Graphics.Rendering.Chart.Axis.Types:linMap from Chart-1.5.3

Percentage Accurate: 68.0% → 89.2%

Time: 21.3s

Alternatives: 21

Speedup: 0.9×

Specification

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 68.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 89.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.1 \cdot 10^{+212} \lor \neg \left(t \leq 5.2 \cdot 10^{+124}\right):\\ \;\;\;\;y + \left(y - x\right) \cdot \frac{a - z}{t}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{x - y}{\frac{a - t}{z - t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -2.1e+212) (not (<= t 5.2e+124)))
   (+ y (* (- y x) (/ (- a z) t)))
   (- x (/ (- x y) (/ (- a t) (- z t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -2.1e+212) || !(t <= 5.2e+124)) {
		tmp = y + ((y - x) * ((a - z) / t));
	} else {
		tmp = x - ((x - y) / ((a - t) / (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) :: tmp
    if ((t <= (-2.1d+212)) .or. (.not. (t <= 5.2d+124))) then
        tmp = y + ((y - x) * ((a - z) / t))
    else
        tmp = x - ((x - y) / ((a - t) / (z - t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -2.1e+212) || !(t <= 5.2e+124)) {
		tmp = y + ((y - x) * ((a - z) / t));
	} else {
		tmp = x - ((x - y) / ((a - t) / (z - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -2.1e+212) or not (t <= 5.2e+124):
		tmp = y + ((y - x) * ((a - z) / t))
	else:
		tmp = x - ((x - y) / ((a - t) / (z - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -2.1e+212) || !(t <= 5.2e+124))
		tmp = Float64(y + Float64(Float64(y - x) * Float64(Float64(a - z) / t)));
	else
		tmp = Float64(x - Float64(Float64(x - y) / Float64(Float64(a - t) / Float64(z - t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -2.1e+212) || ~((t <= 5.2e+124)))
		tmp = y + ((y - x) * ((a - z) / t));
	else
		tmp = x - ((x - y) / ((a - t) / (z - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -2.1e+212], N[Not[LessEqual[t, 5.2e+124]], $MachinePrecision]], N[(y + N[(N[(y - x), $MachinePrecision] * N[(N[(a - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(N[(x - y), $MachinePrecision] / N[(N[(a - t), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -2.1e212 or 5.2000000000000001e124 < t

   1. Initial program 31.5%

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

      1. associate-*l/ 57.1%

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

   3. Simplified 57.1%

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

      1. associate-/r/ 66.6%

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

      2. add-cube-cbrt 65.3%

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

      3. associate-/l* 65.4%

         \[\leadsto x + \color{blue}{\frac{\sqrt[3]{y - x} \cdot \sqrt[3]{y - x}}{\frac{\frac{a - t}{z - t}}{\sqrt[3]{y - x}}}} \]

      4. pow2 65.4%

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

   6. Applied egg-rr 65.4%

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

   7. Taylor expanded in t around inf 67.0%

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

      1. associate--l+ 67.0%

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

      2. associate-*r/ 67.0%

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

      3. associate-*r/ 67.0%

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

      4. div-sub 67.0%

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

      5. distribute-lft-out-- 67.0%

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

      6. distribute-rgt-out-- 67.0%

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

      7. associate-*r/ 67.0%

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

      8. distribute-rgt-out-- 67.0%

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

      9. mul-1-neg 67.0%

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

      10. distribute-rgt-out-- 67.0%

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

      11. unsub-neg 67.0%

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

      12. associate-*r/ 94.0%

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

   9. Simplified 94.0%

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

   if -2.1e212 < t < 5.2000000000000001e124

   1. Initial program 82.2%

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

      1. associate-*l/ 92.2%

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

   3. Simplified 92.2%

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

      1. associate-/r/ 95.6%

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

   6. Applied egg-rr 95.6%

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

4. Final simplification 95.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.1 \cdot 10^{+212} \lor \neg \left(t \leq 5.2 \cdot 10^{+124}\right):\\ \;\;\;\;y + \left(y - x\right) \cdot \frac{a - z}{t}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{x - y}{\frac{a - t}{z - t}}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 47.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.8 \cdot 10^{+190}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -2.6 \cdot 10^{+80}:\\ \;\;\;\;y - x \cdot \frac{a}{t}\\ \mathbf{elif}\;a \leq 4.8 \cdot 10^{+86}:\\ \;\;\;\;y \cdot \frac{t - z}{t}\\ \mathbf{elif}\;a \leq 3.25 \cdot 10^{+159}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.06 \cdot 10^{+183}:\\ \;\;\;\;y \cdot \frac{-t}{a - t}\\ \mathbf{elif}\;a \leq 3 \cdot 10^{+209}:\\ \;\;\;\;y \cdot \frac{z - t}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -1.8e+190)
   x
   (if (<= a -2.6e+80)
     (- y (* x (/ a t)))
     (if (<= a 4.8e+86)
       (* y (/ (- t z) t))
       (if (<= a 3.25e+159)
         x
         (if (<= a 1.06e+183)
           (* y (/ (- t) (- a t)))
           (if (<= a 3e+209) (* y (/ (- z t) a)) x)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.8e+190) {
		tmp = x;
	} else if (a <= -2.6e+80) {
		tmp = y - (x * (a / t));
	} else if (a <= 4.8e+86) {
		tmp = y * ((t - z) / t);
	} else if (a <= 3.25e+159) {
		tmp = x;
	} else if (a <= 1.06e+183) {
		tmp = y * (-t / (a - t));
	} else if (a <= 3e+209) {
		tmp = y * ((z - t) / a);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-1.8d+190)) then
        tmp = x
    else if (a <= (-2.6d+80)) then
        tmp = y - (x * (a / t))
    else if (a <= 4.8d+86) then
        tmp = y * ((t - z) / t)
    else if (a <= 3.25d+159) then
        tmp = x
    else if (a <= 1.06d+183) then
        tmp = y * (-t / (a - t))
    else if (a <= 3d+209) then
        tmp = y * ((z - t) / a)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.8e+190) {
		tmp = x;
	} else if (a <= -2.6e+80) {
		tmp = y - (x * (a / t));
	} else if (a <= 4.8e+86) {
		tmp = y * ((t - z) / t);
	} else if (a <= 3.25e+159) {
		tmp = x;
	} else if (a <= 1.06e+183) {
		tmp = y * (-t / (a - t));
	} else if (a <= 3e+209) {
		tmp = y * ((z - t) / a);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -1.8e+190:
		tmp = x
	elif a <= -2.6e+80:
		tmp = y - (x * (a / t))
	elif a <= 4.8e+86:
		tmp = y * ((t - z) / t)
	elif a <= 3.25e+159:
		tmp = x
	elif a <= 1.06e+183:
		tmp = y * (-t / (a - t))
	elif a <= 3e+209:
		tmp = y * ((z - t) / a)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -1.8e+190)
		tmp = x;
	elseif (a <= -2.6e+80)
		tmp = Float64(y - Float64(x * Float64(a / t)));
	elseif (a <= 4.8e+86)
		tmp = Float64(y * Float64(Float64(t - z) / t));
	elseif (a <= 3.25e+159)
		tmp = x;
	elseif (a <= 1.06e+183)
		tmp = Float64(y * Float64(Float64(-t) / Float64(a - t)));
	elseif (a <= 3e+209)
		tmp = Float64(y * Float64(Float64(z - t) / a));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -1.8e+190)
		tmp = x;
	elseif (a <= -2.6e+80)
		tmp = y - (x * (a / t));
	elseif (a <= 4.8e+86)
		tmp = y * ((t - z) / t);
	elseif (a <= 3.25e+159)
		tmp = x;
	elseif (a <= 1.06e+183)
		tmp = y * (-t / (a - t));
	elseif (a <= 3e+209)
		tmp = y * ((z - t) / a);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -1.8e+190], x, If[LessEqual[a, -2.6e+80], N[(y - N[(x * N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 4.8e+86], N[(y * N[(N[(t - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3.25e+159], x, If[LessEqual[a, 1.06e+183], N[(y * N[((-t) / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3e+209], N[(y * N[(N[(z - t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], x]]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -1.79999999999999989e190 or 4.8000000000000001e86 < a < 3.2500000000000001e159 or 2.99999999999999985e209 < a

   1. Initial program 74.5%

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

      1. associate-*l/ 87.0%

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

   3. Simplified 87.0%

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

   5. Taylor expanded in a around inf 55.3%

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

   if -1.79999999999999989e190 < a < -2.59999999999999982e80

   1. Initial program 68.6%

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

      1. associate-*l/ 78.2%

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

   3. Simplified 78.2%

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

   5. Taylor expanded in z around 0 39.7%

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

      1. associate-*r/ 39.7%

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

      2. mul-1-neg 39.7%

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

      3. distribute-lft-neg-out 39.7%

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

      4. associate-*r/ 46.1%

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

      5. *-commutative 46.1%

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

   7. Simplified 46.1%

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

   8. Taylor expanded in t around inf 28.4%

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

      1. associate-/l* 42.5%

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

   10. Simplified 42.5%

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

       1. associate-/r/ 42.5%

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

   12. Applied egg-rr 42.5%

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

   13. Taylor expanded in y around 0 35.5%

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

       1. mul-1-neg 35.5%

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

       2. *-commutative 35.5%

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

       3. associate-*r/ 42.9%

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

       4. distribute-rgt-neg-in 42.9%

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

       5. mul-1-neg 42.9%

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

       6. associate-*r/ 42.9%

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

       7. neg-mul-1 42.9%

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

   15. Simplified 42.9%

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

   if -2.59999999999999982e80 < a < 4.8000000000000001e86

   1. Initial program 67.7%

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

      1. associate-*l/ 81.3%

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

   3. Simplified 81.3%

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

   5. Taylor expanded in y around inf 65.6%

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

      1. div-sub 65.6%

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

   7. Simplified 65.6%

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

   8. Taylor expanded in a around 0 56.8%

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

      1. mul-1-neg 56.8%

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

   10. Simplified 56.8%

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

   if 3.2500000000000001e159 < a < 1.06e183

   1. Initial program 25.9%

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

      1. associate-*l/ 99.1%

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

   3. Simplified 99.1%

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

   5. Taylor expanded in y around inf 80.8%

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

      1. div-sub 80.8%

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

   7. Simplified 80.8%

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

   8. Taylor expanded in z around 0 61.2%

      \[\leadsto y \cdot \color{blue}{\left(-1 \cdot \frac{t}{a - t}\right)} \]
   9. Step-by-step derivation

      1. associate-*r/ 61.2%

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

      2. neg-mul-1 61.2%

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

   10. Simplified 61.2%

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

   if 1.06e183 < a < 2.99999999999999985e209

   1. Initial program 86.4%

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

      1. associate-*l/ 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around inf 59.8%

