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

Percentage Accurate: 67.3% → 89.2%

Time: 27.2s

Alternatives: 25

Speedup: 0.8×

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: 67.3% 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

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -9.5 \cdot 10^{+99} \lor \neg \left(t \leq 1.8 \cdot 10^{+177}\right):\\ \;\;\;\;y + \frac{x - y}{\frac{t}{z - a}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{\frac{a - t}{z - t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -9.5e+99) (not (<= t 1.8e+177)))
   (+ y (/ (- x y) (/ t (- z a))))
   (+ x (/ (- y x) (/ (- a t) (- z t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -9.5e+99) || !(t <= 1.8e+177)) {
		tmp = y + ((x - y) / (t / (z - a)));
	} else {
		tmp = x + ((y - x) / ((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 <= (-9.5d+99)) .or. (.not. (t <= 1.8d+177))) then
        tmp = y + ((x - y) / (t / (z - a)))
    else
        tmp = x + ((y - x) / ((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 <= -9.5e+99) || !(t <= 1.8e+177)) {
		tmp = y + ((x - y) / (t / (z - a)));
	} else {
		tmp = x + ((y - x) / ((a - t) / (z - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -9.5e+99) or not (t <= 1.8e+177):
		tmp = y + ((x - y) / (t / (z - a)))
	else:
		tmp = x + ((y - x) / ((a - t) / (z - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -9.5e+99) || !(t <= 1.8e+177))
		tmp = Float64(y + Float64(Float64(x - y) / Float64(t / Float64(z - a))));
	else
		tmp = Float64(x + Float64(Float64(y - x) / 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 <= -9.5e+99) || ~((t <= 1.8e+177)))
		tmp = y + ((x - y) / (t / (z - a)));
	else
		tmp = x + ((y - x) / ((a - t) / (z - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -9.5e+99], N[Not[LessEqual[t, 1.8e+177]], $MachinePrecision]], N[(y + N[(N[(x - y), $MachinePrecision] / N[(t / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y - x), $MachinePrecision] / N[(N[(a - t), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -9.49999999999999908e99 or 1.80000000000000001e177 < t

   1. Initial program 23.9%

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

      1. associate-*l/ 51.9%

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

   3. Simplified 51.9%

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

   4. Taylor expanded in t around inf 60.4%

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

      1. associate--l+ 60.4%

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

      2. distribute-lft-out-- 60.4%

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

      3. div-sub 60.4%

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

      4. mul-1-neg 60.4%

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

      5. unsub-neg 60.4%

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

      6. distribute-rgt-out-- 60.6%

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

   6. Simplified 60.6%

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

      1. sub-neg 60.6%

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

      2. associate-/l* 89.3%

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

   8. Applied egg-rr 89.3%

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

   if -9.49999999999999908e99 < t < 1.80000000000000001e177

   1. Initial program 85.4%

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

      1. associate-/l* 91.1%

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

   3. Simplified 91.1%

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

4. Final simplification 90.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -9.5 \cdot 10^{+99} \lor \neg \left(t \leq 1.8 \cdot 10^{+177}\right):\\ \;\;\;\;y + \frac{x - y}{\frac{t}{z - a}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{\frac{a - t}{z - t}}\\ \end{array} \]

