- x (* y (/ t z)))
     (if (<= z -6.2e-79)
       (- x (* z (/ y a)))
       (if (<= z -1.46e-94)
         (* y (- 1.0 (/ t z)))
         (if (<= z 3.05e+71) (+ x (* y (/ t a))) (+ x y)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.4e+170) {
		tmp = x + y;
	} else if (z <= -3750.0) {
		tmp = x - (y * (t / z));
	} else if (z <= -6.2e-79) {
		tmp = x - (z * (y / a));
	} else if (z <= -1.46e-94) {
		tmp = y * (1.0 - (t / z));
	} else if (z <= 3.05e+71) {
		tmp = x + (y * (t / a));
	} 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 <= (-2.4d+170)) then
        tmp = x + y
    else if (z <= (-3750.0d0)) then
        tmp = x - (y * (t / z))
    else if (z <= (-6.2d-79)) then
        tmp = x - (z * (y / a))
    else if (z <= (-1.46d-94)) then
        tmp = y * (1.0d0 - (t / z))
    else if (z <= 3.05d+71) then
        tmp = x + (y * (t / a))
    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 <= -2.4e+170) {
		tmp = x + y;
	} else if (z <= -3750.0) {
		tmp = x - (y * (t / z));
	} else if (z <= -6.2e-79) {
		tmp = x - (z * (y / a));
	} else if (z <= -1.46e-94) {
		tmp = y * (1.0 - (t / z));
	} else if (z <= 3.05e+71) {
		tmp = x + (y * (t / a));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -2.4e+170:
		tmp = x + y
	elif z <= -3750.0:
		tmp = x - (y * (t / z))
	elif z <= -6.2e-79:
		tmp = x - (z * (y / a))
	elif z <= -1.46e-94:
		tmp = y * (1.0 - (t / z))
	elif z <= 3.05e+71:
		tmp = x + (y * (t / a))
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -2.4e+170)
		tmp = Float64(x + y);
	elseif (z <= -3750.0)
		tmp = Float64(x - Float64(y * Float64(t / z)));
	elseif (z <= -6.2e-79)
		tmp = Float64(x - Float64(z * Float64(y / a)));
	elseif (z <= -1.46e-94)
		tmp = Float64(y * Float64(1.0 - Float64(t / z)));
	elseif (z <= 3.05e+71)
		tmp = Float64(x + Float64(y * Float64(t / a)));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -2.4e+170)
		tmp = x + y;
	elseif (z <= -3750.0)
		tmp = x - (y * (t / z));
	elseif (z <= -6.2e-79)
		tmp = x - (z * (y / a));
	elseif (z <= -1.46e-94)
		tmp = y * (1.0 - (t / z));
	elseif (z <= 3.05e+71)
		tmp = x + (y * (t / a));
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -2.4e+170], N[(x + y), $MachinePrecision], If[LessEqual[z, -3750.0], N[(x - N[(y * N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -6.2e-79], N[(x - N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.46e-94], N[(y * N[(1.0 - N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.05e+71], N[(x + N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -2.4e170 or 3.0500000000000002e71 < z

   1. Initial program 62.5%

      \[x + \frac{y \cdot \left(z - t\right)}{z - a} \]
   2. Step-by-step derivation

      1. associate-*l/ 88.7%

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

   3. Simplified 88.7%

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

   4. Taylor expanded in z around inf 90.1%

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

   if -2.4e170 < z < -3750

   1. Initial program 88.9%

      \[x + \frac{y \cdot \left(z - t\right)}{z - a} \]
   2. Step-by-step derivation

      1. associate-*l/ 99.9%

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

   3. Simplified 99.9%

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

      1. associate-/r/ 99.8%

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

   5. Applied egg-rr 99.8%

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

   6. Taylor expanded in t around inf 80.6%

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

      1. associate-*r/ 80.6%

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

      2. neg-mul-1 80.6%

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

   8. Simplified 80.6%

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

      1. frac-2neg 80.6%

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

      2. distribute-frac-neg 80.6%

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

      3. distribute-neg-frac 80.6%

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

      4. remove-double-neg 80.6%

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

      5. *-un-lft-identity 80.6%

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

      6. *-un-lft-identity 80.6%

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

      7. add-sqr-sqrt 9.2%

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

      8. sqrt-unprod 40.8%

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

      9. sqr-neg 40.8%

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

      10. sqrt-unprod 31.4%

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

      11. add-sqr-sqrt 40.7%

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

      12. sub-neg 40.7%

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

      13. associate-/r/ 40.7%

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

      14. associate-*l/ 37.7%

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

      15. add-sqr-sqrt 31.4%

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

      16. sqrt-unprod 37.9%

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

      17. sqr-neg 37.9%

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

   10. Applied egg-rr 75.3%

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

       1. associate-*r/ 80.6%

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

   12. Simplified 80.6%

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

   13. Taylor expanded in z around inf 69.5%

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

   if -3750 < z < -6.1999999999999999e-79

   1. Initial program 99.7%

      \[x + \frac{y \cdot \left(z - t\right)}{z - a} \]
   2. Step-by-step derivation

      1. associate-*l/ 99.6%

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

   3. Simplified 99.6%

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

      1. associate-/r/ 94.0%

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

   5. Applied egg-rr 94.0%

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

   6. Taylor expanded in t around 0 75.3%

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

   7. Taylor expanded in z around 0 75.8%

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

      1. mul-1-neg 75.8%

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

      2. unsub-neg 75.8%

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

      3. associate-/l* 70.0%

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

      4. associate-/r/ 81.4%

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

   9. Simplified 81.4%

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

   if -6.1999999999999999e-79 < z < -1.4599999999999999e-94

   1. Initial program 100.0%

      \[x + \frac{y \cdot \left(z - t\right)}{z - a} \]
   2. Step-by-step derivation

      1. associate-*l/ 81.2%

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

   3. Simplified 81.2%

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

   4. Taylor expanded in a around 0 79.8%

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

   5. Taylor expanded in y around inf 79.8%

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

   if -1.4599999999999999e-94 < z < 3.0500000000000002e71

   1. Initial program 93.7%

      \[x + \frac{y \cdot \left(z - t\right)}{z - a} \]
   2. Step-by-step derivation

      1. associate-*l/ 95.2%

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

   3. Simplified 95.2%

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

   4. Taylor expanded in z around 0 85.6%

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

      1. associate-/l* 87.1%

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

      2. associate-/r/ 89.4%

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

   6. Simplified 89.4%

      \[\leadsto x + \color{blue}{\frac{t}{a} \cdot y} \]
3. Recombined 5 regimes into one program.