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

      1. div-sub 59.8%

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

   7. Simplified 59.8%

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

   8. Taylor expanded in a around inf 59.8%

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

4. Final simplification 55.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.8 \cdot 10^{+190}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -2.6 \cdot 10^{+80}:\\ \;\;\;\;y - x \cdot \frac{a}{t}\\ \mathbf{elif}\;a \leq 4.8 \cdot 10^{+86}:\\ \;\;\;\;y \cdot \frac{t - z}{t}\\ \mathbf{elif}\;a \leq 3.25 \cdot 10^{+159}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.06 \cdot 10^{+183}:\\ \;\;\;\;y \cdot \frac{-t}{a - t}\\ \mathbf{elif}\;a \leq 3 \cdot 10^{+209}:\\ \;\;\;\;y \cdot \frac{z - t}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 38.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y}{t - a}\\ \mathbf{if}\;t \leq -105:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -1.05 \cdot 10^{-274}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 1.55 \cdot 10^{-187}:\\ \;\;\;\;z \cdot \frac{y}{a}\\ \mathbf{elif}\;t \leq 1.95 \cdot 10^{-36}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 1.75 \cdot 10^{+80}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ y (- t a)))))
   (if (<= t -105.0)
     t_1
     (if (<= t -1.05e-274)
       x
       (if (<= t 1.55e-187)
         (* z (/ y a))
         (if (<= t 1.95e-36) x (if (<= t 1.75e+80) t_1 y)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (y / (t - a));
	double tmp;
	if (t <= -105.0) {
		tmp = t_1;
	} else if (t <= -1.05e-274) {
		tmp = x;
	} else if (t <= 1.55e-187) {
		tmp = z * (y / a);
	} else if (t <= 1.95e-36) {
		tmp = x;
	} else if (t <= 1.75e+80) {
		tmp = t_1;
	} else {
		tmp = 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 = t * (y / (t - a))
    if (t <= (-105.0d0)) then
        tmp = t_1
    else if (t <= (-1.05d-274)) then
        tmp = x
    else if (t <= 1.55d-187) then
        tmp = z * (y / a)
    else if (t <= 1.95d-36) then
        tmp = x
    else if (t <= 1.75d+80) then
        tmp = t_1
    else
        tmp = 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 = t * (y / (t - a));
	double tmp;
	if (t <= -105.0) {
		tmp = t_1;
	} else if (t <= -1.05e-274) {
		tmp = x;
	} else if (t <= 1.55e-187) {
		tmp = z * (y / a);
	} else if (t <= 1.95e-36) {
		tmp = x;
	} else if (t <= 1.75e+80) {
		tmp = t_1;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * (y / (t - a))
	tmp = 0
	if t <= -105.0:
		tmp = t_1
	elif t <= -1.05e-274:
		tmp = x
	elif t <= 1.55e-187:
		tmp = z * (y / a)
	elif t <= 1.95e-36:
		tmp = x
	elif t <= 1.75e+80:
		tmp = t_1
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(y / Float64(t - a)))
	tmp = 0.0
	if (t <= -105.0)
		tmp = t_1;
	elseif (t <= -1.05e-274)
		tmp = x;
	elseif (t <= 1.55e-187)
		tmp = Float64(z * Float64(y / a));
	elseif (t <= 1.95e-36)
		tmp = x;
	elseif (t <= 1.75e+80)
		tmp = t_1;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * (y / (t - a));
	tmp = 0.0;
	if (t <= -105.0)
		tmp = t_1;
	elseif (t <= -1.05e-274)
		tmp = x;
	elseif (t <= 1.55e-187)
		tmp = z * (y / a);
	elseif (t <= 1.95e-36)
		tmp = x;
	elseif (t <= 1.75e+80)
		tmp = t_1;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(y / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -105.0], t$95$1, If[LessEqual[t, -1.05e-274], x, If[LessEqual[t, 1.55e-187], N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.95e-36], x, If[LessEqual[t, 1.75e+80], t$95$1, y]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -105 or 1.95e-36 < t < 1.74999999999999997e80

   1. Initial program 58.6%

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

      1. associate-*l/ 83.8%

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

   3. Simplified 83.8%

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

   5. Taylor expanded in z around 0 39.7%

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

      1. associate-*r/ 39.7%

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

      2. mul-1-neg 39.7%

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

      3. distribute-lft-neg-out 39.7%

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

      4. associate-*r/ 54.1%

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

      5. *-commutative 54.1%

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

   7. Simplified 54.1%

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

   8. Taylor expanded in x around 0 35.7%

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

      1. mul-1-neg 35.7%

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

      2. associate-/l* 50.0%

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

      3. distribute-neg-frac 50.0%

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

   10. Simplified 50.0%

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

       1. frac-2neg 50.0%

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

       2. div-inv 49.8%

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

       3. remove-double-neg 49.8%

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

       4. distribute-neg-frac 49.8%

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

       5. sub-neg 49.8%

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

       6. distribute-neg-in 49.8%

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

       7. remove-double-neg 49.8%

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

   12. Applied egg-rr 49.8%

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

       1. associate-/r/ 49.9%

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

       2. associate-*l/ 50.0%

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

       3. *-lft-identity 50.0%

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

       4. +-commutative 50.0%

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

       5. unsub-neg 50.0%

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

   14. Simplified 50.0%

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

   if -105 < t < -1.04999999999999997e-274 or 1.5500000000000001e-187 < t < 1.95e-36

   1. Initial program 93.0%

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

      1. associate-*l/ 93.7%

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

   3. Simplified 93.7%

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

   5. Taylor expanded in a around inf 40.3%

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

   if -1.04999999999999997e-274 < t < 1.5500000000000001e-187

   1. Initial program 91.0%

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

      1. associate-*l/ 95.5%

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

   3. Simplified 95.5%

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

   5. Taylor expanded in y around inf 60.7%

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

      1. div-sub 60.7%

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

   7. Simplified 60.7%

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

   8. Taylor expanded in t around 0 56.1%

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

   9. Taylor expanded in y around 0 56.1%

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

       1. associate-*l/ 60.2%

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

   11. Simplified 60.2%

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

   if 1.74999999999999997e80 < t

   1. Initial program 39.1%

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

      1. associate-*l/ 58.9%

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

   3. Simplified 58.9%

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

   5. Taylor expanded in t around inf 49.2%

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

4. Final simplification 47.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -105:\\ \;\;\;\;t \cdot \frac{y}{t - a}\\ \mathbf{elif}\;t \leq -1.05 \cdot 10^{-274}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 1.55 \cdot 10^{-187}:\\ \;\;\;\;z \cdot \frac{y}{a}\\ \mathbf{elif}\;t \leq 1.95 \cdot 10^{-36}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 1.75 \cdot 10^{+80}:\\ \;\;\;\;t \cdot \frac{y}{t - a}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 36.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \frac{y}{a - t}\\ t_2 := t \cdot \frac{y}{t - a}\\ \mathbf{if}\;t \leq -7.2 \cdot 10^{+52}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -9.2 \cdot 10^{-69}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -6 \cdot 10^{-101}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -1.06 \cdot 10^{-272}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 7 \cdot 10^{-45}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* z (/ y (- a t)))) (t_2 (* t (/ y (- t a)))))
   (if (<= t -7.2e+52)
     t_2
     (if (<= t -9.2e-69)
       t_1
       (if (<= t -6e-101)
         y
         (if (<= t -1.06e-272) x (if (<= t 7e-45) t_1 t_2)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = z * (y / (a - t));
	double t_2 = t * (y / (t - a));
	double tmp;
	if (t <= -7.2e+52) {
		tmp = t_2;
	} else if (t <= -9.2e-69) {
		tmp = t_1;
	} else if (t <= -6e-101) {
		tmp = y;
	} else if (t <= -1.06e-272) {
		tmp = x;
	} else if (t <= 7e-45) {
		tmp = t_1;
	} 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 = z * (y / (a - t))
    t_2 = t * (y / (t - a))
    if (t <= (-7.2d+52)) then
        tmp = t_2
    else if (t <= (-9.2d-69)) then
        tmp = t_1
    else if (t <= (-6d-101)) then
        tmp = y
    else if (t <= (-1.06d-272)) then
        tmp = x
    else if (t <= 7d-45) then
        tmp = t_1
    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 = z * (y / (a - t));
	double t_2 = t * (y / (t - a));
	double tmp;
	if (t <= -7.2e+52) {
		tmp = t_2;
	} else if (t <= -9.2e-69) {
		tmp = t_1;
	} else if (t <= -6e-101) {
		tmp = y;
	} else if (t <= -1.06e-272) {
		tmp = x;
	} else if (t <= 7e-45) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = z * (y / (a - t))
	t_2 = t * (y / (t - a))
	tmp = 0
	if t <= -7.2e+52:
		tmp = t_2
	elif t <= -9.2e-69:
		tmp = t_1
	elif t <= -6e-101:
		tmp = y
	elif t <= -1.06e-272:
		tmp = x
	elif t <= 7e-45:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(z * Float64(y / Float64(a - t)))
	t_2 = Float64(t * Float64(y / Float64(t - a)))
	tmp = 0.0
	if (t <= -7.2e+52)
		tmp = t_2;
	elseif (t <= -9.2e-69)
		tmp = t_1;
	elseif (t <= -6e-101)
		tmp = y;
	elseif (t <= -1.06e-272)
		tmp = x;
	elseif (t <= 7e-45)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = z * (y / (a - t));
	t_2 = t * (y / (t - a));
	tmp = 0.0;
	if (t <= -7.2e+52)
		tmp = t_2;
	elseif (t <= -9.2e-69)
		tmp = t_1;
	elseif (t <= -6e-101)
		tmp = y;
	elseif (t <= -1.06e-272)
		tmp = x;
	elseif (t <= 7e-45)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(z * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(y / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -7.2e+52], t$95$2, If[LessEqual[t, -9.2e-69], t$95$1, If[LessEqual[t, -6e-101], y, If[LessEqual[t, -1.06e-272], x, If[LessEqual[t, 7e-45], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -7.2e52 or 7e-45 < t

   1. Initial program 51.6%

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

      1. associate-*l/ 73.9%

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

   3. Simplified 73.9%

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

   5. Taylor expanded in z around 0 35.2%

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

      1. associate-*r/ 35.2%

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

      2. mul-1-neg 35.2%

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

      3. distribute-lft-neg-out 35.2%

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

      4. associate-*r/ 51.1%

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

      5. *-commutative 51.1%

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

   7. Simplified 51.1%

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

   8. Taylor expanded in x around 0 33.9%

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

      1. mul-1-neg 33.9%

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

      2. associate-/l* 48.4%

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

      3. distribute-neg-frac 48.4%

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

   10. Simplified 48.4%

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

       1. frac-2neg 48.4%

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

       2. div-inv 48.3%

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

       3. remove-double-neg 48.3%

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

       4. distribute-neg-frac 48.3%

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

       5. sub-neg 48.3%

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

       6. distribute-neg-in 48.3%

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

       7. remove-double-neg 48.3%

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

   12. Applied egg-rr 48.3%

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

       1. associate-/r/ 48.8%

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

       2. associate-*l/ 48.9%

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

       3. *-lft-identity 48.9%

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

       4. +-commutative 48.9%

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

       5. unsub-neg 48.9%

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

   14. Simplified 48.9%

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

   if -7.2e52 < t < -9.2000000000000003e-69 or -1.05999999999999994e-272 < t < 7e-45