4. Final simplification 86.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.4 \cdot 10^{+170}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq -3750:\\ \;\;\;\;x - y \cdot \frac{t}{z}\\ \mathbf{elif}\;z \leq -6.2 \cdot 10^{-79}:\\ \;\;\;\;x - z \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq -1.46 \cdot 10^{-94}:\\ \;\;\;\;y \cdot \left(1 - \frac{t}{z}\right)\\ \mathbf{elif}\;z \leq 3.05 \cdot 10^{+71}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 3: 81.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + y \cdot \left(1 - \frac{t}{z}\right)\\ \mathbf{if}\;z \leq -3.2 \cdot 10^{+41}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -5.3 \cdot 10^{-67}:\\ \;\;\;\;x + z \cdot \frac{y}{z - a}\\ \mathbf{elif}\;z \leq -1.46 \cdot 10^{-94} \lor \neg \left(z \leq 2.2 \cdot 10^{-62}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* y (- 1.0 (/ t z))))))
   (if (<= z -3.2e+41)
     t_1
     (if (<= z -5.3e-67)
       (+ x (* z (/ y (- z a))))
       (if (or (<= z -1.46e-94) (not (<= z 2.2e-62)))
         t_1
         (+ x (* y (/ t a))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y * (1.0 - (t / z)));
	double tmp;
	if (z <= -3.2e+41) {
		tmp = t_1;
	} else if (z <= -5.3e-67) {
		tmp = x + (z * (y / (z - a)));
	} else if ((z <= -1.46e-94) || !(z <= 2.2e-62)) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = x + (y * (1.0d0 - (t / z)))
    if (z <= (-3.2d+41)) then
        tmp = t_1
    else if (z <= (-5.3d-67)) then
        tmp = x + (z * (y / (z - a)))
    else if ((z <= (-1.46d-94)) .or. (.not. (z <= 2.2d-62))) then
        tmp = t_1
    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 t_1 = x + (y * (1.0 - (t / z)));
	double tmp;
	if (z <= -3.2e+41) {
		tmp = t_1;
	} else if (z <= -5.3e-67) {
		tmp = x + (z * (y / (z - a)));
	} else if ((z <= -1.46e-94) || !(z <= 2.2e-62)) {
		tmp = t_1;
	} else {
		tmp = x + (y * (t / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (y * (1.0 - (t / z)))
	tmp = 0
	if z <= -3.2e+41:
		tmp = t_1
	elif z <= -5.3e-67:
		tmp = x + (z * (y / (z - a)))
	elif (z <= -1.46e-94) or not (z <= 2.2e-62):
		tmp = t_1
	else:
		tmp = x + (y * (t / a))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(y * Float64(1.0 - Float64(t / z))))
	tmp = 0.0
	if (z <= -3.2e+41)
		tmp = t_1;
	elseif (z <= -5.3e-67)
		tmp = Float64(x + Float64(z * Float64(y / Float64(z - a))));
	elseif ((z <= -1.46e-94) || !(z <= 2.2e-62))
		tmp = t_1;
	else
		tmp = Float64(x + Float64(y * Float64(t / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (y * (1.0 - (t / z)));
	tmp = 0.0;
	if (z <= -3.2e+41)
		tmp = t_1;
	elseif (z <= -5.3e-67)
		tmp = x + (z * (y / (z - a)));
	elseif ((z <= -1.46e-94) || ~((z <= 2.2e-62)))
		tmp = t_1;
	else
		tmp = x + (y * (t / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(y * N[(1.0 - N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.2e+41], t$95$1, If[LessEqual[z, -5.3e-67], N[(x + N[(z * N[(y / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, -1.46e-94], N[Not[LessEqual[z, 2.2e-62]], $MachinePrecision]], t$95$1, N[(x + N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.2000000000000001e41 or -5.29999999999999971e-67 < z < -1.4599999999999999e-94 or 2.20000000000000017e-62 < z

   1. Initial program 75.9%

      \[x + \frac{y \cdot \left(z - t\right)}{z - a} \]
   2. Step-by-step derivation

      1. associate-*l/ 92.6%

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

   3. Simplified 92.6%

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

   4. Taylor expanded in a around 0 66.8%

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

   5. Taylor expanded in y around 0 87.4%

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

   if -3.2000000000000001e41 < z < -5.29999999999999971e-67

   1. Initial program 92.1%

      \[x + \frac{y \cdot \left(z - t\right)}{z - a} \]
   2. Step-by-step derivation

      1. associate-*l/ 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in t around 0 71.8%

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

      1. *-commutative 71.8%

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

      2. associate-*r/ 75.8%

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

   6. Simplified 75.8%

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

   if -1.4599999999999999e-94 < z < 2.20000000000000017e-62

   1. Initial program 92.9%

      \[x + \frac{y \cdot \left(z - t\right)}{z - a} \]
   2. Step-by-step derivation

      1. associate-*l/ 93.9%

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

   3. Simplified 93.9%

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

   4. Taylor expanded in z around 0 88.0%

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

      1. associate-/l* 89.9%

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

      2. associate-/r/ 93.9%

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

   6. Simplified 93.9%

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

4. Final simplification 88.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.2 \cdot 10^{+41}:\\ \;\;\;\;x + y \cdot \left(1 - \frac{t}{z}\right)\\ \mathbf{elif}\;z \leq -5.3 \cdot 10^{-67}:\\ \;\;\;\;x + z \cdot \frac{y}{z - a}\\ \mathbf{elif}\;z \leq -1.46 \cdot 10^{-94} \lor \neg \left(z \leq 2.2 \cdot 10^{-62}\right):\\ \;\;\;\;x + y \cdot \left(1 - \frac{t}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \end{array} \]

Alternative 4: 80.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(1 - \frac{t}{z}\right)\\ t_2 := x + t_1\\ \mathbf{if}\;z \leq -2.4 \cdot 10^{+36}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -6.5 \cdot 10^{-79}:\\ \;\;\;\;x - z \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq -1.46 \cdot 10^{-94}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.65 \cdot 10^{-62}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (- 1.0 (/ t z)))) (t_2 (+ x t_1)))
   (if (<= z -2.4e+36)
     t_2
     (if (<= z -6.5e-79)
       (- x (* z (/ y a)))
       (if (<= z -1.46e-94)
         t_1
         (if (<= z 1.65e-62) (+ x (* y (/ t a))) t_2))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * (1.0 - (t / z));
	double t_2 = x + t_1;
	double tmp;
	if (z <= -2.4e+36) {
		tmp = t_2;
	} else if (z <= -6.5e-79) {
		tmp = x - (z * (y / a));
	} else if (z <= -1.46e-94) {
		tmp = t_1;
	} else if (z <= 1.65e-62) {
		tmp = x + (y * (t / a));
	} else {
		tmp = t_2;
	}
	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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = y * (1.0d0 - (t / z))
    t_2 = x + t_1
    if (z <= (-2.4d+36)) then
        tmp = t_2
    else if (z <= (-6.5d-79)) then
        tmp = x - (z * (y / a))
    else if (z <= (-1.46d-94)) then
        tmp = t_1
    else if (z <= 1.65d-62) then
        tmp = x + (y * (t / a))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y * (1.0 - (t / z));
	double t_2 = x + t_1;
	double tmp;
	if (z <= -2.4e+36) {
		tmp = t_2;
	} else if (z <= -6.5e-79) {
		tmp = x - (z * (y / a));
	} else if (z <= -1.46e-94) {
		tmp = t_1;
	} else if (z <= 1.65e-62) {
		tmp = x + (y * (t / a));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * (1.0 - (t / z))
	t_2 = x + t_1
	tmp = 0
	if z <= -2.4e+36:
		tmp = t_2
	elif z <= -6.5e-79:
		tmp = x - (z * (y / a))
	elif z <= -1.46e-94:
		tmp = t_1
	elif z <= 1.65e-62:
		tmp = x + (y * (t / a))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(1.0 - Float64(t / z)))
	t_2 = Float64(x + t_1)
	tmp = 0.0
	if (z <= -2.4e+36)
		tmp = t_2;
	elseif (z <= -6.5e-79)
		tmp = Float64(x - Float64(z * Float64(y / a)));
	elseif (z <= -1.46e-94)
		tmp = t_1;
	elseif (z <= 1.65e-62)
		tmp = Float64(x + Float64(y * Float64(t / a)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * (1.0 - (t / z));
	t_2 = x + t_1;
	tmp = 0.0;
	if (z <= -2.4e+36)
		tmp = t_2;
	elseif (z <= -6.5e-79)
		tmp = x - (z * (y / a));
	elseif (z <= -1.46e-94)
		tmp = t_1;
	elseif (z <= 1.65e-62)
		tmp = x + (y * (t / a));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(1.0 - N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + t$95$1), $MachinePrecision]}, If[LessEqual[z, -2.4e+36], t$95$2, If[LessEqual[z, -6.5e-79], N[(x - N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.46e-94], t$95$1, If[LessEqual[z, 1.65e-62], N[(x + N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2.39999999999999992e36 or 1.65000000000000002e-62 < z

   1. Initial program 74.6%

      \[x + \frac{y \cdot \left(z - t\right)}{z - a} \]
   2. Step-by-step derivation

      1. associate-*l/ 93.0%

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

   3. Simplified 93.0%

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

   4. Taylor expanded in a around 0 66.5%

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

   5. Taylor expanded in y around 0 88.2%

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

   if -2.39999999999999992e36 < z < -6.5000000000000003e-79

   1. Initial program 92.7%

      \[x + \frac{y \cdot \left(z - t\right)}{z - a} \]
   2. Step-by-step derivation

      1. associate-*l/ 99.8%

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

   3. Simplified 99.8%

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

      1. associate-/r/ 96.3%

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

   5. Applied egg-rr 96.3%

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

   6. Taylor expanded in t around 0 70.2%

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

   7. Taylor expanded in z around 0 66.4%

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

      1. mul-1-neg 66.4%

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

      2. unsub-neg 66.4%

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

      3. associate-/l* 66.5%

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

      4. associate-/r/ 73.6%

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

   9. Simplified 73.6%

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

   if -6.5000000000000003e-79 < z < -1.4599999999999999e-94

   1. Initial program 100.0%

      \[x + \frac{y \cdot \left(z - t\right)}{z - a} \]
   2. Step-by-step derivation

      1. associate-*l/ 81.2%

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

   3. Simplified 81.2%

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

   4. Taylor expanded in a around 0 79.8%

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

   5. Taylor expanded in y around inf 79.8%

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

   if -1.4599999999999999e-94 < z < 1.65000000000000002e-62

   1. Initial program 92.9%

      \[x + \frac{y \cdot \left(z - t\right)}{z - a} \]
   2. Step-by-step derivation

      1. associate-*l/ 93.9%

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

   3. Simplified 93.9%

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

   4. Taylor expanded in z around 0 88.0%

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

      1. associate-/l* 89.9%

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

      2. associate-/r/ 93.9%

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

   6. Simplified 93.9%

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

4. Final simplification 88.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.4 \cdot 10^{+36}:\\ \;\;\;\;x + y \cdot \left(1 - \frac{t}{z}\right)\\ \mathbf{elif}\;z \leq -6.5 \cdot 10^{-79}:\\ \;\;\;\;x - z \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq -1.46 \cdot 10^{-94}:\\ \;\;\;\;y \cdot \left(1 - \frac{t}{z}\right)\\ \mathbf{elif}\;z \leq 1.65 \cdot 10^{-62}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(1 - \frac{t}{z}\right)\\ \end{array} \]

Alternative 5: 81.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + y \cdot \left(1 - \frac{t}{z}\right)\\ \mathbf{if}\;z \leq -2.2 \cdot 10^{+41}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -7.4 \cdot 10^{-67}:\\ \;\;\;\;x + z \cdot \frac{y}{z - a}\\ \mathbf{elif}\;z \leq -1.14 \cdot 10^{-94}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.72 \cdot 10^{-62}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{z}{z - t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* y (- 1.0 (/ t z))))))
   (if (<= z -2.2e+41)
     t_1
     (if (<= z -7.4e-67)
       (+ x (* z (/ y (- z a))))
       (if (<= z -1.14e-94)
         t_1
         (if (<= z 1.72e-62)
           (+ x (* y (/ t a)))
           (+ x (/ y (/ z (- z t))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y * (1.0 - (t / z)));
	double tmp;
	if (z <= -2.2e+41) {
		tmp = t_1;
	} else if (z <= -7.4e-67) {
		tmp = x + (z * (y / (z - a)));
	} else if (z <= -1.14e-94) {
		tmp = t_1;
	} else if (z <= 1.72e-62) {
		tmp = x + (y * (t / a));
	} else {
		tmp = x + (y / (z / (z - 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) :: t_1
    real(8) :: tmp
    t_1 = x + (y * (1.0d0 - (t / z)))
    if (z <= (-2.2d+41)) then
        tmp = t_1
    else if (z <= (-7.4d-67)) then
        tmp = x + (z * (y / (z - a)))
    else if (z <= (-1.14d-94)) then
        tmp = t_1
    else if (z <= 1.72d-62) then
        tmp = x + (y * (t / a))
    else
        tmp = x + (y / (z / (z - t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y * (1.0 - (t / z)));
	double tmp;
	if (z <= -2.2e+41) {
		tmp = t_1;
	} else if (z <= -7.4e-67) {
		tmp = x + (z * (y / (z - a)));
	} else if (z <= -1.14e-94) {
		tmp = t_1;
	} else if (z <= 1.72e-62) {
		tmp = x + (y * (t / a));
	} else {
		tmp = x + (y / (z / (z - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (y * (1.0 - (t / z)))
	tmp = 0
	if z <= -2.2e+41:
		tmp = t_1
	elif z <= -7.4e-67:
		tmp = x + (z * (y / (z - a)))
	elif z <= -1.14e-94:
		tmp = t_1
	elif z <= 1.72e-62:
		tmp = x + (y * (t / a))
	else:
		tmp = x + (y / (z / (z - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(y * Float64(1.0 - Float64(t / z))))
	tmp = 0.0
	if (z <= -2.2e+41)
		tmp = t_1;
	elseif (z <= -7.4e-67)
		tmp = Float64(x + Float64(z * Float64(y / Float64(z - a))));
	elseif (z <= -1.14e-94)
		tmp = t_1;
	elseif (z <= 1.72e-62)
		tmp = Float64(x + Float64(y * Float64(t / a)));
	else
		tmp = Float64(x + Float64(y / Float64(z / Float64(z - t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (y * (1.0 - (t / z)));
	tmp = 0.0;
	if (z <= -2.2e+41)
		tmp = t_1;
	elseif (z <= -7.4e-67)
		tmp = x + (z * (y / (z - a)));
	elseif (z <= -1.14e-94)
		tmp = t_1;
	elseif (z <= 1.72e-62)
		tmp = x + (y * (t / a));
	else
		tmp = x + (y / (z / (z - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(y * N[(1.0 - N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.2e+41], t$95$1, If[LessEqual[z, -7.4e-67], N[(x + N[(z * N[(y / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.14e-94], t$95$1, If[LessEqual[z, 1.72e-62], N[(x + N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y / N[(z / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2.1999999999999999e41 or -7.3999999999999999e-67 < z < -1.14e-94

   1. Initial program 76.3%

      \[x + \frac{y \cdot \left(z - t\right)}{z - a} \]
   2. Step-by-step derivation

      1. associate-*l/ 91.4%

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

   3. Simplified 91.4%

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

   4. Taylor expanded in a around 0 65.8%

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

   5. Taylor expanded in y around 0 86.1%

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

   if -2.1999999999999999e41 < z < -7.3999999999999999e-67

   1. Initial program 92.1%

      \[x + \frac{y \cdot \left(z - t\right)}{z - a} \]
   2. Step-by-step derivation

      1. associate-*l/ 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in t around 0 71.8%

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

      1. *-commutative 71.8%

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

      2. associate-*r/ 75.8%

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

   6. Simplified 75.8%

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

   if -1.14e-94 < z < 1.7199999999999999e-62

   1. Initial program 92.9%

      \[x + \frac{y \cdot \left(z - t\right)}{z - a} \]
   2. Step-by-step derivation

      1. associate-*l/ 93.9%

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

   3. Simplified 93.9%

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

   4. Taylor expanded in z around 0 88.0%

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

      1. associate-/l* 89.9%

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

      2. associate-/r/ 93.9%

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

   6. Simplified 93.9%

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

   if 1.7199999999999999e-62 < z

   1. Initial program 75.6%

      \[x + \frac{y \cdot \left(z - t\right)}{z - a} \]
   2. Step-by-step derivation

      1. associate-*l/ 93.5%

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

   3. Simplified 93.5%

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

   4. Taylor expanded in a around 0 67.5%

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

      1. associate-/l* 88.3%

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

   6. Simplified 88.3%

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

4. Final simplification 88.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.2 \cdot 10^{+41}:\\ \;\;\;\;x + y \cdot \left(1 - \frac{t}{z}\right)\\ \mathbf{elif}\;z \leq -7.4 \cdot 10^{-67}:\\ \;\;\;\;x + z \cdot \frac{y}{z - a}\\ \mathbf{elif}\;z \leq -1.14 \cdot 10^{-94}:\\ \;\;\;\;x + y \cdot \left(1 - \frac{t}{z}\right)\\ \mathbf{elif}\;z \leq 1.72 \cdot 10^{-62}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{z}{z - t}}\\ \end{array} \]