   1. Initial program 88.8%

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

      1. associate-*l/ 97.0%

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

   3. Simplified 97.0%

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

   5. Taylor expanded in z around -inf 64.3%

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

   6. Taylor expanded in y around inf 40.6%

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

      1. associate-/l* 47.0%

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

   8. Simplified 47.0%

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

      1. associate-/r/ 46.9%

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

   10. Applied egg-rr 46.9%

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

   if -9.2000000000000003e-69 < t < -6.0000000000000006e-101

   1. Initial program 75.6%

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

      1. associate-*l/ 75.6%

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

   3. Simplified 75.6%

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

   5. Taylor expanded in t around inf 51.4%

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

   if -6.0000000000000006e-101 < t < -1.05999999999999994e-272

   1. Initial program 97.3%

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

      1. associate-*l/ 92.4%

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

   3. Simplified 92.4%

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

   5. Taylor expanded in a around inf 48.7%

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

4. Final simplification 48.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7.2 \cdot 10^{+52}:\\ \;\;\;\;t \cdot \frac{y}{t - a}\\ \mathbf{elif}\;t \leq -9.2 \cdot 10^{-69}:\\ \;\;\;\;z \cdot \frac{y}{a - t}\\ \mathbf{elif}\;t \leq -6 \cdot 10^{-101}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -1.06 \cdot 10^{-272}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 7 \cdot 10^{-45}:\\ \;\;\;\;z \cdot \frac{y}{a - t}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y}{t - a}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 36.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \frac{y}{a - t}\\ t_2 := t \cdot \frac{y}{t - a}\\ \mathbf{if}\;t \leq -7.2 \cdot 10^{+52}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -7.5 \cdot 10^{-90}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -1.36 \cdot 10^{-139}:\\ \;\;\;\;y + \frac{y \cdot a}{t}\\ \mathbf{elif}\;t \leq -9 \cdot 10^{-275}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 6.5 \cdot 10^{-45}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* z (/ y (- a t)))) (t_2 (* t (/ y (- t a)))))
   (if (<= t -7.2e+52)
     t_2
     (if (<= t -7.5e-90)
       t_1
       (if (<= t -1.36e-139)
         (+ y (/ (* y a) t))
         (if (<= t -9e-275) x (if (<= t 6.5e-45) t_1 t_2)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = z * (y / (a - t));
	double t_2 = t * (y / (t - a));
	double tmp;
	if (t <= -7.2e+52) {
		tmp = t_2;
	} else if (t <= -7.5e-90) {
		tmp = t_1;
	} else if (t <= -1.36e-139) {
		tmp = y + ((y * a) / t);
	} else if (t <= -9e-275) {
		tmp = x;
	} else if (t <= 6.5e-45) {
		tmp = t_1;
	} 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 = z * (y / (a - t))
    t_2 = t * (y / (t - a))
    if (t <= (-7.2d+52)) then
        tmp = t_2
    else if (t <= (-7.5d-90)) then
        tmp = t_1
    else if (t <= (-1.36d-139)) then
        tmp = y + ((y * a) / t)
    else if (t <= (-9d-275)) then
        tmp = x
    else if (t <= 6.5d-45) then
        tmp = t_1
    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 = z * (y / (a - t));
	double t_2 = t * (y / (t - a));
	double tmp;
	if (t <= -7.2e+52) {
		tmp = t_2;
	} else if (t <= -7.5e-90) {
		tmp = t_1;
	} else if (t <= -1.36e-139) {
		tmp = y + ((y * a) / t);
	} else if (t <= -9e-275) {
		tmp = x;
	} else if (t <= 6.5e-45) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = z * (y / (a - t))
	t_2 = t * (y / (t - a))
	tmp = 0
	if t <= -7.2e+52:
		tmp = t_2
	elif t <= -7.5e-90:
		tmp = t_1
	elif t <= -1.36e-139:
		tmp = y + ((y * a) / t)
	elif t <= -9e-275:
		tmp = x
	elif t <= 6.5e-45:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(z * Float64(y / Float64(a - t)))
	t_2 = Float64(t * Float64(y / Float64(t - a)))
	tmp = 0.0
	if (t <= -7.2e+52)
		tmp = t_2;
	elseif (t <= -7.5e-90)
		tmp = t_1;
	elseif (t <= -1.36e-139)
		tmp = Float64(y + Float64(Float64(y * a) / t));
	elseif (t <= -9e-275)
		tmp = x;
	elseif (t <= 6.5e-45)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = z * (y / (a - t));
	t_2 = t * (y / (t - a));
	tmp = 0.0;
	if (t <= -7.2e+52)
		tmp = t_2;
	elseif (t <= -7.5e-90)
		tmp = t_1;
	elseif (t <= -1.36e-139)
		tmp = y + ((y * a) / t);
	elseif (t <= -9e-275)
		tmp = x;
	elseif (t <= 6.5e-45)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(z * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(y / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -7.2e+52], t$95$2, If[LessEqual[t, -7.5e-90], t$95$1, If[LessEqual[t, -1.36e-139], N[(y + N[(N[(y * a), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -9e-275], x, If[LessEqual[t, 6.5e-45], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -7.2e52 or 6.4999999999999995e-45 < t

   1. Initial program 51.6%

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

      1. associate-*l/ 73.9%

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

   3. Simplified 73.9%

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

   5. Taylor expanded in z around 0 35.2%

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

      1. associate-*r/ 35.2%

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

      2. mul-1-neg 35.2%

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

      3. distribute-lft-neg-out 35.2%

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

      4. associate-*r/ 51.1%

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

      5. *-commutative 51.1%

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

   7. Simplified 51.1%

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

   8. Taylor expanded in x around 0 33.9%

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

      1. mul-1-neg 33.9%

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

      2. associate-/l* 48.4%

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

      3. distribute-neg-frac 48.4%

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

   10. Simplified 48.4%

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

       1. frac-2neg 48.4%

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

       2. div-inv 48.3%

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

       3. remove-double-neg 48.3%

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

       4. distribute-neg-frac 48.3%

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

       5. sub-neg 48.3%

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

       6. distribute-neg-in 48.3%

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

       7. remove-double-neg 48.3%

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

   12. Applied egg-rr 48.3%

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

       1. associate-/r/ 48.8%

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

       2. associate-*l/ 48.9%

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

       3. *-lft-identity 48.9%

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

       4. +-commutative 48.9%

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

       5. unsub-neg 48.9%

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

   14. Simplified 48.9%

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

   if -7.2e52 < t < -7.4999999999999999e-90 or -8.99999999999999957e-275 < t < 6.4999999999999995e-45

   1. Initial program 88.9%

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

      1. associate-*l/ 97.0%

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

   3. Simplified 97.0%

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

   5. Taylor expanded in z around -inf 63.4%

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

   6. Taylor expanded in y around inf 40.1%

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

      1. associate-/l* 46.4%

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

   8. Simplified 46.4%

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

      1. associate-/r/ 46.3%

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

   10. Applied egg-rr 46.3%

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

   if -7.4999999999999999e-90 < t < -1.36000000000000003e-139

   1. Initial program 86.0%

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

      1. associate-*l/ 72.3%

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

   3. Simplified 72.3%

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

   5. Taylor expanded in z around 0 43.7%

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

      1. associate-*r/ 43.7%

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

      2. mul-1-neg 43.7%

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

      3. distribute-lft-neg-out 43.7%

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

      4. associate-*r/ 30.2%

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

      5. *-commutative 30.2%

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

   7. Simplified 30.2%

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

   8. Taylor expanded in t around inf 45.4%

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

      1. associate-/l* 31.9%

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

   10. Simplified 31.9%

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

   11. Taylor expanded in y around inf 45.5%

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

   if -1.36000000000000003e-139 < t < -8.99999999999999957e-275

   1. Initial program 97.0%

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

      1. associate-*l/ 94.3%

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

   3. Simplified 94.3%

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

   5. Taylor expanded in a around inf 51.3%

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

4. Final simplification 48.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7.2 \cdot 10^{+52}:\\ \;\;\;\;t \cdot \frac{y}{t - a}\\ \mathbf{elif}\;t \leq -7.5 \cdot 10^{-90}:\\ \;\;\;\;z \cdot \frac{y}{a - t}\\ \mathbf{elif}\;t \leq -1.36 \cdot 10^{-139}:\\ \;\;\;\;y + \frac{y \cdot a}{t}\\ \mathbf{elif}\;t \leq -9 \cdot 10^{-275}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 6.5 \cdot 10^{-45}:\\ \;\;\;\;z \cdot \frac{y}{a - t}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y}{t - a}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 47.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.02 \cdot 10^{+142}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 4.4 \cdot 10^{+86}:\\ \;\;\;\;y \cdot \frac{t - z}{t}\\ \mathbf{elif}\;a \leq 2.45 \cdot 10^{+154}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 4.6 \cdot 10^{+183}:\\ \;\;\;\;t \cdot \frac{y}{t - a}\\ \mathbf{elif}\;a \leq 10^{+208}:\\ \;\;\;\;y \cdot \frac{z - t}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -2.02e+142)
   x
   (if (<= a 4.4e+86)
     (* y (/ (- t z) t))
     (if (<= a 2.45e+154)
       x
       (if (<= a 4.6e+183)
         (* t (/ y (- t a)))
         (if (<= a 1e+208) (* y (/ (- z t) a)) x))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -2.02e+142) {
		tmp = x;
	} else if (a <= 4.4e+86) {
		tmp = y * ((t - z) / t);
	} else if (a <= 2.45e+154) {
		tmp = x;
	} else if (a <= 4.6e+183) {
		tmp = t * (y / (t - a));
	} else if (a <= 1e+208) {
		tmp = y * ((z - t) / a);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-2.02d+142)) then
        tmp = x
    else if (a <= 4.4d+86) then
        tmp = y * ((t - z) / t)
    else if (a <= 2.45d+154) then
        tmp = x
    else if (a <= 4.6d+183) then
        tmp = t * (y / (t - a))
    else if (a <= 1d+208) then
        tmp = y * ((z - t) / a)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -2.02e+142) {
		tmp = x;
	} else if (a <= 4.4e+86) {
		tmp = y * ((t - z) / t);
	} else if (a <= 2.45e+154) {
		tmp = x;
	} else if (a <= 4.6e+183) {
		tmp = t * (y / (t - a));
	} else if (a <= 1e+208) {
		tmp = y * ((z - t) / a);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -2.02e+142:
		tmp = x
	elif a <= 4.4e+86:
		tmp = y * ((t - z) / t)
	elif a <= 2.45e+154:
		tmp = x
	elif a <= 4.6e+183:
		tmp = t * (y / (t - a))
	elif a <= 1e+208:
		tmp = y * ((z - t) / a)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -2.02e+142)
		tmp = x;
	elseif (a <= 4.4e+86)
		tmp = Float64(y * Float64(Float64(t - z) / t));
	elseif (a <= 2.45e+154)
		tmp = x;
	elseif (a <= 4.6e+183)
		tmp = Float64(t * Float64(y / Float64(t - a)));
	elseif (a <= 1e+208)
		tmp = Float64(y * Float64(Float64(z - t) / a));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -2.02e+142)
		tmp = x;
	elseif (a <= 4.4e+86)
		tmp = y * ((t - z) / t);
	elseif (a <= 2.45e+154)
		tmp = x;
	elseif (a <= 4.6e+183)
		tmp = t * (y / (t - a));
	elseif (a <= 1e+208)
		tmp = y * ((z - t) / a);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -2.02e+142], x, If[LessEqual[a, 4.4e+86], N[(y * N[(N[(t - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.45e+154], x, If[LessEqual[a, 4.6e+183], N[(t * N[(y / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1e+208], N[(y * N[(N[(z - t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], x]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -2.02000000000000013e142 or 4.40000000000000006e86 < a < 2.4500000000000001e154 or 9.9999999999999998e207 < a

   1. Initial program 77.1%

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

      1. associate-*l/ 87.5%

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

   3. Simplified 87.5%

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

   5. Taylor expanded in a around inf 51.5%

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

   if -2.02000000000000013e142 < a < 4.40000000000000006e86

   1. Initial program 66.6%

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

      1. associate-*l/ 80.3%

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

   3. Simplified 80.3%

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

   5. Taylor expanded in y around inf 63.3%

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

      1. div-sub 63.3%

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

   7. Simplified 63.3%

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

   8. Taylor expanded in a around 0 53.4%

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

      1. mul-1-neg 53.4%

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

   10. Simplified 53.4%

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

   if 2.4500000000000001e154 < a < 4.5999999999999996e183

   1. Initial program 25.9%

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

      1. associate-*l/ 99.1%

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

   3. Simplified 99.1%

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

   5. Taylor expanded in z around 0 6.5%

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

      1. associate-*r/ 6.5%

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

      2. mul-1-neg 6.5%

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

      3. distribute-lft-neg-out 6.5%

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

      4. associate-*r/ 60.4%

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

      5. *-commutative 60.4%

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

   7. Simplified 60.4%

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

   8. Taylor expanded in x around 0 6.4%

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

      1. mul-1-neg 6.4%

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

      2. associate-/l* 61.2%

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

      3. distribute-neg-frac 61.2%

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

   10. Simplified 61.2%

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

       1. frac-2neg 61.2%

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

       2. div-inv 60.9%

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

       3. remove-double-neg 60.9%

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

       4. distribute-neg-frac 60.9%

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

       5. sub-neg 60.9%

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

       6. distribute-neg-in 60.9%

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

       7. remove-double-neg 60.9%

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

   12. Applied egg-rr 60.9%

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

       1. associate-/r/ 61.2%

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

       2. associate-*l/ 60.9%

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

       3. *-lft-identity 60.9%

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

       4. +-commutative 60.9%

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

       5. unsub-neg 60.9%

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

   14. Simplified 60.9%

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

   if 4.5999999999999996e183 < a < 9.9999999999999998e207

   1. Initial program 86.4%

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

      1. associate-*l/ 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around inf 59.8%