Alternative 6: 81.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + y \cdot \left(1 - \frac{t}{z}\right)\\ \mathbf{if}\;z \leq -2.5 \cdot 10^{+41}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -4.9 \cdot 10^{-67}:\\ \;\;\;\;x + z \cdot \frac{y}{z - a}\\ \mathbf{elif}\;z \leq -2.7 \cdot 10^{-95}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{-64}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{z - a}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* y (- 1.0 (/ t z))))))
   (if (<= z -2.5e+41)
     t_1
     (if (<= z -4.9e-67)
       (+ x (* z (/ y (- z a))))
       (if (<= z -2.7e-95)
         t_1
         (if (<= z 1.6e-64) (+ x (* y (/ t a))) (+ x (/ y (/ (- z a) z)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y * (1.0 - (t / z)));
	double tmp;
	if (z <= -2.5e+41) {
		tmp = t_1;
	} else if (z <= -4.9e-67) {
		tmp = x + (z * (y / (z - a)));
	} else if (z <= -2.7e-95) {
		tmp = t_1;
	} else if (z <= 1.6e-64) {
		tmp = x + (y * (t / a));
	} else {
		tmp = x + (y / ((z - 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) :: t_1
    real(8) :: tmp
    t_1 = x + (y * (1.0d0 - (t / z)))
    if (z <= (-2.5d+41)) then
        tmp = t_1
    else if (z <= (-4.9d-67)) then
        tmp = x + (z * (y / (z - a)))
    else if (z <= (-2.7d-95)) then
        tmp = t_1
    else if (z <= 1.6d-64) then
        tmp = x + (y * (t / a))
    else
        tmp = x + (y / ((z - a) / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y * (1.0 - (t / z)));
	double tmp;
	if (z <= -2.5e+41) {
		tmp = t_1;
	} else if (z <= -4.9e-67) {
		tmp = x + (z * (y / (z - a)));
	} else if (z <= -2.7e-95) {
		tmp = t_1;
	} else if (z <= 1.6e-64) {
		tmp = x + (y * (t / a));
	} else {
		tmp = x + (y / ((z - a) / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (y * (1.0 - (t / z)))
	tmp = 0
	if z <= -2.5e+41:
		tmp = t_1
	elif z <= -4.9e-67:
		tmp = x + (z * (y / (z - a)))
	elif z <= -2.7e-95:
		tmp = t_1
	elif z <= 1.6e-64:
		tmp = x + (y * (t / a))
	else:
		tmp = x + (y / ((z - a) / z))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(y * Float64(1.0 - Float64(t / z))))
	tmp = 0.0
	if (z <= -2.5e+41)
		tmp = t_1;
	elseif (z <= -4.9e-67)
		tmp = Float64(x + Float64(z * Float64(y / Float64(z - a))));
	elseif (z <= -2.7e-95)
		tmp = t_1;
	elseif (z <= 1.6e-64)
		tmp = Float64(x + Float64(y * Float64(t / a)));
	else
		tmp = Float64(x + Float64(y / Float64(Float64(z - a) / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (y * (1.0 - (t / z)));
	tmp = 0.0;
	if (z <= -2.5e+41)
		tmp = t_1;
	elseif (z <= -4.9e-67)
		tmp = x + (z * (y / (z - a)));
	elseif (z <= -2.7e-95)
		tmp = t_1;
	elseif (z <= 1.6e-64)
		tmp = x + (y * (t / a));
	else
		tmp = x + (y / ((z - a) / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(y * N[(1.0 - N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.5e+41], t$95$1, If[LessEqual[z, -4.9e-67], N[(x + N[(z * N[(y / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -2.7e-95], t$95$1, If[LessEqual[z, 1.6e-64], N[(x + N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y / N[(N[(z - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2.50000000000000011e41 or -4.89999999999999993e-67 < z < -2.7e-95

   1. Initial program 76.3%

      \[x + \frac{y \cdot \left(z - t\right)}{z - a} \]
   2. Step-by-step derivation

      1. associate-*l/ 91.4%

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

   3. Simplified 91.4%

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

   4. Taylor expanded in a around 0 65.8%

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

   5. Taylor expanded in y around 0 86.1%

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

   if -2.50000000000000011e41 < z < -4.89999999999999993e-67

   1. Initial program 92.1%

      \[x + \frac{y \cdot \left(z - t\right)}{z - a} \]
   2. Step-by-step derivation

      1. associate-*l/ 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in t around 0 71.8%

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

      1. *-commutative 71.8%

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

      2. associate-*r/ 75.8%

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

   6. Simplified 75.8%

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

   if -2.7e-95 < z < 1.59999999999999988e-64

   1. Initial program 92.9%

      \[x + \frac{y \cdot \left(z - t\right)}{z - a} \]
   2. Step-by-step derivation

      1. associate-*l/ 93.9%

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

   3. Simplified 93.9%

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

   4. Taylor expanded in z around 0 88.8%

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

      1. associate-/l* 90.8%

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

      2. associate-/r/ 94.8%

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

   6. Simplified 94.8%

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

   if 1.59999999999999988e-64 < z

   1. Initial program 75.9%

      \[x + \frac{y \cdot \left(z - t\right)}{z - a} \]
   2. Step-by-step derivation

      1. associate-*l/ 93.5%

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

   3. Simplified 93.5%

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

      1. associate-/r/ 99.7%

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

   5. Applied egg-rr 99.7%

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

   6. Taylor expanded in t around 0 90.1%

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

4. Final simplification 89.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.5 \cdot 10^{+41}:\\ \;\;\;\;x + y \cdot \left(1 - \frac{t}{z}\right)\\ \mathbf{elif}\;z \leq -4.9 \cdot 10^{-67}:\\ \;\;\;\;x + z \cdot \frac{y}{z - a}\\ \mathbf{elif}\;z \leq -2.7 \cdot 10^{-95}:\\ \;\;\;\;x + y \cdot \left(1 - \frac{t}{z}\right)\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{-64}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{z - a}{z}}\\ \end{array} \]

Alternative 7: 74.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + t \cdot \frac{y}{a}\\ \mathbf{if}\;z \leq -3.5 \cdot 10^{+76}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq -2.55 \cdot 10^{-39}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.46 \cdot 10^{-94}:\\ \;\;\;\;y \cdot \left(1 - \frac{t}{z}\right)\\ \mathbf{elif}\;z \leq 3.15 \cdot 10^{+75}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* t (/ y a)))))
   (if (<= z -3.5e+76)
     (+ x y)
     (if (<= z -2.55e-39)
       t_1
       (if (<= z -1.46e-94)
         (* y (- 1.0 (/ t z)))
         (if (<= z 3.15e+75) t_1 (+ x y)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (t * (y / a));
	double tmp;
	if (z <= -3.5e+76) {
		tmp = x + y;
	} else if (z <= -2.55e-39) {
		tmp = t_1;
	} else if (z <= -1.46e-94) {
		tmp = y * (1.0 - (t / z));
	} else if (z <= 3.15e+75) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = x + (t * (y / a))
    if (z <= (-3.5d+76)) then
        tmp = x + y
    else if (z <= (-2.55d-39)) then
        tmp = t_1
    else if (z <= (-1.46d-94)) then
        tmp = y * (1.0d0 - (t / z))
    else if (z <= 3.15d+75) then
        tmp = t_1
    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 t_1 = x + (t * (y / a));
	double tmp;
	if (z <= -3.5e+76) {
		tmp = x + y;
	} else if (z <= -2.55e-39) {
		tmp = t_1;
	} else if (z <= -1.46e-94) {
		tmp = y * (1.0 - (t / z));
	} else if (z <= 3.15e+75) {
		tmp = t_1;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (t * (y / a))
	tmp = 0
	if z <= -3.5e+76:
		tmp = x + y
	elif z <= -2.55e-39:
		tmp = t_1
	elif z <= -1.46e-94:
		tmp = y * (1.0 - (t / z))
	elif z <= 3.15e+75:
		tmp = t_1
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(t * Float64(y / a)))
	tmp = 0.0
	if (z <= -3.5e+76)
		tmp = Float64(x + y);
	elseif (z <= -2.55e-39)
		tmp = t_1;
	elseif (z <= -1.46e-94)
		tmp = Float64(y * Float64(1.0 - Float64(t / z)));
	elseif (z <= 3.15e+75)
		tmp = t_1;
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (t * (y / a));
	tmp = 0.0;
	if (z <= -3.5e+76)
		tmp = x + y;
	elseif (z <= -2.55e-39)
		tmp = t_1;
	elseif (z <= -1.46e-94)
		tmp = y * (1.0 - (t / z));
	elseif (z <= 3.15e+75)
		tmp = t_1;
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.5e+76], N[(x + y), $MachinePrecision], If[LessEqual[z, -2.55e-39], t$95$1, If[LessEqual[z, -1.46e-94], N[(y * N[(1.0 - N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.15e+75], t$95$1, N[(x + y), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.5e76 or 3.15000000000000018e75 < z