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

      1. div-sub 59.8%

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

   7. Simplified 59.8%

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

   8. Taylor expanded in a around inf 59.8%

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

4. Final simplification 53.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.02 \cdot 10^{+142}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 4.4 \cdot 10^{+86}:\\ \;\;\;\;y \cdot \frac{t - z}{t}\\ \mathbf{elif}\;a \leq 2.45 \cdot 10^{+154}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 4.6 \cdot 10^{+183}:\\ \;\;\;\;t \cdot \frac{y}{t - a}\\ \mathbf{elif}\;a \leq 10^{+208}:\\ \;\;\;\;y \cdot \frac{z - t}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 47.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.55 \cdot 10^{+146}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.15 \cdot 10^{+87}:\\ \;\;\;\;y \cdot \frac{t - z}{t}\\ \mathbf{elif}\;a \leq 2.5 \cdot 10^{+152}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 2.55 \cdot 10^{+185}:\\ \;\;\;\;y \cdot \frac{-t}{a - t}\\ \mathbf{elif}\;a \leq 1.4 \cdot 10^{+211}:\\ \;\;\;\;y \cdot \frac{z - t}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -1.55e+146)
   x
   (if (<= a 1.15e+87)
     (* y (/ (- t z) t))
     (if (<= a 2.5e+152)
       x
       (if (<= a 2.55e+185)
         (* y (/ (- t) (- a t)))
         (if (<= a 1.4e+211) (* y (/ (- z t) a)) x))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.55e+146) {
		tmp = x;
	} else if (a <= 1.15e+87) {
		tmp = y * ((t - z) / t);
	} else if (a <= 2.5e+152) {
		tmp = x;
	} else if (a <= 2.55e+185) {
		tmp = y * (-t / (a - t));
	} else if (a <= 1.4e+211) {
		tmp = y * ((z - t) / a);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-1.55d+146)) then
        tmp = x
    else if (a <= 1.15d+87) then
        tmp = y * ((t - z) / t)
    else if (a <= 2.5d+152) then
        tmp = x
    else if (a <= 2.55d+185) then
        tmp = y * (-t / (a - t))
    else if (a <= 1.4d+211) then
        tmp = y * ((z - t) / a)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.55e+146) {
		tmp = x;
	} else if (a <= 1.15e+87) {
		tmp = y * ((t - z) / t);
	} else if (a <= 2.5e+152) {
		tmp = x;
	} else if (a <= 2.55e+185) {
		tmp = y * (-t / (a - t));
	} else if (a <= 1.4e+211) {
		tmp = y * ((z - t) / a);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -1.55e+146:
		tmp = x
	elif a <= 1.15e+87:
		tmp = y * ((t - z) / t)
	elif a <= 2.5e+152:
		tmp = x
	elif a <= 2.55e+185:
		tmp = y * (-t / (a - t))
	elif a <= 1.4e+211:
		tmp = y * ((z - t) / a)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -1.55e+146)
		tmp = x;
	elseif (a <= 1.15e+87)
		tmp = Float64(y * Float64(Float64(t - z) / t));
	elseif (a <= 2.5e+152)
		tmp = x;
	elseif (a <= 2.55e+185)
		tmp = Float64(y * Float64(Float64(-t) / Float64(a - t)));
	elseif (a <= 1.4e+211)
		tmp = Float64(y * Float64(Float64(z - t) / a));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -1.55e+146)
		tmp = x;
	elseif (a <= 1.15e+87)
		tmp = y * ((t - z) / t);
	elseif (a <= 2.5e+152)
		tmp = x;
	elseif (a <= 2.55e+185)
		tmp = y * (-t / (a - t));
	elseif (a <= 1.4e+211)
		tmp = y * ((z - t) / a);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -1.55e+146], x, If[LessEqual[a, 1.15e+87], N[(y * N[(N[(t - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.5e+152], x, If[LessEqual[a, 2.55e+185], N[(y * N[((-t) / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.4e+211], N[(y * N[(N[(z - t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], x]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -1.5500000000000001e146 or 1.1500000000000001e87 < a < 2.5e152 or 1.4e211 < a

   1. Initial program 77.1%

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

      1. associate-*l/ 87.5%

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

   3. Simplified 87.5%

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

   5. Taylor expanded in a around inf 51.5%

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

   if -1.5500000000000001e146 < a < 1.1500000000000001e87

   1. Initial program 66.6%

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

      1. associate-*l/ 80.3%

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

   3. Simplified 80.3%

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

   5. Taylor expanded in y around inf 63.3%

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

      1. div-sub 63.3%

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

   7. Simplified 63.3%

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

   8. Taylor expanded in a around 0 53.4%

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

      1. mul-1-neg 53.4%

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

   10. Simplified 53.4%

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

   if 2.5e152 < a < 2.54999999999999998e185

   1. Initial program 25.9%

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

      1. associate-*l/ 99.1%

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

   3. Simplified 99.1%

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

   5. Taylor expanded in y around inf 80.8%

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

      1. div-sub 80.8%

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

   7. Simplified 80.8%

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

   8. Taylor expanded in z around 0 61.2%

      \[\leadsto y \cdot \color{blue}{\left(-1 \cdot \frac{t}{a - t}\right)} \]
   9. Step-by-step derivation

      1. associate-*r/ 61.2%

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

      2. neg-mul-1 61.2%

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

   10. Simplified 61.2%

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

   if 2.54999999999999998e185 < a < 1.4e211

   1. Initial program 86.4%

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

      1. associate-*l/ 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around inf 59.8%

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

      1. div-sub 59.8%

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

   7. Simplified 59.8%

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

   8. Taylor expanded in a around inf 59.8%

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

4. Final simplification 53.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.55 \cdot 10^{+146}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.15 \cdot 10^{+87}:\\ \;\;\;\;y \cdot \frac{t - z}{t}\\ \mathbf{elif}\;a \leq 2.5 \cdot 10^{+152}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 2.55 \cdot 10^{+185}:\\ \;\;\;\;y \cdot \frac{-t}{a - t}\\ \mathbf{elif}\;a \leq 1.4 \cdot 10^{+211}:\\ \;\;\;\;y \cdot \frac{z - t}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 66.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{z - t}{a - t}\\ \mathbf{if}\;t \leq -4.7 \cdot 10^{+156}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -5.2 \cdot 10^{+132}:\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \mathbf{elif}\;t \leq -195 \lor \neg \left(t \leq 1.8 \cdot 10^{-35}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y - x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ (- z t) (- a t)))))
   (if (<= t -4.7e+156)
     t_1
     (if (<= t -5.2e+132)
       (* z (/ (- y x) (- a t)))
       (if (or (<= t -195.0) (not (<= t 1.8e-35)))
         t_1
         (+ x (/ z (/ a (- y x)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((z - t) / (a - t));
	double tmp;
	if (t <= -4.7e+156) {
		tmp = t_1;
	} else if (t <= -5.2e+132) {
		tmp = z * ((y - x) / (a - t));
	} else if ((t <= -195.0) || !(t <= 1.8e-35)) {
		tmp = t_1;
	} else {
		tmp = x + (z / (a / (y - 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) :: t_1
    real(8) :: tmp
    t_1 = y * ((z - t) / (a - t))
    if (t <= (-4.7d+156)) then
        tmp = t_1
    else if (t <= (-5.2d+132)) then
        tmp = z * ((y - x) / (a - t))
    else if ((t <= (-195.0d0)) .or. (.not. (t <= 1.8d-35))) then
        tmp = t_1
    else
        tmp = x + (z / (a / (y - x)))
    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 * ((z - t) / (a - t));
	double tmp;
	if (t <= -4.7e+156) {
		tmp = t_1;
	} else if (t <= -5.2e+132) {
		tmp = z * ((y - x) / (a - t));
	} else if ((t <= -195.0) || !(t <= 1.8e-35)) {
		tmp = t_1;
	} else {
		tmp = x + (z / (a / (y - x)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * ((z - t) / (a - t))
	tmp = 0
	if t <= -4.7e+156:
		tmp = t_1
	elif t <= -5.2e+132:
		tmp = z * ((y - x) / (a - t))
	elif (t <= -195.0) or not (t <= 1.8e-35):
		tmp = t_1
	else:
		tmp = x + (z / (a / (y - x)))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(Float64(z - t) / Float64(a - t)))
	tmp = 0.0
	if (t <= -4.7e+156)
		tmp = t_1;
	elseif (t <= -5.2e+132)
		tmp = Float64(z * Float64(Float64(y - x) / Float64(a - t)));
	elseif ((t <= -195.0) || !(t <= 1.8e-35))
		tmp = t_1;
	else
		tmp = Float64(x + Float64(z / Float64(a / Float64(y - x))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * ((z - t) / (a - t));
	tmp = 0.0;
	if (t <= -4.7e+156)
		tmp = t_1;
	elseif (t <= -5.2e+132)
		tmp = z * ((y - x) / (a - t));
	elseif ((t <= -195.0) || ~((t <= 1.8e-35)))
		tmp = t_1;
	else
		tmp = x + (z / (a / (y - x)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -4.7e+156], t$95$1, If[LessEqual[t, -5.2e+132], N[(z * N[(N[(y - x), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[t, -195.0], N[Not[LessEqual[t, 1.8e-35]], $MachinePrecision]], t$95$1, N[(x + N[(z / N[(a / N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -4.7e156 or -5.2e132 < t < -195 or 1.80000000000000009e-35 < t

   1. Initial program 51.5%

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

      1. associate-*l/ 74.5%

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

   3. Simplified 74.5%

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

   5. Taylor expanded in y around inf 67.7%

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

      1. div-sub 67.7%

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

   7. Simplified 67.7%

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

   if -4.7e156 < t < -5.2e132

   1. Initial program 53.1%

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

      1. associate-*l/ 80.7%

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

   3. Simplified 80.7%

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

   5. Taylor expanded in z around inf 71.0%

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

      1. div-sub 71.0%

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

   7. Simplified 71.0%

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

   if -195 < t < 1.80000000000000009e-35

   1. Initial program 92.6%

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

      1. associate-*l/ 94.1%

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

   3. Simplified 94.1%

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

   5. Taylor expanded in t around 0 78.7%

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

      1. associate-/l* 82.1%

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

   7. Simplified 82.1%

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

4. Final simplification 73.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.7 \cdot 10^{+156}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;t \leq -5.2 \cdot 10^{+132}:\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \mathbf{elif}\;t \leq -195 \lor \neg \left(t \leq 1.8 \cdot 10^{-35}\right):\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y - x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 67.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{z - t}{a - t}\\ \mathbf{if}\;t \leq -2.5 \cdot 10^{+155}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -1.2 \cdot 10^{+133}:\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \mathbf{elif}\;t \leq -150 \lor \neg \left(t \leq 7.9 \cdot 10^{-35}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{\frac{a}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ (- z t) (- a t)))))
   (if (<= t -2.5e+155)
     t_1
     (if (<= t -1.2e+133)
       (* z (/ (- y x) (- a t)))
       (if (or (<= t -150.0) (not (<= t 7.9e-35)))
         t_1
         (+ x (/ (- y x) (/ a z))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((z - t) / (a - t));
	double tmp;
	if (t <= -2.5e+155) {
		tmp = t_1;
	} else if (t <= -1.2e+133) {
		tmp = z * ((y - x) / (a - t));
	} else if ((t <= -150.0) || !(t <= 7.9e-35)) {
		tmp = t_1;
	} else {
		tmp = x + ((y - x) / (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 = y * ((z - t) / (a - t))
    if (t <= (-2.5d+155)) then
        tmp = t_1
    else if (t <= (-1.2d+133)) then
        tmp = z * ((y - x) / (a - t))
    else if ((t <= (-150.0d0)) .or. (.not. (t <= 7.9d-35))) then
        tmp = t_1
    else
        tmp = x + ((y - x) / (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 = y * ((z - t) / (a - t));
	double tmp;
	if (t <= -2.5e+155) {
		tmp = t_1;
	} else if (t <= -1.2e+133) {
		tmp = z * ((y - x) / (a - t));
	} else if ((t <= -150.0) || !(t <= 7.9e-35)) {
		tmp = t_1;
	} else {
		tmp = x + ((y - x) / (a / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * ((z - t) / (a - t))
	tmp = 0
	if t <= -2.5e+155:
		tmp = t_1
	elif t <= -1.2e+133:
		tmp = z * ((y - x) / (a - t))
	elif (t <= -150.0) or not (t <= 7.9e-35):
		tmp = t_1
	else:
		tmp = x + ((y - x) / (a / z))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(Float64(z - t) / Float64(a - t)))
	tmp = 0.0
	if (t <= -2.5e+155)
		tmp = t_1;
	elseif (t <= -1.2e+133)
		tmp = Float64(z * Float64(Float64(y - x) / Float64(a - t)));
	elseif ((t <= -150.0) || !(t <= 7.9e-35))
		tmp = t_1;
	else
		tmp = Float64(x + Float64(Float64(y - x) / Float64(a / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * ((z - t) / (a - t));
	tmp = 0.0;
	if (t <= -2.5e+155)
		tmp = t_1;
	elseif (t <= -1.2e+133)
		tmp = z * ((y - x) / (a - t));
	elseif ((t <= -150.0) || ~((t <= 7.9e-35)))
		tmp = t_1;
	else
		tmp = x + ((y - x) / (a / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.5e+155], t$95$1, If[LessEqual[t, -1.2e+133], N[(z * N[(N[(y - x), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[t, -150.0], N[Not[LessEqual[t, 7.9e-35]], $MachinePrecision]], t$95$1, N[(x + N[(N[(y - x), $MachinePrecision] / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.5e155 or -1.1999999999999999e133 < t < -150 or 7.89999999999999983e-35 < t