   1. Initial program 67.1%

      \[x + \frac{y \cdot \left(z - t\right)}{z - a} \]
   2. Step-by-step derivation

      1. associate-*l/ 90.7%

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

   3. Simplified 90.7%

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

   4. Taylor expanded in z around inf 84.7%

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

   if -3.5e76 < z < -2.54999999999999994e-39 or -1.4599999999999999e-94 < z < 3.15000000000000018e75

   1. Initial program 93.4%

      \[x + \frac{y \cdot \left(z - t\right)}{z - a} \]
   2. Step-by-step derivation

      1. associate-*l/ 96.0%

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

   3. Simplified 96.0%

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

      1. associate-/r/ 98.4%

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

   5. Applied egg-rr 98.4%

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

   6. Taylor expanded in z around 0 82.6%

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

      1. associate-*r/ 83.7%

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

   8. Simplified 83.7%

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

   if -2.54999999999999994e-39 < z < -1.4599999999999999e-94

   1. Initial program 99.8%

      \[x + \frac{y \cdot \left(z - t\right)}{z - a} \]
   2. Step-by-step derivation

      1. associate-*l/ 92.8%

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

   3. Simplified 92.8%

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

   4. Taylor expanded in a around 0 66.1%

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

   5. Taylor expanded in y around inf 52.4%

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

4. Final simplification 82.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.5 \cdot 10^{+76}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq -2.55 \cdot 10^{-39}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq -1.46 \cdot 10^{-94}:\\ \;\;\;\;y \cdot \left(1 - \frac{t}{z}\right)\\ \mathbf{elif}\;z \leq 3.15 \cdot 10^{+75}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 8: 74.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + y \cdot \frac{t}{a}\\ \mathbf{if}\;z \leq -3.1 \cdot 10^{+76}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq -2.55 \cdot 10^{-39}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.46 \cdot 10^{-94}:\\ \;\;\;\;y \cdot \left(1 - \frac{t}{z}\right)\\ \mathbf{elif}\;z \leq 1.02 \cdot 10^{+76}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* y (/ t a)))))
   (if (<= z -3.1e+76)
     (+ x y)
     (if (<= z -2.55e-39)
       t_1
       (if (<= z -1.46e-94)
         (* y (- 1.0 (/ t z)))
         (if (<= z 1.02e+76) t_1 (+ x y)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y * (t / a));
	double tmp;
	if (z <= -3.1e+76) {
		tmp = x + y;
	} else if (z <= -2.55e-39) {
		tmp = t_1;
	} else if (z <= -1.46e-94) {
		tmp = y * (1.0 - (t / z));
	} else if (z <= 1.02e+76) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = x + (y * (t / a))
    if (z <= (-3.1d+76)) then
        tmp = x + y
    else if (z <= (-2.55d-39)) then
        tmp = t_1
    else if (z <= (-1.46d-94)) then
        tmp = y * (1.0d0 - (t / z))
    else if (z <= 1.02d+76) then
        tmp = t_1
    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 t_1 = x + (y * (t / a));
	double tmp;
	if (z <= -3.1e+76) {
		tmp = x + y;
	} else if (z <= -2.55e-39) {
		tmp = t_1;
	} else if (z <= -1.46e-94) {
		tmp = y * (1.0 - (t / z));
	} else if (z <= 1.02e+76) {
		tmp = t_1;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (y * (t / a))
	tmp = 0
	if z <= -3.1e+76:
		tmp = x + y
	elif z <= -2.55e-39:
		tmp = t_1
	elif z <= -1.46e-94:
		tmp = y * (1.0 - (t / z))
	elif z <= 1.02e+76:
		tmp = t_1
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(y * Float64(t / a)))
	tmp = 0.0
	if (z <= -3.1e+76)
		tmp = Float64(x + y);
	elseif (z <= -2.55e-39)
		tmp = t_1;
	elseif (z <= -1.46e-94)
		tmp = Float64(y * Float64(1.0 - Float64(t / z)));
	elseif (z <= 1.02e+76)
		tmp = t_1;
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (y * (t / a));
	tmp = 0.0;
	if (z <= -3.1e+76)
		tmp = x + y;
	elseif (z <= -2.55e-39)
		tmp = t_1;
	elseif (z <= -1.46e-94)
		tmp = y * (1.0 - (t / z));
	elseif (z <= 1.02e+76)
		tmp = t_1;
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.1e+76], N[(x + y), $MachinePrecision], If[LessEqual[z, -2.55e-39], t$95$1, If[LessEqual[z, -1.46e-94], N[(y * N[(1.0 - N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.02e+76], t$95$1, N[(x + y), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.10000000000000011e76 or 1.02000000000000007e76 < z

   1. Initial program 67.1%

      \[x + \frac{y \cdot \left(z - t\right)}{z - a} \]
   2. Step-by-step derivation

      1. associate-*l/ 90.7%

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

   3. Simplified 90.7%

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

   4. Taylor expanded in z around inf 84.7%

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

   if -3.10000000000000011e76 < z < -2.54999999999999994e-39 or -1.4599999999999999e-94 < z < 1.02000000000000007e76

   1. Initial program 93.4%

      \[x + \frac{y \cdot \left(z - t\right)}{z - a} \]
   2. Step-by-step derivation

      1. associate-*l/ 96.0%

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

   3. Simplified 96.0%

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

   4. Taylor expanded in z around 0 82.6%

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

      1. associate-/l* 83.8%

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

      2. associate-/r/ 85.8%

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

   6. Simplified 85.8%

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

   if -2.54999999999999994e-39 < z < -1.4599999999999999e-94

   1. Initial program 99.8%

      \[x + \frac{y \cdot \left(z - t\right)}{z - a} \]
   2. Step-by-step derivation

      1. associate-*l/ 92.8%

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

   3. Simplified 92.8%

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

   4. Taylor expanded in a around 0 66.1%

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

   5. Taylor expanded in y around inf 52.4%

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

4. Final simplification 83.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.1 \cdot 10^{+76}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq -2.55 \cdot 10^{-39}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{elif}\;z \leq -1.46 \cdot 10^{-94}:\\ \;\;\;\;y \cdot \left(1 - \frac{t}{z}\right)\\ \mathbf{elif}\;z \leq 1.02 \cdot 10^{+76}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 9: 60.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.8 \cdot 10^{-60}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq -4.4 \cdot 10^{-91}:\\ \;\;\;\;z \cdot \frac{-y}{a}\\ \mathbf{elif}\;z \leq -3.3 \cdot 10^{-140}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{-308}:\\ \;\;\;\;y \cdot \frac{t}{a}\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{+71}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -2.8e-60)
   (+ x y)
   (if (<= z -4.4e-91)
     (* z (/ (- y) a))
     (if (<= z -3.3e-140)
       x
       (if (<= z 1.7e-308) (* y (/ t a)) (if (<= z 9.5e+71) x (+ x y)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.8e-60) {
		tmp = x + y;
	} else if (z <= -4.4e-91) {
		tmp = z * (-y / a);
	} else if (z <= -3.3e-140) {
		tmp = x;
	} else if (z <= 1.7e-308) {
		tmp = y * (t / a);
	} else if (z <= 9.5e+71) {
		tmp = x;
	} 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 <= (-2.8d-60)) then
        tmp = x + y
    else if (z <= (-4.4d-91)) then
        tmp = z * (-y / a)
    else if (z <= (-3.3d-140)) then
        tmp = x
    else if (z <= 1.7d-308) then
        tmp = y * (t / a)
    else if (z <= 9.5d+71) then
        tmp = x
    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 <= -2.8e-60) {
		tmp = x + y;
	} else if (z <= -4.4e-91) {
		tmp = z * (-y / a);
	} else if (z <= -3.3e-140) {
		tmp = x;
	} else if (z <= 1.7e-308) {
		tmp = y * (t / a);
	} else if (z <= 9.5e+71) {
		tmp = x;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -2.8e-60:
		tmp = x + y
	elif z <= -4.4e-91:
		tmp = z * (-y / a)
	elif z <= -3.3e-140:
		tmp = x
	elif z <= 1.7e-308:
		tmp = y * (t / a)
	elif z <= 9.5e+71:
		tmp = x
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -2.8e-60)
		tmp = Float64(x + y);
	elseif (z <= -4.4e-91)
		tmp = Float64(z * Float64(Float64(-y) / a));
	elseif (z <= -3.3e-140)
		tmp = x;
	elseif (z <= 1.7e-308)
		tmp = Float64(y * Float64(t / a));
	elseif (z <= 9.5e+71)
		tmp = x;
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -2.8e-60)
		tmp = x + y;
	elseif (z <= -4.4e-91)
		tmp = z * (-y / a);
	elseif (z <= -3.3e-140)
		tmp = x;
	elseif (z <= 1.7e-308)
		tmp = y * (t / a);
	elseif (z <= 9.5e+71)
		tmp = x;
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -2.8e-60], N[(x + y), $MachinePrecision], If[LessEqual[z, -4.4e-91], N[(z * N[((-y) / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -3.3e-140], x, If[LessEqual[z, 1.7e-308], N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 9.5e+71], x, N[(x + y), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2.8000000000000002e-60 or 9.50000000000000015e71 < z

   1. Initial program 72.7%

      \[x + \frac{y \cdot \left(z - t\right)}{z - a} \]
   2. Step-by-step derivation

      1. associate-*l/ 92.6%

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

   3. Simplified 92.6%

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

   4. Taylor expanded in z around inf 75.7%

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

   if -2.8000000000000002e-60 < z < -4.4000000000000002e-91

   1. Initial program 99.8%

      \[x + \frac{y \cdot \left(z - t\right)}{z - a} \]
   2. Step-by-step derivation

      1. associate-*l/ 99.5%

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

   3. Simplified 99.5%

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

      1. associate-/r/ 100.0%

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

   5. Applied egg-rr 100.0%

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

   6. Taylor expanded in t around 0 60.9%

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

   7. Taylor expanded in z around 0 55.8%

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

      1. mul-1-neg 55.8%

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

      2. unsub-neg 55.8%

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

      3. associate-/l* 55.9%

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

      4. associate-/r/ 74.0%

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

   9. Simplified 74.0%

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

   10. Taylor expanded in x around 0 36.1%

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

       1. *-commutative 36.1%

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

       2. associate-*r/ 54.3%

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

       3. mul-1-neg 54.3%

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

       4. distribute-rgt-neg-in 54.3%

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

       5. distribute-neg-frac 54.3%

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

   12. Simplified 54.3%

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

   if -4.4000000000000002e-91 < z < -3.29999999999999987e-140 or 1.7000000000000002e-308 < z < 9.50000000000000015e71

   1. Initial program 95.9%

      \[x + \frac{y \cdot \left(z - t\right)}{z - a} \]
   2. Step-by-step derivation

      1. associate-*l/ 94.2%

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

   3. Simplified 94.2%

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

   4. Taylor expanded in z around 0 84.6%

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

   5. Taylor expanded in x around inf 67.5%

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

   if -3.29999999999999987e-140 < z < 1.7000000000000002e-308

   1. Initial program 85.6%

      \[x + \frac{y \cdot \left(z - t\right)}{z - a} \]
   2. Step-by-step derivation

      1. associate-*l/ 95.6%

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

   3. Simplified 95.6%

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

   4. Taylor expanded in z around 0 85.6%

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

      1. div-inv 85.5%

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

      2. add-sqr-sqrt 51.0%

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

      3. sqrt-unprod 66.6%

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

      4. sqr-neg 66.6%

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

      5. sqrt-unprod 15.6%

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

      6. add-sqr-sqrt 35.1%

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

      7. distribute-rgt-neg-in 35.1%

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

      8. cancel-sign-sub-inv 35.1%

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

      9. associate-*l* 35.3%

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

      10. div-inv 35.3%

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

   6. Applied egg-rr 35.3%

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

   7. Taylor expanded in x around 0 1.7%

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

      1. mul-1-neg 1.7%

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

      2. *-commutative 1.7%

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

      3. associate-*l/ 1.8%

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

      4. distribute-rgt-neg-out 1.8%

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

      5. *-commutative 1.8%

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

   9. Simplified 1.8%

      \[\leadsto \color{blue}{\left(-t\right) \cdot \frac{y}{a}} \]
   10. Step-by-step derivation

       1. expm1-log1p-u 1.7%

          \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\left(-t\right) \cdot \frac{y}{a}\right)\right)} \]

       2. expm1-udef 1.8%

          \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\left(-t\right) \cdot \frac{y}{a}\right)} - 1} \]

       3. associate-*r/ 1.7%

          \[\leadsto e^{\mathsf{log1p}\left(\color{blue}{\frac{\left(-t\right) \cdot y}{a}}\right)} - 1 \]

       4. associate-/l* 1.8%

          \[\leadsto e^{\mathsf{log1p}\left(\color{blue}{\frac{-t}{\frac{a}{y}}}\right)} - 1 \]

       5. add-sqr-sqrt 0.5%

          \[\leadsto e^{\mathsf{log1p}\left(\frac{\color{blue}{\sqrt{-t} \cdot \sqrt{-t}}}{\frac{a}{y}}\right)} - 1 \]

       6. sqrt-unprod 16.7%

          \[\leadsto e^{\mathsf{log1p}\left(\frac{\color{blue}{\sqrt{\left(-t\right) \cdot \left(-t\right)}}}{\frac{a}{y}}\right)} - 1 \]

       7. sqr-neg 16.7%

          \[\leadsto e^{\mathsf{log1p}\left(\frac{\sqrt{\color{blue}{t \cdot t}}}{\frac{a}{y}}\right)} - 1 \]

       8. sqrt-unprod 22.4%

          \[\leadsto e^{\mathsf{log1p}\left(\frac{\color{blue}{\sqrt{t} \cdot \sqrt{t}}}{\frac{a}{y}}\right)} - 1 \]

       9. add-sqr-sqrt 33.6%

          \[\leadsto e^{\mathsf{log1p}\left(\frac{\color{blue}{t}}{\frac{a}{y}}\right)} - 1 \]

   11. Applied egg-rr 33.6%

       \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\frac{t}{\frac{a}{y}}\right)} - 1} \]
   12. Step-by-step derivation

       1. expm1-def 37.3%

          \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{t}{\frac{a}{y}}\right)\right)} \]

       2. expm1-log1p 58.4%

          \[\leadsto \color{blue}{\frac{t}{\frac{a}{y}}} \]

       3. associate-/r/ 65.6%

          \[\leadsto \color{blue}{\frac{t}{a} \cdot y} \]

   13. Simplified 65.6%

       \[\leadsto \color{blue}{\frac{t}{a} \cdot y} \]
3. Recombined 4 regimes into one program.

4. Final simplification 70.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.8 \cdot 10^{-60}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq -4.4 \cdot 10^{-91}:\\ \;\;\;\;z \cdot \frac{-y}{a}\\ \mathbf{elif}\;z \leq -3.3 \cdot 10^{-140}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{-308}:\\ \;\;\;\;y \cdot \frac{t}{a}\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{+71}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 10: 75.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.7 \cdot 10^{+170}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq -3.2 \cdot 10^{-95}:\\ \;\;\;\;x - y \cdot \frac{t}{z}\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{+74}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.7e+170)
   (+ x y)
   (if (<= z -3.2e-95)
     (- x (* y (/ t z)))
     (if (<= z 4.5e+74) (+ x (* y (/ t a))) (+ x y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.7e+170) {
		tmp = x + y;
	} else if (z <= -3.2e-95) {
		tmp = x - (y * (t / z));
	} else if (z <= 4.5e+74) {
		tmp = x + (y * (t / a));
	} 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 <= (-1.7d+170)) then
        tmp = x + y
    else if (z <= (-3.2d-95)) then
        tmp = x - (y * (t / z))
    else if (z <= 4.5d+74) then
        tmp = x + (y * (t / a))
    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 <= -1.7e+170) {
		tmp = x + y;
	} else if (z <= -3.2e-95) {
		tmp = x - (y * (t / z));
	} else if (z <= 4.5e+74) {
		tmp = x + (y * (t / a));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.7e+170:
		tmp = x + y
	elif z <= -3.2e-95:
		tmp = x - (y * (t / z))
	elif z <= 4.5e+74:
		tmp = x + (y * (t / a))
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.7e+170)
		tmp = Float64(x + y);
	elseif (z <= -3.2e-95)
		tmp = Float64(x - Float64(y * Float64(t / z)));
	elseif (z <= 4.5e+74)
		tmp = Float64(x + Float64(y * Float64(t / a)));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.7e+170)
		tmp = x + y;
	elseif (z <= -3.2e-95)
		tmp = x - (y * (t / z));
	elseif (z <= 4.5e+74)
		tmp = x + (y * (t / a));
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.7e+170], N[(x + y), $MachinePrecision], If[LessEqual[z, -3.2e-95], N[(x - N[(y * N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.5e+74], N[(x + N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.7000000000000001e170 or 4.5e74 < z