   1. Initial program 51.5%

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

      1. associate-*l/ 74.5%

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

   3. Simplified 74.5%

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

   5. Taylor expanded in y around inf 67.7%

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

      1. div-sub 67.7%

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

   7. Simplified 67.7%

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

   if -2.5e155 < t < -1.1999999999999999e133

   1. Initial program 53.1%

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

      1. associate-*l/ 80.7%

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

   3. Simplified 80.7%

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

   5. Taylor expanded in z around inf 71.0%

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

      1. div-sub 71.0%

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

   7. Simplified 71.0%

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

   if -150 < t < 7.89999999999999983e-35

   1. Initial program 92.6%

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

      1. associate-*l/ 94.1%

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

   3. Simplified 94.1%

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

      1. associate-/r/ 98.2%

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

   6. Applied egg-rr 98.2%

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

   7. Taylor expanded in t around 0 84.0%

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

4. Final simplification 74.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.5 \cdot 10^{+155}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;t \leq -1.2 \cdot 10^{+133}:\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \mathbf{elif}\;t \leq -150 \lor \neg \left(t \leq 7.9 \cdot 10^{-35}\right):\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{\frac{a}{z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 71.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + x \cdot \frac{z - a}{t}\\ \mathbf{if}\;t \leq -9.6 \cdot 10^{+131}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -74:\\ \;\;\;\;\frac{y}{\frac{a - t}{z - t}}\\ \mathbf{elif}\;t \leq 3.6 \cdot 10^{-34}:\\ \;\;\;\;x + \frac{y - x}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 5.2 \cdot 10^{+171}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ y (* x (/ (- z a) t)))))
   (if (<= t -9.6e+131)
     t_1
     (if (<= t -74.0)
       (/ y (/ (- a t) (- z t)))
       (if (<= t 3.6e-34)
         (+ x (/ (- y x) (/ a z)))
         (if (<= t 5.2e+171) (* y (/ (- z t) (- a t))) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y + (x * ((z - a) / t));
	double tmp;
	if (t <= -9.6e+131) {
		tmp = t_1;
	} else if (t <= -74.0) {
		tmp = y / ((a - t) / (z - t));
	} else if (t <= 3.6e-34) {
		tmp = x + ((y - x) / (a / z));
	} else if (t <= 5.2e+171) {
		tmp = y * ((z - t) / (a - t));
	} else {
		tmp = t_1;
	}
	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 = y + (x * ((z - a) / t))
    if (t <= (-9.6d+131)) then
        tmp = t_1
    else if (t <= (-74.0d0)) then
        tmp = y / ((a - t) / (z - t))
    else if (t <= 3.6d-34) then
        tmp = x + ((y - x) / (a / z))
    else if (t <= 5.2d+171) then
        tmp = y * ((z - t) / (a - t))
    else
        tmp = t_1
    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 + (x * ((z - a) / t));
	double tmp;
	if (t <= -9.6e+131) {
		tmp = t_1;
	} else if (t <= -74.0) {
		tmp = y / ((a - t) / (z - t));
	} else if (t <= 3.6e-34) {
		tmp = x + ((y - x) / (a / z));
	} else if (t <= 5.2e+171) {
		tmp = y * ((z - t) / (a - t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y + (x * ((z - a) / t))
	tmp = 0
	if t <= -9.6e+131:
		tmp = t_1
	elif t <= -74.0:
		tmp = y / ((a - t) / (z - t))
	elif t <= 3.6e-34:
		tmp = x + ((y - x) / (a / z))
	elif t <= 5.2e+171:
		tmp = y * ((z - t) / (a - t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y + Float64(x * Float64(Float64(z - a) / t)))
	tmp = 0.0
	if (t <= -9.6e+131)
		tmp = t_1;
	elseif (t <= -74.0)
		tmp = Float64(y / Float64(Float64(a - t) / Float64(z - t)));
	elseif (t <= 3.6e-34)
		tmp = Float64(x + Float64(Float64(y - x) / Float64(a / z)));
	elseif (t <= 5.2e+171)
		tmp = Float64(y * Float64(Float64(z - t) / Float64(a - t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y + (x * ((z - a) / t));
	tmp = 0.0;
	if (t <= -9.6e+131)
		tmp = t_1;
	elseif (t <= -74.0)
		tmp = y / ((a - t) / (z - t));
	elseif (t <= 3.6e-34)
		tmp = x + ((y - x) / (a / z));
	elseif (t <= 5.2e+171)
		tmp = y * ((z - t) / (a - t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y + N[(x * N[(N[(z - a), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -9.6e+131], t$95$1, If[LessEqual[t, -74.0], N[(y / N[(N[(a - t), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.6e-34], N[(x + N[(N[(y - x), $MachinePrecision] / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 5.2e+171], N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -9.5999999999999998e131 or 5.2e171 < t

   1. Initial program 38.3%

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

      1. associate-*l/ 67.7%

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

   3. Simplified 67.7%

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

      1. associate-/r/ 74.3%

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

      2. add-cube-cbrt 72.7%

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

      3. associate-/l* 72.8%

         \[\leadsto x + \color{blue}{\frac{\sqrt[3]{y - x} \cdot \sqrt[3]{y - x}}{\frac{\frac{a - t}{z - t}}{\sqrt[3]{y - x}}}} \]

      4. pow2 72.8%

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

   6. Applied egg-rr 72.8%

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

   7. Taylor expanded in t around inf 59.3%

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

      1. associate--l+ 59.3%

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

      2. associate-*r/ 59.3%

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

      3. associate-*r/ 59.3%

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

      4. div-sub 59.3%

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

      5. distribute-lft-out-- 59.3%

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

      6. distribute-rgt-out-- 59.4%

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

      7. associate-*r/ 59.4%

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

      8. distribute-rgt-out-- 59.3%

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

      9. mul-1-neg 59.3%

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

      10. distribute-rgt-out-- 59.4%

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

      11. unsub-neg 59.4%

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

      12. associate-*r/ 88.6%

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

   9. Simplified 88.6%

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

   10. Taylor expanded in y around 0 68.1%

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

       1. mul-1-neg 68.1%

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

       2. associate-*r/ 84.5%

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

       3. distribute-rgt-neg-in 84.5%

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

       4. distribute-frac-neg 84.5%

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

       5. neg-sub0 84.5%

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

       6. associate--r- 84.5%

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

       7. neg-sub0 84.5%

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

   12. Simplified 84.5%

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

   if -9.5999999999999998e131 < t < -74

   1. Initial program 67.1%

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

      1. associate-*l/ 91.3%

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

   3. Simplified 91.3%

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

      1. associate-/r/ 95.6%

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

   6. Applied egg-rr 95.6%

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

   7. Taylor expanded in x around 0 54.4%

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

      1. associate-/l* 78.7%

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

   9. Simplified 78.7%

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

   if -74 < t < 3.60000000000000008e-34

   1. Initial program 92.6%

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

      1. associate-*l/ 94.1%

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

   3. Simplified 94.1%

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

      1. associate-/r/ 98.2%

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

   6. Applied egg-rr 98.2%

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

   7. Taylor expanded in t around 0 84.0%

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

   if 3.60000000000000008e-34 < t < 5.2e171

   1. Initial program 69.5%

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

      1. associate-*l/ 80.2%

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

   3. Simplified 80.2%

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

   5. Taylor expanded in y around inf 63.0%

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

      1. div-sub 63.0%

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

   7. Simplified 63.0%

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

4. Final simplification 80.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -9.6 \cdot 10^{+131}:\\ \;\;\;\;y + x \cdot \frac{z - a}{t}\\ \mathbf{elif}\;t \leq -74:\\ \;\;\;\;\frac{y}{\frac{a - t}{z - t}}\\ \mathbf{elif}\;t \leq 3.6 \cdot 10^{-34}:\\ \;\;\;\;x + \frac{y - x}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 5.2 \cdot 10^{+171}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;y + x \cdot \frac{z - a}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 75.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + \left(y - x\right) \cdot \frac{a - z}{t}\\ \mathbf{if}\;t \leq -4.4 \cdot 10^{+131}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -105:\\ \;\;\;\;\frac{y}{\frac{a - t}{z - t}}\\ \mathbf{elif}\;t \leq 3.9 \cdot 10^{-34}:\\ \;\;\;\;x + \frac{y - x}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ y (* (- y x) (/ (- a z) t)))))
   (if (<= t -4.4e+131)
     t_1
     (if (<= t -105.0)
       (/ y (/ (- a t) (- z t)))
       (if (<= t 3.9e-34) (+ x (/ (- y x) (/ a z))) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y + ((y - x) * ((a - z) / t));
	double tmp;
	if (t <= -4.4e+131) {
		tmp = t_1;
	} else if (t <= -105.0) {
		tmp = y / ((a - t) / (z - t));
	} else if (t <= 3.9e-34) {
		tmp = x + ((y - x) / (a / z));
	} else {
		tmp = t_1;
	}
	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 = y + ((y - x) * ((a - z) / t))
    if (t <= (-4.4d+131)) then
        tmp = t_1
    else if (t <= (-105.0d0)) then
        tmp = y / ((a - t) / (z - t))
    else if (t <= 3.9d-34) then
        tmp = x + ((y - x) / (a / z))
    else
        tmp = t_1
    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 + ((y - x) * ((a - z) / t));
	double tmp;
	if (t <= -4.4e+131) {
		tmp = t_1;
	} else if (t <= -105.0) {
		tmp = y / ((a - t) / (z - t));
	} else if (t <= 3.9e-34) {
		tmp = x + ((y - x) / (a / z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y + ((y - x) * ((a - z) / t))
	tmp = 0
	if t <= -4.4e+131:
		tmp = t_1
	elif t <= -105.0:
		tmp = y / ((a - t) / (z - t))
	elif t <= 3.9e-34:
		tmp = x + ((y - x) / (a / z))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y + Float64(Float64(y - x) * Float64(Float64(a - z) / t)))
	tmp = 0.0
	if (t <= -4.4e+131)
		tmp = t_1;
	elseif (t <= -105.0)
		tmp = Float64(y / Float64(Float64(a - t) / Float64(z - t)));
	elseif (t <= 3.9e-34)
		tmp = Float64(x + Float64(Float64(y - x) / Float64(a / z)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y + ((y - x) * ((a - z) / t));
	tmp = 0.0;
	if (t <= -4.4e+131)
		tmp = t_1;
	elseif (t <= -105.0)
		tmp = y / ((a - t) / (z - t));
	elseif (t <= 3.9e-34)
		tmp = x + ((y - x) / (a / z));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y + N[(N[(y - x), $MachinePrecision] * N[(N[(a - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -4.4e+131], t$95$1, If[LessEqual[t, -105.0], N[(y / N[(N[(a - t), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.9e-34], N[(x + N[(N[(y - x), $MachinePrecision] / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -4.3999999999999998e131 or 3.89999999999999991e-34 < t

   1. Initial program 48.8%

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

      1. associate-*l/ 71.9%

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

   3. Simplified 71.9%

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

      1. associate-/r/ 77.8%

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

      2. add-cube-cbrt 76.4%

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

      3. associate-/l* 76.4%

         \[\leadsto x + \color{blue}{\frac{\sqrt[3]{y - x} \cdot \sqrt[3]{y - x}}{\frac{\frac{a - t}{z - t}}{\sqrt[3]{y - x}}}} \]