   1. Initial program 62.5%

      \[x + \frac{y \cdot \left(z - t\right)}{z - a} \]
   2. Step-by-step derivation

      1. associate-*l/ 88.7%

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

   3. Simplified 88.7%

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

   4. Taylor expanded in z around inf 90.1%

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

   if -1.7000000000000001e170 < z < -3.1999999999999997e-95

   1. Initial program 93.1%

      \[x + \frac{y \cdot \left(z - t\right)}{z - a} \]
   2. Step-by-step derivation

      1. associate-*l/ 98.1%

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

   3. Simplified 98.1%

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

      1. associate-/r/ 98.1%

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

   5. Applied egg-rr 98.1%

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

   6. Taylor expanded in t around inf 75.8%

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

      1. associate-*r/ 75.8%

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

      2. neg-mul-1 75.8%

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

   8. Simplified 75.8%

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

      1. frac-2neg 75.8%

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

      2. distribute-frac-neg 75.8%

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

      3. distribute-neg-frac 75.8%

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

      4. remove-double-neg 75.8%

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

      5. *-un-lft-identity 75.8%

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

      6. *-un-lft-identity 75.8%

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

      7. add-sqr-sqrt 16.7%

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

      8. sqrt-unprod 42.2%

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

      9. sqr-neg 42.2%

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

      10. sqrt-unprod 25.3%

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

      11. add-sqr-sqrt 40.3%

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

      12. sub-neg 40.3%

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

      13. associate-/r/ 40.3%

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

      14. associate-*l/ 38.5%

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

      15. add-sqr-sqrt 25.4%

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

      16. sqrt-unprod 40.4%

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

      17. sqr-neg 40.4%

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

   10. Applied egg-rr 72.5%

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

       1. associate-*r/ 75.8%

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

   12. Simplified 75.8%

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

   13. Taylor expanded in z around inf 63.5%

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

   if -3.1999999999999997e-95 < z < 4.5e74

   1. Initial program 93.7%

      \[x + \frac{y \cdot \left(z - t\right)}{z - a} \]
   2. Step-by-step derivation

      1. associate-*l/ 95.2%

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

   3. Simplified 95.2%

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

   4. Taylor expanded in z around 0 85.6%

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

      1. associate-/l* 87.1%

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

      2. associate-/r/ 89.4%

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

   6. Simplified 89.4%

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

4. Final simplification 84.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.7 \cdot 10^{+170}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq -3.2 \cdot 10^{-95}:\\ \;\;\;\;x - y \cdot \frac{t}{z}\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{+74}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 11: 86.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.75 \cdot 10^{+83}:\\ \;\;\;\;x + y \cdot \left(1 - \frac{t}{z}\right)\\ \mathbf{elif}\;z \leq 5.3 \cdot 10^{+76}:\\ \;\;\;\;x - y \cdot \frac{t}{z - a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{z - a}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -2.75e+83)
   (+ x (* y (- 1.0 (/ t z))))
   (if (<= z 5.3e+76) (- x (* y (/ t (- z a)))) (+ x (/ y (/ (- z a) z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.75e+83) {
		tmp = x + (y * (1.0 - (t / z)));
	} else if (z <= 5.3e+76) {
		tmp = x - (y * (t / (z - a)));
	} else {
		tmp = x + (y / ((z - 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 (z <= (-2.75d+83)) then
        tmp = x + (y * (1.0d0 - (t / z)))
    else if (z <= 5.3d+76) then
        tmp = x - (y * (t / (z - a)))
    else
        tmp = x + (y / ((z - 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 (z <= -2.75e+83) {
		tmp = x + (y * (1.0 - (t / z)));
	} else if (z <= 5.3e+76) {
		tmp = x - (y * (t / (z - a)));
	} else {
		tmp = x + (y / ((z - a) / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -2.75e+83:
		tmp = x + (y * (1.0 - (t / z)))
	elif z <= 5.3e+76:
		tmp = x - (y * (t / (z - a)))
	else:
		tmp = x + (y / ((z - a) / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -2.75e+83)
		tmp = Float64(x + Float64(y * Float64(1.0 - Float64(t / z))));
	elseif (z <= 5.3e+76)
		tmp = Float64(x - Float64(y * Float64(t / Float64(z - a))));
	else
		tmp = Float64(x + Float64(y / Float64(Float64(z - a) / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -2.75e+83)
		tmp = x + (y * (1.0 - (t / z)));
	elseif (z <= 5.3e+76)
		tmp = x - (y * (t / (z - a)));
	else
		tmp = x + (y / ((z - a) / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -2.75e+83], N[(x + N[(y * N[(1.0 - N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.3e+76], N[(x - N[(y * N[(t / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y / N[(N[(z - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.7499999999999998e83

   1. Initial program 66.8%

      \[x + \frac{y \cdot \left(z - t\right)}{z - a} \]
   2. Step-by-step derivation

      1. associate-*l/ 90.5%

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

   3. Simplified 90.5%

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

   4. Taylor expanded in a around 0 61.8%

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

   5. Taylor expanded in y around 0 90.2%

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

   if -2.7499999999999998e83 < z < 5.30000000000000015e76

   1. Initial program 94.0%

      \[x + \frac{y \cdot \left(z - t\right)}{z - a} \]
   2. Step-by-step derivation

      1. associate-*l/ 95.8%

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

   3. Simplified 95.8%

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

      1. associate-/r/ 98.5%

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

   5. Applied egg-rr 98.5%

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

   6. Taylor expanded in t around inf 91.3%

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

      1. associate-*r/ 91.3%

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

      2. neg-mul-1 91.3%

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

   8. Simplified 91.3%

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

      1. frac-2neg 91.3%

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

      2. distribute-frac-neg 91.3%

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

      3. distribute-neg-frac 91.3%

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

      4. remove-double-neg 91.3%

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

      5. *-un-lft-identity 91.3%

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

      6. *-un-lft-identity 91.3%

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

      7. add-sqr-sqrt 47.4%

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

      8. sqrt-unprod 65.4%

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

      9. sqr-neg 65.4%

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

      10. sqrt-unprod 24.4%

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

      11. add-sqr-sqrt 55.2%

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

      12. sub-neg 55.2%

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

      13. associate-/r/ 54.4%

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

      14. associate-*l/ 54.6%

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

      15. add-sqr-sqrt 24.4%

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

      16. sqrt-unprod 64.8%

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

      17. sqr-neg 64.8%

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

   10. Applied egg-rr 87.4%

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

       1. associate-*r/ 90.9%

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

   12. Simplified 90.9%

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

   if 5.30000000000000015e76 < z

   1. Initial program 66.1%

      \[x + \frac{y \cdot \left(z - t\right)}{z - a} \]
   2. Step-by-step derivation

      1. associate-*l/ 90.5%

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

   3. Simplified 90.5%

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

      1. associate-/r/ 100.0%

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

   5. Applied egg-rr 100.0%

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

   6. Taylor expanded in t around 0 94.0%

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

4. Final simplification 91.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.75 \cdot 10^{+83}:\\ \;\;\;\;x + y \cdot \left(1 - \frac{t}{z}\right)\\ \mathbf{elif}\;z \leq 5.3 \cdot 10^{+76}:\\ \;\;\;\;x - y \cdot \frac{t}{z - a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{z - a}{z}}\\ \end{array} \]

Alternative 12: 86.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.32 \cdot 10^{+86}:\\ \;\;\;\;x + y \cdot \left(1 - \frac{t}{z}\right)\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{+73}:\\ \;\;\;\;x + \frac{y}{\frac{a - z}{t}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{z - a}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.32e+86)
   (+ x (* y (- 1.0 (/ t z))))
   (if (<= z 4.5e+73) (+ x (/ y (/ (- a z) t))) (+ x (/ y (/ (- z a) z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.32e+86) {
		tmp = x + (y * (1.0 - (t / z)));
	} else if (z <= 4.5e+73) {
		tmp = x + (y / ((a - z) / t));
	} else {
		tmp = x + (y / ((z - 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 (z <= (-1.32d+86)) then
        tmp = x + (y * (1.0d0 - (t / z)))
    else if (z <= 4.5d+73) then
        tmp = x + (y / ((a - z) / t))
    else
        tmp = x + (y / ((z - 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 (z <= -1.32e+86) {
		tmp = x + (y * (1.0 - (t / z)));
	} else if (z <= 4.5e+73) {
		tmp = x + (y / ((a - z) / t));
	} else {
		tmp = x + (y / ((z - a) / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.32e+86:
		tmp = x + (y * (1.0 - (t / z)))
	elif z <= 4.5e+73:
		tmp = x + (y / ((a - z) / t))
	else:
		tmp = x + (y / ((z - a) / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.32e+86)
		tmp = Float64(x + Float64(y * Float64(1.0 - Float64(t / z))));
	elseif (z <= 4.5e+73)
		tmp = Float64(x + Float64(y / Float64(Float64(a - z) / t)));
	else
		tmp = Float64(x + Float64(y / Float64(Float64(z - a) / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.32e+86)
		tmp = x + (y * (1.0 - (t / z)));
	elseif (z <= 4.5e+73)
		tmp = x + (y / ((a - z) / t));
	else
		tmp = x + (y / ((z - a) / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.32e+86], N[(x + N[(y * N[(1.0 - N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.5e+73], N[(x + N[(y / N[(N[(a - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y / N[(N[(z - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.32e86

   1. Initial program 66.8%

      \[x + \frac{y \cdot \left(z - t\right)}{z - a} \]
   2. Step-by-step derivation

      1. associate-*l/ 90.5%

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

   3. Simplified 90.5%

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

   4. Taylor expanded in a around 0 61.8%

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

   5. Taylor expanded in y around 0 90.2%

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

   if -1.32e86 < z < 4.49999999999999985e73

   1. Initial program 94.0%

      \[x + \frac{y \cdot \left(z - t\right)}{z - a} \]
   2. Step-by-step derivation

      1. associate-*l/ 95.8%

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

   3. Simplified 95.8%

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

      1. associate-/r/ 98.5%

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

   5. Applied egg-rr 98.5%

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

   6. Taylor expanded in t around inf 91.3%

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

      1. associate-*r/ 91.3%

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

      2. neg-mul-1 91.3%

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

   8. Simplified 91.3%

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

   if 4.49999999999999985e73 < z

   1. Initial program 66.1%

      \[x + \frac{y \cdot \left(z - t\right)}{z - a} \]
   2. Step-by-step derivation

      1. associate-*l/ 90.5%

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

   3. Simplified 90.5%

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

      1. associate-/r/ 100.0%

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

   5. Applied egg-rr 100.0%

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

   6. Taylor expanded in t around 0 94.0%

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

4. Final simplification 91.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.32 \cdot 10^{+86}:\\ \;\;\;\;x + y \cdot \left(1 - \frac{t}{z}\right)\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{+73}:\\ \;\;\;\;x + \frac{y}{\frac{a - z}{t}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{z - a}{z}}\\ \end{array} \]

Alternative 13: 95.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq 2 \cdot 10^{+218}:\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y}{z - a}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(1 - \frac{t}{z}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z 2e+218)
   (+ x (* (- z t) (/ y (- z a))))
   (+ x (* y (- 1.0 (/ t z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= 2e+218) {
		tmp = x + ((z - t) * (y / (z - a)));
	} else {
		tmp = x + (y * (1.0 - (t / 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 (z <= 2d+218) then
        tmp = x + ((z - t) * (y / (z - a)))
    else
        tmp = x + (y * (1.0d0 - (t / 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 (z <= 2e+218) {
		tmp = x + ((z - t) * (y / (z - a)));
	} else {
		tmp = x + (y * (1.0 - (t / z)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= 2e+218:
		tmp = x + ((z - t) * (y / (z - a)))
	else:
		tmp = x + (y * (1.0 - (t / z)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= 2e+218)
		tmp = Float64(x + Float64(Float64(z - t) * Float64(y / Float64(z - a))));
	else
		tmp = Float64(x + Float64(y * Float64(1.0 - Float64(t / z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= 2e+218)
		tmp = x + ((z - t) * (y / (z - a)));
	else
		tmp = x + (y * (1.0 - (t / z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, 2e+218], N[(x + N[(N[(z - t), $MachinePrecision] * N[(y / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(1.0 - N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 2.00000000000000017e218

   1. Initial program 87.1%

      \[x + \frac{y \cdot \left(z - t\right)}{z - a} \]
   2. Step-by-step derivation

      1. associate-*l/ 95.0%

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

   3. Simplified 95.0%

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

   if 2.00000000000000017e218 < z

   1. Initial program 56.1%

      \[x + \frac{y \cdot \left(z - t\right)}{z - a} \]
   2. Step-by-step derivation

      1. associate-*l/ 84.2%

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

   3. Simplified 84.2%

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

   4. Taylor expanded in a around 0 56.1%

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

   5. Taylor expanded in y around 0 100.0%

      \[\leadsto \color{blue}{x + y \cdot \left(1 - \frac{t}{z}\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 95.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 2 \cdot 10^{+218}:\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y}{z - a}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(1 - \frac{t}{z}\right)\\ \end{array} \]

Alternative 14: 62.3% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.65 \cdot 10^{+81} \lor \neg \left(z \leq 1.5 \cdot 10^{+71}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.65e+81) (not (<= z 1.5e+71))) (+ x y) x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.65e+81) || !(z <= 1.5e+71)) {
		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 ((z <= (-1.65d+81)) .or. (.not. (z <= 1.5d+71))) 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 ((z <= -1.65e+81) || !(z <= 1.5e+71)) {
		tmp = x + y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.65e+81) or not (z <= 1.5e+71):
		tmp = x + y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.65e+81) || !(z <= 1.5e+71))
		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 ((z <= -1.65e+81) || ~((z <= 1.5e+71)))
		tmp = x + y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.65e+81], N[Not[LessEqual[z, 1.5e+71]], $MachinePrecision]], N[(x + y), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -1.65e81 or 1.50000000000000006e71 < z

   1. Initial program 66.4%

      \[x + \frac{y \cdot \left(z - t\right)}{z - a} \]
   2. Step-by-step derivation

      1. associate-*l/ 90.5%

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

   3. Simplified 90.5%

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

   4. Taylor expanded in z around inf 85.4%

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

   if -1.65e81 < z < 1.50000000000000006e71

   1. Initial program 94.0%

      \[x + \frac{y \cdot \left(z - t\right)}{z - a} \]
   2. Step-by-step derivation

      1. associate-*l/ 95.8%

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

   3. Simplified 95.8%

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

   4. Taylor expanded in z around 0 76.9%

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

   5. Taylor expanded in x around inf 55.9%

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

4. Final simplification 66.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.65 \cdot 10^{+81} \lor \neg \left(z \leq 1.5 \cdot 10^{+71}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 15: 51.5% 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 83.7%

   \[x + \frac{y \cdot \left(z - t\right)}{z - a} \]
2. Step-by-step derivation

   1. associate-*l/ 93.8%

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

3. Simplified 93.8%

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

4. Taylor expanded in z around 0 62.6%

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

5. Taylor expanded in x around inf 52.4%

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

6. Final simplification 52.4%

   \[\leadsto x \]

Developer target: 98.4% 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 2023301 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTicks from plot-0.2.3.4, A"
  :precision binary64

  :herbie-target
  (+ x (/ y (/ (- z a) (- z t))))

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