      4. pow2 76.4%

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

   6. Applied egg-rr 76.4%

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

   7. Taylor expanded in t around inf 58.4%

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

      1. associate--l+ 58.4%

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

      2. associate-*r/ 58.4%

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

      3. associate-*r/ 58.4%

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

      4. div-sub 58.4%

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

      5. distribute-lft-out-- 58.4%

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

      6. distribute-rgt-out-- 58.5%

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

      7. associate-*r/ 58.5%

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

      8. distribute-rgt-out-- 58.4%

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

      9. mul-1-neg 58.4%

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

      10. distribute-rgt-out-- 58.5%

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

      11. unsub-neg 58.5%

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

      12. associate-*r/ 80.8%

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

   9. Simplified 80.8%

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

   if -4.3999999999999998e131 < t < -105

   1. Initial program 67.1%

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

      1. associate-*l/ 91.3%

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

   3. Simplified 91.3%

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

      1. associate-/r/ 95.6%

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

   6. Applied egg-rr 95.6%

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

   7. Taylor expanded in x around 0 54.4%

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

      1. associate-/l* 78.7%

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

   9. Simplified 78.7%

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

   if -105 < t < 3.89999999999999991e-34

   1. Initial program 92.6%

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

      1. associate-*l/ 94.1%

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

   3. Simplified 94.1%

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

      1. associate-/r/ 98.2%

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

   6. Applied egg-rr 98.2%

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

   7. Taylor expanded in t around 0 84.0%

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

4. Final simplification 82.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.4 \cdot 10^{+131}:\\ \;\;\;\;y + \left(y - x\right) \cdot \frac{a - z}{t}\\ \mathbf{elif}\;t \leq -105:\\ \;\;\;\;\frac{y}{\frac{a - t}{z - t}}\\ \mathbf{elif}\;t \leq 3.9 \cdot 10^{-34}:\\ \;\;\;\;x + \frac{y - x}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;y + \left(y - x\right) \cdot \frac{a - z}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 87.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.6 \cdot 10^{+212} \lor \neg \left(t \leq 3.1 \cdot 10^{+124}\right):\\ \;\;\;\;y + \left(y - x\right) \cdot \frac{a - z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y - x}{a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -1.6e+212) (not (<= t 3.1e+124)))
   (+ y (* (- y x) (/ (- a z) t)))
   (+ x (* (- z t) (/ (- y x) (- a t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -1.6e+212) || !(t <= 3.1e+124)) {
		tmp = y + ((y - x) * ((a - z) / t));
	} else {
		tmp = x + ((z - t) * ((y - x) / (a - t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-1.6d+212)) .or. (.not. (t <= 3.1d+124))) then
        tmp = y + ((y - x) * ((a - z) / t))
    else
        tmp = x + ((z - t) * ((y - x) / (a - t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -1.6e+212) || !(t <= 3.1e+124)) {
		tmp = y + ((y - x) * ((a - z) / t));
	} else {
		tmp = x + ((z - t) * ((y - x) / (a - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -1.6e+212) or not (t <= 3.1e+124):
		tmp = y + ((y - x) * ((a - z) / t))
	else:
		tmp = x + ((z - t) * ((y - x) / (a - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -1.6e+212) || !(t <= 3.1e+124))
		tmp = Float64(y + Float64(Float64(y - x) * Float64(Float64(a - z) / t)));
	else
		tmp = Float64(x + Float64(Float64(z - t) * Float64(Float64(y - x) / Float64(a - t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -1.6e+212) || ~((t <= 3.1e+124)))
		tmp = y + ((y - x) * ((a - z) / t));
	else
		tmp = x + ((z - t) * ((y - x) / (a - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -1.6e+212], N[Not[LessEqual[t, 3.1e+124]], $MachinePrecision]], N[(y + N[(N[(y - x), $MachinePrecision] * N[(N[(a - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(z - t), $MachinePrecision] * N[(N[(y - x), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.5999999999999999e212 or 3.1000000000000002e124 < t

   1. Initial program 31.5%

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

      1. associate-*l/ 57.1%

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

   3. Simplified 57.1%

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

      1. associate-/r/ 66.6%

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

      2. add-cube-cbrt 65.3%

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

      3. associate-/l* 65.4%

         \[\leadsto x + \color{blue}{\frac{\sqrt[3]{y - x} \cdot \sqrt[3]{y - x}}{\frac{\frac{a - t}{z - t}}{\sqrt[3]{y - x}}}} \]

      4. pow2 65.4%

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

   6. Applied egg-rr 65.4%

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

   7. Taylor expanded in t around inf 67.0%

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

      1. associate--l+ 67.0%

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

      2. associate-*r/ 67.0%

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

      3. associate-*r/ 67.0%

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

      4. div-sub 67.0%

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

      5. distribute-lft-out-- 67.0%

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

      6. distribute-rgt-out-- 67.0%

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

      7. associate-*r/ 67.0%

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

      8. distribute-rgt-out-- 67.0%

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

      9. mul-1-neg 67.0%

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

      10. distribute-rgt-out-- 67.0%

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

      11. unsub-neg 67.0%

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

      12. associate-*r/ 94.0%

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

   9. Simplified 94.0%

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

   if -1.5999999999999999e212 < t < 3.1000000000000002e124

   1. Initial program 82.2%

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

      1. associate-*l/ 92.2%

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

   3. Simplified 92.2%

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

4. Final simplification 92.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.6 \cdot 10^{+212} \lor \neg \left(t \leq 3.1 \cdot 10^{+124}\right):\\ \;\;\;\;y + \left(y - x\right) \cdot \frac{a - z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y - x}{a - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 37.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y}{t - a}\\ \mathbf{if}\;t \leq -1.5 \cdot 10^{+51}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -1.35 \cdot 10^{-72}:\\ \;\;\;\;\frac{y}{\frac{a - t}{z}}\\ \mathbf{elif}\;t \leq -1.5 \cdot 10^{-275}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 4 \cdot 10^{-45}:\\ \;\;\;\;z \cdot \frac{y}{a - t}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ y (- t a)))))
   (if (<= t -1.5e+51)
     t_1
     (if (<= t -1.35e-72)
       (/ y (/ (- a t) z))
       (if (<= t -1.5e-275) x (if (<= t 4e-45) (* z (/ y (- a t))) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (y / (t - a));
	double tmp;
	if (t <= -1.5e+51) {
		tmp = t_1;
	} else if (t <= -1.35e-72) {
		tmp = y / ((a - t) / z);
	} else if (t <= -1.5e-275) {
		tmp = x;
	} else if (t <= 4e-45) {
		tmp = z * (y / (a - t));
	} else {
		tmp = t_1;
	}
	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 = t * (y / (t - a))
    if (t <= (-1.5d+51)) then
        tmp = t_1
    else if (t <= (-1.35d-72)) then
        tmp = y / ((a - t) / z)
    else if (t <= (-1.5d-275)) then
        tmp = x
    else if (t <= 4d-45) then
        tmp = z * (y / (a - t))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (y / (t - a));
	double tmp;
	if (t <= -1.5e+51) {
		tmp = t_1;
	} else if (t <= -1.35e-72) {
		tmp = y / ((a - t) / z);
	} else if (t <= -1.5e-275) {
		tmp = x;
	} else if (t <= 4e-45) {
		tmp = z * (y / (a - t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * (y / (t - a))
	tmp = 0
	if t <= -1.5e+51:
		tmp = t_1
	elif t <= -1.35e-72:
		tmp = y / ((a - t) / z)
	elif t <= -1.5e-275:
		tmp = x
	elif t <= 4e-45:
		tmp = z * (y / (a - t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(y / Float64(t - a)))
	tmp = 0.0
	if (t <= -1.5e+51)
		tmp = t_1;
	elseif (t <= -1.35e-72)
		tmp = Float64(y / Float64(Float64(a - t) / z));
	elseif (t <= -1.5e-275)
		tmp = x;
	elseif (t <= 4e-45)
		tmp = Float64(z * Float64(y / Float64(a - t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * (y / (t - a));
	tmp = 0.0;
	if (t <= -1.5e+51)
		tmp = t_1;
	elseif (t <= -1.35e-72)
		tmp = y / ((a - t) / z);
	elseif (t <= -1.5e-275)
		tmp = x;
	elseif (t <= 4e-45)
		tmp = z * (y / (a - t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(y / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.5e+51], t$95$1, If[LessEqual[t, -1.35e-72], N[(y / N[(N[(a - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -1.5e-275], x, If[LessEqual[t, 4e-45], N[(z * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -1.5e51 or 3.99999999999999994e-45 < t

   1. Initial program 51.6%

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

      1. associate-*l/ 73.9%

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

   3. Simplified 73.9%

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

   5. Taylor expanded in z around 0 35.2%

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

      1. associate-*r/ 35.2%

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

      2. mul-1-neg 35.2%

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

      3. distribute-lft-neg-out 35.2%

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

      4. associate-*r/ 51.1%

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

      5. *-commutative 51.1%

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

   7. Simplified 51.1%

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

   8. Taylor expanded in x around 0 33.9%

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

      1. mul-1-neg 33.9%

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

      2. associate-/l* 48.4%

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

      3. distribute-neg-frac 48.4%

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

   10. Simplified 48.4%

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

       1. frac-2neg 48.4%

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

       2. div-inv 48.3%

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

       3. remove-double-neg 48.3%

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

       4. distribute-neg-frac 48.3%

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

       5. sub-neg 48.3%

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

       6. distribute-neg-in 48.3%

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

       7. remove-double-neg 48.3%

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

   12. Applied egg-rr 48.3%

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

       1. associate-/r/ 48.8%

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

       2. associate-*l/ 48.9%

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

       3. *-lft-identity 48.9%

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

       4. +-commutative 48.9%

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

       5. unsub-neg 48.9%

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

   14. Simplified 48.9%

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

   if -1.5e51 < t < -1.35e-72

   1. Initial program 74.3%

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

      1. associate-*l/ 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in z around -inf 47.6%

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

   6. Taylor expanded in y around inf 30.4%

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

      1. associate-/l* 50.0%

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

   8. Simplified 50.0%

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

   if -1.35e-72 < t < -1.5e-275

   1. Initial program 95.2%

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

      1. associate-*l/ 90.8%

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

   3. Simplified 90.8%

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

   5. Taylor expanded in a around inf 46.7%

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

   if -1.5e-275 < t < 3.99999999999999994e-45

   1. Initial program 93.8%

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

      1. associate-*l/ 96.0%

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

   3. Simplified 96.0%

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

   5. Taylor expanded in z around -inf 70.1%

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

   6. Taylor expanded in y around inf 44.1%

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

      1. associate-/l* 45.9%

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

   8. Simplified 45.9%

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

      1. associate-/r/ 47.7%

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

   10. Applied egg-rr 47.7%

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

4. Final simplification 48.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.5 \cdot 10^{+51}:\\ \;\;\;\;t \cdot \frac{y}{t - a}\\ \mathbf{elif}\;t \leq -1.35 \cdot 10^{-72}:\\ \;\;\;\;\frac{y}{\frac{a - t}{z}}\\ \mathbf{elif}\;t \leq -1.5 \cdot 10^{-275}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 4 \cdot 10^{-45}:\\ \;\;\;\;z \cdot \frac{y}{a - t}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y}{t - a}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 53.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x \cdot \left(-z\right)}{a - t}\\ \mathbf{if}\;x \leq -1.65 \cdot 10^{+290}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -1.12 \cdot 10^{+206}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 2.9 \cdot 10^{+217}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* x (- z)) (- a t))))
   (if (<= x -1.65e+290)
     t_1
     (if (<= x -1.12e+206)
       x
       (if (<= x 2.9e+217) (* y (/ (- z t) (- a t))) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (x * -z) / (a - t);
	double tmp;
	if (x <= -1.65e+290) {
		tmp = t_1;
	} else if (x <= -1.12e+206) {
		tmp = x;
	} else if (x <= 2.9e+217) {
		tmp = y * ((z - t) / (a - t));
	} else {
		tmp = t_1;
	}
	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 * -z) / (a - t)
    if (x <= (-1.65d+290)) then
        tmp = t_1
    else if (x <= (-1.12d+206)) then
        tmp = x
    else if (x <= 2.9d+217) then
        tmp = y * ((z - t) / (a - t))
    else
        tmp = t_1
    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 * -z) / (a - t);
	double tmp;
	if (x <= -1.65e+290) {
		tmp = t_1;
	} else if (x <= -1.12e+206) {
		tmp = x;
	} else if (x <= 2.9e+217) {
		tmp = y * ((z - t) / (a - t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (x * -z) / (a - t)
	tmp = 0
	if x <= -1.65e+290:
		tmp = t_1
	elif x <= -1.12e+206:
		tmp = x
	elif x <= 2.9e+217:
		tmp = y * ((z - t) / (a - t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(x * Float64(-z)) / Float64(a - t))
	tmp = 0.0
	if (x <= -1.65e+290)
		tmp = t_1;
	elseif (x <= -1.12e+206)
		tmp = x;
	elseif (x <= 2.9e+217)
		tmp = Float64(y * Float64(Float64(z - t) / Float64(a - t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (x * -z) / (a - t);
	tmp = 0.0;
	if (x <= -1.65e+290)
		tmp = t_1;
	elseif (x <= -1.12e+206)
		tmp = x;
	elseif (x <= 2.9e+217)
		tmp = y * ((z - t) / (a - t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(x * (-z)), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.65e+290], t$95$1, If[LessEqual[x, -1.12e+206], x, If[LessEqual[x, 2.9e+217], N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.65e290 or 2.89999999999999985e217 < x

   1. Initial program 69.6%

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

      1. associate-*l/ 78.0%

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

   3. Simplified 78.0%

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

   5. Taylor expanded in z around -inf 56.1%

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

   6. Taylor expanded in y around 0 56.1%

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

      1. associate-*r/ 56.1%

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

      2. mul-1-neg 56.1%

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

      3. distribute-rgt-neg-in 56.1%

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

   8. Simplified 56.1%

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

   if -1.65e290 < x < -1.11999999999999997e206

   1. Initial program 54.5%

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

      1. associate-*l/ 84.7%

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

   3. Simplified 84.7%

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

   5. Taylor expanded in a around inf 57.8%

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

   if -1.11999999999999997e206 < x < 2.89999999999999985e217

   1. Initial program 69.7%

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

      1. associate-*l/ 83.4%

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

   3. Simplified 83.4%

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

   5. Taylor expanded in y around inf 64.4%

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

      1. div-sub 64.4%

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

   7. Simplified 64.4%

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

4. Final simplification 63.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.65 \cdot 10^{+290}:\\ \;\;\;\;\frac{x \cdot \left(-z\right)}{a - t}\\ \mathbf{elif}\;x \leq -1.12 \cdot 10^{+206}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 2.9 \cdot 10^{+217}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \left(-z\right)}{a - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 71.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y - \frac{z}{\frac{t}{y - x}}\\ \mathbf{if}\;t \leq -1.55 \cdot 10^{+130}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -180:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;t \leq 6.5 \cdot 10^{-36}:\\ \;\;\;\;x + \frac{y - x}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- y (/ z (/ t (- y x))))))
   (if (<= t -1.55e+130)
     t_1
     (if (<= t -180.0)
       (* y (/ (- z t) (- a t)))
       (if (<= t 6.5e-36) (+ x (/ (- y x) (/ a z))) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y - (z / (t / (y - x)));
	double tmp;
	if (t <= -1.55e+130) {
		tmp = t_1;
	} else if (t <= -180.0) {
		tmp = y * ((z - t) / (a - t));
	} else if (t <= 6.5e-36) {
		tmp = x + ((y - x) / (a / z));
	} else {
		tmp = t_1;
	}
	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 = y - (z / (t / (y - x)))
    if (t <= (-1.55d+130)) then
        tmp = t_1
    else if (t <= (-180.0d0)) then
        tmp = y * ((z - t) / (a - t))
    else if (t <= 6.5d-36) then
        tmp = x + ((y - x) / (a / z))
    else
        tmp = t_1
    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 - (z / (t / (y - x)));
	double tmp;
	if (t <= -1.55e+130) {
		tmp = t_1;
	} else if (t <= -180.0) {
		tmp = y * ((z - t) / (a - t));
	} else if (t <= 6.5e-36) {
		tmp = x + ((y - x) / (a / z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y - (z / (t / (y - x)))
	tmp = 0
	if t <= -1.55e+130:
		tmp = t_1
	elif t <= -180.0:
		tmp = y * ((z - t) / (a - t))
	elif t <= 6.5e-36:
		tmp = x + ((y - x) / (a / z))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y - Float64(z / Float64(t / Float64(y - x))))
	tmp = 0.0
	if (t <= -1.55e+130)
		tmp = t_1;
	elseif (t <= -180.0)
		tmp = Float64(y * Float64(Float64(z - t) / Float64(a - t)));
	elseif (t <= 6.5e-36)
		tmp = Float64(x + Float64(Float64(y - x) / Float64(a / z)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y - (z / (t / (y - x)));
	tmp = 0.0;
	if (t <= -1.55e+130)
		tmp = t_1;
	elseif (t <= -180.0)
		tmp = y * ((z - t) / (a - t));
	elseif (t <= 6.5e-36)
		tmp = x + ((y - x) / (a / z));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y - N[(z / N[(t / N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.55e+130], t$95$1, If[LessEqual[t, -180.0], N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 6.5e-36], N[(x + N[(N[(y - x), $MachinePrecision] / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.55e130 or 6.50000000000000012e-36 < t

   1. Initial program 48.8%

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

      1. associate-*l/ 71.9%

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

   3. Simplified 71.9%

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

   5. Taylor expanded in t around inf 58.4%

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

      1. associate--l+ 58.4%

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

      2. distribute-lft-out-- 58.4%

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

      3. div-sub 58.4%

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

      4. mul-1-neg 58.4%

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

      5. unsub-neg 58.4%

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

      6. distribute-rgt-out-- 58.5%

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

   7. Simplified 58.5%

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

   8. Taylor expanded in z around inf 57.8%

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

      1. associate-/l* 72.0%

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

   10. Simplified 72.0%

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

   if -1.55e130 < t < -180

   1. Initial program 67.1%

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

      1. associate-*l/ 91.3%

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

   3. Simplified 91.3%

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

   5. Taylor expanded in y around inf 78.7%

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

      1. div-sub 78.7%

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

   7. Simplified 78.7%

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

   if -180 < t < 6.50000000000000012e-36

   1. Initial program 92.6%

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

      1. associate-*l/ 94.1%

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

   3. Simplified 94.1%

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

      1. associate-/r/ 98.2%

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

   6. Applied egg-rr 98.2%

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

   7. Taylor expanded in t around 0 84.0%

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

4. Final simplification 77.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.55 \cdot 10^{+130}:\\ \;\;\;\;y - \frac{z}{\frac{t}{y - x}}\\ \mathbf{elif}\;t \leq -180:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;t \leq 6.5 \cdot 10^{-36}:\\ \;\;\;\;x + \frac{y - x}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;y - \frac{z}{\frac{t}{y - x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 71.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y - \frac{z}{\frac{t}{y - x}}\\ \mathbf{if}\;t \leq -2.05 \cdot 10^{+131}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -210:\\ \;\;\;\;\frac{y}{\frac{a - t}{z - t}}\\ \mathbf{elif}\;t \leq 5.7 \cdot 10^{-36}:\\ \;\;\;\;x + \frac{y - x}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- y (/ z (/ t (- y x))))))
   (if (<= t -2.05e+131)
     t_1
     (if (<= t -210.0)
       (/ y (/ (- a t) (- z t)))
       (if (<= t 5.7e-36) (+ x (/ (- y x) (/ a z))) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y - (z / (t / (y - x)));
	double tmp;
	if (t <= -2.05e+131) {
		tmp = t_1;
	} else if (t <= -210.0) {
		tmp = y / ((a - t) / (z - t));
	} else if (t <= 5.7e-36) {
		tmp = x + ((y - x) / (a / z));
	} else {
		tmp = t_1;
	}
	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 = y - (z / (t / (y - x)))
    if (t <= (-2.05d+131)) then
        tmp = t_1
    else if (t <= (-210.0d0)) then
        tmp = y / ((a - t) / (z - t))
    else if (t <= 5.7d-36) then
        tmp = x + ((y - x) / (a / z))
    else
        tmp = t_1
    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 - (z / (t / (y - x)));
	double tmp;
	if (t <= -2.05e+131) {
		tmp = t_1;
	} else if (t <= -210.0) {
		tmp = y / ((a - t) / (z - t));
	} else if (t <= 5.7e-36) {
		tmp = x + ((y - x) / (a / z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y - (z / (t / (y - x)))
	tmp = 0
	if t <= -2.05e+131:
		tmp = t_1
	elif t <= -210.0:
		tmp = y / ((a - t) / (z - t))
	elif t <= 5.7e-36:
		tmp = x + ((y - x) / (a / z))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y - Float64(z / Float64(t / Float64(y - x))))
	tmp = 0.0
	if (t <= -2.05e+131)
		tmp = t_1;
	elseif (t <= -210.0)
		tmp = Float64(y / Float64(Float64(a - t) / Float64(z - t)));
	elseif (t <= 5.7e-36)
		tmp = Float64(x + Float64(Float64(y - x) / Float64(a / z)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y - (z / (t / (y - x)));
	tmp = 0.0;
	if (t <= -2.05e+131)
		tmp = t_1;
	elseif (t <= -210.0)
		tmp = y / ((a - t) / (z - t));
	elseif (t <= 5.7e-36)
		tmp = x + ((y - x) / (a / z));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y - N[(z / N[(t / N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.05e+131], t$95$1, If[LessEqual[t, -210.0], N[(y / N[(N[(a - t), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 5.7e-36], N[(x + N[(N[(y - x), $MachinePrecision] / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.05000000000000004e131 or 5.6999999999999999e-36 < t

   1. Initial program 48.8%

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

      1. associate-*l/ 71.9%

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

   3. Simplified 71.9%

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

   5. Taylor expanded in t around inf 58.4%

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

      1. associate--l+ 58.4%

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

      2. distribute-lft-out-- 58.4%

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

      3. div-sub 58.4%

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

      4. mul-1-neg 58.4%

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

      5. unsub-neg 58.4%

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

      6. distribute-rgt-out-- 58.5%

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

   7. Simplified 58.5%

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

   8. Taylor expanded in z around inf 57.8%

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

      1. associate-/l* 72.0%

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

   10. Simplified 72.0%

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

   if -2.05000000000000004e131 < t < -210

   1. Initial program 67.1%

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

      1. associate-*l/ 91.3%

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

   3. Simplified 91.3%

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

      1. associate-/r/ 95.6%

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

   6. Applied egg-rr 95.6%

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

   7. Taylor expanded in x around 0 54.4%

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

      1. associate-/l* 78.7%

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

   9. Simplified 78.7%

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

   if -210 < t < 5.6999999999999999e-36

   1. Initial program 92.6%

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

      1. associate-*l/ 94.1%

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

   3. Simplified 94.1%

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

      1. associate-/r/ 98.2%

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

   6. Applied egg-rr 98.2%

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

   7. Taylor expanded in t around 0 84.0%

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

4. Final simplification 77.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.05 \cdot 10^{+131}:\\ \;\;\;\;y - \frac{z}{\frac{t}{y - x}}\\ \mathbf{elif}\;t \leq -210:\\ \;\;\;\;\frac{y}{\frac{a - t}{z - t}}\\ \mathbf{elif}\;t \leq 5.7 \cdot 10^{-36}:\\ \;\;\;\;x + \frac{y - x}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;y - \frac{z}{\frac{t}{y - x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 59.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.6 \cdot 10^{-5} \lor \neg \left(z \leq 5.8 \cdot 10^{+71}\right):\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -4.6e-5) (not (<= z 5.8e+71)))
   (* z (/ (- y x) (- a t)))
   (* y (/ (- z t) (- a t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -4.6e-5) || !(z <= 5.8e+71)) {
		tmp = z * ((y - x) / (a - t));
	} else {
		tmp = y * ((z - t) / (a - t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-4.6d-5)) .or. (.not. (z <= 5.8d+71))) then
        tmp = z * ((y - x) / (a - t))
    else
        tmp = y * ((z - t) / (a - t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -4.6e-5) || !(z <= 5.8e+71)) {
		tmp = z * ((y - x) / (a - t));
	} else {
		tmp = y * ((z - t) / (a - t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -4.6e-5) or not (z <= 5.8e+71):
		tmp = z * ((y - x) / (a - t))
	else:
		tmp = y * ((z - t) / (a - t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -4.6e-5) || !(z <= 5.8e+71))
		tmp = Float64(z * Float64(Float64(y - x) / Float64(a - t)));
	else
		tmp = Float64(y * Float64(Float64(z - t) / Float64(a - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -4.6e-5) || ~((z <= 5.8e+71)))
		tmp = z * ((y - x) / (a - t));
	else
		tmp = y * ((z - t) / (a - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -4.6e-5], N[Not[LessEqual[z, 5.8e+71]], $MachinePrecision]], N[(z * N[(N[(y - x), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4.6e-5 or 5.80000000000000014e71 < z

   1. Initial program 69.8%

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

      1. associate-*l/ 87.1%

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

   3. Simplified 87.1%

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

   5. Taylor expanded in z around inf 72.2%

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

      1. div-sub 72.2%

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

   7. Simplified 72.2%

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

   if -4.6e-5 < z < 5.80000000000000014e71

   1. Initial program 68.0%

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

      1. associate-*l/ 78.8%

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

   3. Simplified 78.8%

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

   5. Taylor expanded in y around inf 61.1%

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

      1. div-sub 61.1%

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

   7. Simplified 61.1%

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

4. Final simplification 66.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.6 \cdot 10^{-5} \lor \neg \left(z \leq 5.8 \cdot 10^{+71}\right):\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 36.7% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.08 \cdot 10^{-101}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -2.3 \cdot 10^{-200}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 1.15 \cdot 10^{-186}:\\ \;\;\;\;y \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq 4.8 \cdot 10^{-35}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -1.08e-101)
   y
   (if (<= t -2.3e-200)
     x
     (if (<= t 1.15e-186) (* y (/ z a)) (if (<= t 4.8e-35) x y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.08e-101) {
		tmp = y;
	} else if (t <= -2.3e-200) {
		tmp = x;
	} else if (t <= 1.15e-186) {
		tmp = y * (z / a);
	} else if (t <= 4.8e-35) {
		tmp = x;
	} else {
		tmp = 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 (t <= (-1.08d-101)) then
        tmp = y
    else if (t <= (-2.3d-200)) then
        tmp = x
    else if (t <= 1.15d-186) then
        tmp = y * (z / a)
    else if (t <= 4.8d-35) then
        tmp = x
    else
        tmp = 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 (t <= -1.08e-101) {
		tmp = y;
	} else if (t <= -2.3e-200) {
		tmp = x;
	} else if (t <= 1.15e-186) {
		tmp = y * (z / a);
	} else if (t <= 4.8e-35) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -1.08e-101:
		tmp = y
	elif t <= -2.3e-200:
		tmp = x
	elif t <= 1.15e-186:
		tmp = y * (z / a)
	elif t <= 4.8e-35:
		tmp = x
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -1.08e-101)
		tmp = y;
	elseif (t <= -2.3e-200)
		tmp = x;
	elseif (t <= 1.15e-186)
		tmp = Float64(y * Float64(z / a));
	elseif (t <= 4.8e-35)
		tmp = x;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -1.08e-101)
		tmp = y;
	elseif (t <= -2.3e-200)
		tmp = x;
	elseif (t <= 1.15e-186)
		tmp = y * (z / a);
	elseif (t <= 4.8e-35)
		tmp = x;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -1.08e-101], y, If[LessEqual[t, -2.3e-200], x, If[LessEqual[t, 1.15e-186], N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4.8e-35], x, y]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.08e-101 or 4.8000000000000003e-35 < t

   1. Initial program 54.3%

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

      1. associate-*l/ 76.6%

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

   3. Simplified 76.6%

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

   5. Taylor expanded in t around inf 41.0%

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

   if -1.08e-101 < t < -2.30000000000000007e-200 or 1.15e-186 < t < 4.8000000000000003e-35

   1. Initial program 94.1%

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

      1. associate-*l/ 93.5%

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

   3. Simplified 93.5%

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

   5. Taylor expanded in a around inf 47.3%

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

   if -2.30000000000000007e-200 < t < 1.15e-186

   1. Initial program 95.0%

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

      1. associate-*l/ 95.1%

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

   3. Simplified 95.1%

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

   5. Taylor expanded in y around inf 50.7%

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

      1. div-sub 50.7%

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

   7. Simplified 50.7%

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

   8. Taylor expanded in t around 0 48.1%

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

4. Final simplification 43.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.08 \cdot 10^{-101}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -2.3 \cdot 10^{-200}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 1.15 \cdot 10^{-186}:\\ \;\;\;\;y \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq 4.8 \cdot 10^{-35}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 36.7% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.75 \cdot 10^{-101}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -3.5 \cdot 10^{-277}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 1.15 \cdot 10^{-188}:\\ \;\;\;\;z \cdot \frac{y}{a}\\ \mathbf{elif}\;t \leq 1.6 \cdot 10^{-35}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -2.75e-101)
   y
   (if (<= t -3.5e-277)
     x
     (if (<= t 1.15e-188) (* z (/ y a)) (if (<= t 1.6e-35) x y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -2.75e-101) {
		tmp = y;
	} else if (t <= -3.5e-277) {
		tmp = x;
	} else if (t <= 1.15e-188) {
		tmp = z * (y / a);
	} else if (t <= 1.6e-35) {
		tmp = x;
	} else {
		tmp = 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 (t <= (-2.75d-101)) then
        tmp = y
    else if (t <= (-3.5d-277)) then
        tmp = x
    else if (t <= 1.15d-188) then
        tmp = z * (y / a)
    else if (t <= 1.6d-35) then
        tmp = x
    else
        tmp = 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 (t <= -2.75e-101) {
		tmp = y;
	} else if (t <= -3.5e-277) {
		tmp = x;
	} else if (t <= 1.15e-188) {
		tmp = z * (y / a);
	} else if (t <= 1.6e-35) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -2.75e-101:
		tmp = y
	elif t <= -3.5e-277:
		tmp = x
	elif t <= 1.15e-188:
		tmp = z * (y / a)
	elif t <= 1.6e-35:
		tmp = x
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -2.75e-101)
		tmp = y;
	elseif (t <= -3.5e-277)
		tmp = x;
	elseif (t <= 1.15e-188)
		tmp = Float64(z * Float64(y / a));
	elseif (t <= 1.6e-35)
		tmp = x;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -2.75e-101)
		tmp = y;
	elseif (t <= -3.5e-277)
		tmp = x;
	elseif (t <= 1.15e-188)
		tmp = z * (y / a);
	elseif (t <= 1.6e-35)
		tmp = x;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -2.75e-101], y, If[LessEqual[t, -3.5e-277], x, If[LessEqual[t, 1.15e-188], N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.6e-35], x, y]]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.74999999999999986e-101 or 1.5999999999999999e-35 < t

   1. Initial program 54.3%

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

      1. associate-*l/ 76.6%

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

   3. Simplified 76.6%

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

   5. Taylor expanded in t around inf 41.0%

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

   if -2.74999999999999986e-101 < t < -3.49999999999999983e-277 or 1.15e-188 < t < 1.5999999999999999e-35

   1. Initial program 95.5%

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

      1. associate-*l/ 93.8%

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

   3. Simplified 93.8%

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

   5. Taylor expanded in a around inf 44.1%

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

   if -3.49999999999999983e-277 < t < 1.15e-188

   1. Initial program 91.0%

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

      1. associate-*l/ 95.5%

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

   3. Simplified 95.5%

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

   5. Taylor expanded in y around inf 60.7%

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

      1. div-sub 60.7%

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

   7. Simplified 60.7%

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

   8. Taylor expanded in t around 0 56.1%

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

   9. Taylor expanded in y around 0 56.1%

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

       1. associate-*l/ 60.2%

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

   11. Simplified 60.2%

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

4. Final simplification 43.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.75 \cdot 10^{-101}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -3.5 \cdot 10^{-277}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 1.15 \cdot 10^{-188}:\\ \;\;\;\;z \cdot \frac{y}{a}\\ \mathbf{elif}\;t \leq 1.6 \cdot 10^{-35}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 37.0% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -6 \cdot 10^{-101}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 1.6 \cdot 10^{-35}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -6e-101) y (if (<= t 1.6e-35) x y)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -6e-101) {
		tmp = y;
	} else if (t <= 1.6e-35) {
		tmp = x;
	} else {
		tmp = 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 (t <= (-6d-101)) then
        tmp = y
    else if (t <= 1.6d-35) then
        tmp = x
    else
        tmp = 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 (t <= -6e-101) {
		tmp = y;
	} else if (t <= 1.6e-35) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -6e-101:
		tmp = y
	elif t <= 1.6e-35:
		tmp = x
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -6e-101)
		tmp = y;
	elseif (t <= 1.6e-35)
		tmp = x;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -6e-101)
		tmp = y;
	elseif (t <= 1.6e-35)
		tmp = x;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -6e-101], y, If[LessEqual[t, 1.6e-35], x, y]]

Derivation

1. Split input into 2 regimes

2. if t < -6.0000000000000006e-101 or 1.5999999999999999e-35 < t

   1. Initial program 54.3%

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

      1. associate-*l/ 76.6%

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

   3. Simplified 76.6%

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

   5. Taylor expanded in t around inf 41.0%

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

   if -6.0000000000000006e-101 < t < 1.5999999999999999e-35

   1. Initial program 94.4%

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

      1. associate-*l/ 94.2%

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

   3. Simplified 94.2%

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

   5. Taylor expanded in a around inf 34.6%

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

4. Final simplification 38.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6 \cdot 10^{-101}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 1.6 \cdot 10^{-35}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 25.2% accurate, 13.0× 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 68.9%

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

   1. associate-*l/ 83.0%

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

3. Simplified 83.0%

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

5. Taylor expanded in a around inf 19.1%

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

6. Final simplification 19.1%

   \[\leadsto x \]
7. Add Preprocessing

Developer target: 86.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y - x}{1} \cdot \frac{z - t}{a - t}\\ \mathbf{if}\;a < -1.6153062845442575 \cdot 10^{-142}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a < 3.774403170083174 \cdot 10^{-182}:\\ \;\;\;\;y - \frac{z}{t} \cdot \left(y - x\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (/ (- y x) 1.0) (/ (- z t) (- a t))))))
   (if (< a -1.6153062845442575e-142)
     t_1
     (if (< a 3.774403170083174e-182) (- y (* (/ z t) (- y x))) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (((y - x) / 1.0) * ((z - t) / (a - t)));
	double tmp;
	if (a < -1.6153062845442575e-142) {
		tmp = t_1;
	} else if (a < 3.774403170083174e-182) {
		tmp = y - ((z / t) * (y - x));
	} else {
		tmp = t_1;
	}
	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 - x) / 1.0d0) * ((z - t) / (a - t)))
    if (a < (-1.6153062845442575d-142)) then
        tmp = t_1
    else if (a < 3.774403170083174d-182) then
        tmp = y - ((z / t) * (y - x))
    else
        tmp = t_1
    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 - x) / 1.0) * ((z - t) / (a - t)));
	double tmp;
	if (a < -1.6153062845442575e-142) {
		tmp = t_1;
	} else if (a < 3.774403170083174e-182) {
		tmp = y - ((z / t) * (y - x));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (((y - x) / 1.0) * ((z - t) / (a - t)))
	tmp = 0
	if a < -1.6153062845442575e-142:
		tmp = t_1
	elif a < 3.774403170083174e-182:
		tmp = y - ((z / t) * (y - x))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(Float64(y - x) / 1.0) * Float64(Float64(z - t) / Float64(a - t))))
	tmp = 0.0
	if (a < -1.6153062845442575e-142)
		tmp = t_1;
	elseif (a < 3.774403170083174e-182)
		tmp = Float64(y - Float64(Float64(z / t) * Float64(y - x)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (((y - x) / 1.0) * ((z - t) / (a - t)));
	tmp = 0.0;
	if (a < -1.6153062845442575e-142)
		tmp = t_1;
	elseif (a < 3.774403170083174e-182)
		tmp = y - ((z / t) * (y - x));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(N[(y - x), $MachinePrecision] / 1.0), $MachinePrecision] * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Less[a, -1.6153062845442575e-142], t$95$1, If[Less[a, 3.774403170083174e-182], N[(y - N[(N[(z / t), $MachinePrecision] * N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Reproduce

herbie shell --seed 2024011 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Chart.Axis.Types:linMap from Chart-1.5.3"
  :precision binary64

  :herbie-target
  (if (< a -1.6153062845442575e-142) (+ x (* (/ (- y x) 1.0) (/ (- z t) (- a t)))) (if (< a 3.774403170083174e-182) (- y (* (/ z t) (- y x))) (+ x (* (/ (- y x) 1.0) (/ (- z t) (- a t))))))

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