Alternative 2: 65.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{z}{\frac{a}{y - x}}\\ t_2 := y \cdot \frac{z - t}{a - t}\\ \mathbf{if}\;t \leq -4.4 \cdot 10^{+86}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -1.08 \cdot 10^{+17}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -1.4 \cdot 10^{-18}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -2.05 \cdot 10^{-161}:\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;t \leq 1.3 \cdot 10^{-72}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.7 \cdot 10^{-17}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ z (/ a (- y x))))) (t_2 (* y (/ (- z t) (- a t)))))
   (if (<= t -4.4e+86)
     t_2
     (if (<= t -1.08e+17)
       t_1
       (if (<= t -1.4e-18)
         t_2
         (if (<= t -2.05e-161)
           (+ x (* (- z t) (/ y a)))
           (if (<= t 1.3e-72)
             t_1
             (if (<= t 1.7e-17) (+ x (/ (* y (- z t)) a)) t_2))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (z / (a / (y - x)));
	double t_2 = y * ((z - t) / (a - t));
	double tmp;
	if (t <= -4.4e+86) {
		tmp = t_2;
	} else if (t <= -1.08e+17) {
		tmp = t_1;
	} else if (t <= -1.4e-18) {
		tmp = t_2;
	} else if (t <= -2.05e-161) {
		tmp = x + ((z - t) * (y / a));
	} else if (t <= 1.3e-72) {
		tmp = t_1;
	} else if (t <= 1.7e-17) {
		tmp = x + ((y * (z - t)) / a);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x + (z / (a / (y - x)))
    t_2 = y * ((z - t) / (a - t))
    if (t <= (-4.4d+86)) then
        tmp = t_2
    else if (t <= (-1.08d+17)) then
        tmp = t_1
    else if (t <= (-1.4d-18)) then
        tmp = t_2
    else if (t <= (-2.05d-161)) then
        tmp = x + ((z - t) * (y / a))
    else if (t <= 1.3d-72) then
        tmp = t_1
    else if (t <= 1.7d-17) then
        tmp = x + ((y * (z - t)) / a)
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (z / (a / (y - x)));
	double t_2 = y * ((z - t) / (a - t));
	double tmp;
	if (t <= -4.4e+86) {
		tmp = t_2;
	} else if (t <= -1.08e+17) {
		tmp = t_1;
	} else if (t <= -1.4e-18) {
		tmp = t_2;
	} else if (t <= -2.05e-161) {
		tmp = x + ((z - t) * (y / a));
	} else if (t <= 1.3e-72) {
		tmp = t_1;
	} else if (t <= 1.7e-17) {
		tmp = x + ((y * (z - t)) / a);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (z / (a / (y - x)))
	t_2 = y * ((z - t) / (a - t))
	tmp = 0
	if t <= -4.4e+86:
		tmp = t_2
	elif t <= -1.08e+17:
		tmp = t_1
	elif t <= -1.4e-18:
		tmp = t_2
	elif t <= -2.05e-161:
		tmp = x + ((z - t) * (y / a))
	elif t <= 1.3e-72:
		tmp = t_1
	elif t <= 1.7e-17:
		tmp = x + ((y * (z - t)) / a)
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(z / Float64(a / Float64(y - x))))
	t_2 = Float64(y * Float64(Float64(z - t) / Float64(a - t)))
	tmp = 0.0
	if (t <= -4.4e+86)
		tmp = t_2;
	elseif (t <= -1.08e+17)
		tmp = t_1;
	elseif (t <= -1.4e-18)
		tmp = t_2;
	elseif (t <= -2.05e-161)
		tmp = Float64(x + Float64(Float64(z - t) * Float64(y / a)));
	elseif (t <= 1.3e-72)
		tmp = t_1;
	elseif (t <= 1.7e-17)
		tmp = Float64(x + Float64(Float64(y * Float64(z - t)) / a));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (z / (a / (y - x)));
	t_2 = y * ((z - t) / (a - t));
	tmp = 0.0;
	if (t <= -4.4e+86)
		tmp = t_2;
	elseif (t <= -1.08e+17)
		tmp = t_1;
	elseif (t <= -1.4e-18)
		tmp = t_2;
	elseif (t <= -2.05e-161)
		tmp = x + ((z - t) * (y / a));
	elseif (t <= 1.3e-72)
		tmp = t_1;
	elseif (t <= 1.7e-17)
		tmp = x + ((y * (z - t)) / a);
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(z / N[(a / N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -4.4e+86], t$95$2, If[LessEqual[t, -1.08e+17], t$95$1, If[LessEqual[t, -1.4e-18], t$95$2, If[LessEqual[t, -2.05e-161], N[(x + N[(N[(z - t), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.3e-72], t$95$1, If[LessEqual[t, 1.7e-17], N[(x + N[(N[(y * N[(z - t), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -4.40000000000000006e86 or -1.08e17 < t < -1.40000000000000006e-18 or 1.6999999999999999e-17 < t

   1. Initial program 41.2%

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

      1. associate-*l/ 63.0%

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

   3. Simplified 63.0%

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

   4. Taylor expanded in x around 0 45.7%

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

      1. associate-*r/ 67.5%

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

   6. Simplified 67.5%

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

   if -4.40000000000000006e86 < t < -1.08e17 or -2.0499999999999999e-161 < t < 1.29999999999999998e-72

   1. Initial program 92.9%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   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. Taylor expanded in t around 0 76.9%

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

      1. associate-/l* 80.5%

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

   6. Simplified 80.5%

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

   if -1.40000000000000006e-18 < t < -2.0499999999999999e-161

   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/ 92.5%

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

   3. Simplified 92.5%

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

   4. Taylor expanded in a around inf 70.2%

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

   5. Taylor expanded in y around inf 73.9%

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

   if 1.29999999999999998e-72 < t < 1.6999999999999999e-17

   1. Initial program 81.6%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   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. Taylor expanded in a around inf 69.5%

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

   5. Taylor expanded in y around inf 67.6%

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

4. Final simplification 72.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.4 \cdot 10^{+86}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;t \leq -1.08 \cdot 10^{+17}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y - x}}\\ \mathbf{elif}\;t \leq -1.4 \cdot 10^{-18}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;t \leq -2.05 \cdot 10^{-161}:\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;t \leq 1.3 \cdot 10^{-72}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y - x}}\\ \mathbf{elif}\;t \leq 1.7 \cdot 10^{-17}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \end{array} \]

Alternative 3: 66.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{z - t}{a - t}\\ \mathbf{if}\;t \leq -4.1 \cdot 10^{+82}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -48000000000000:\\ \;\;\;\;x + \frac{z}{\frac{a}{y - x}}\\ \mathbf{elif}\;t \leq -1.3 \cdot 10^{-18}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -8.2 \cdot 10^{-160}:\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;t \leq 1.85 \cdot 10^{-14}:\\ \;\;\;\;x + \frac{y - x}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 7.5 \cdot 10^{+177}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;y + \frac{a}{\frac{t}{y - x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ (- z t) (- a t)))))
   (if (<= t -4.1e+82)
     t_1
     (if (<= t -48000000000000.0)
       (+ x (/ z (/ a (- y x))))
       (if (<= t -1.3e-18)
         t_1
         (if (<= t -8.2e-160)
           (+ x (* (- z t) (/ y a)))
           (if (<= t 1.85e-14)
             (+ x (/ (- y x) (/ a z)))
             (if (<= t 7.5e+177) t_1 (+ y (/ a (/ t (- 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 <= -4.1e+82) {
		tmp = t_1;
	} else if (t <= -48000000000000.0) {
		tmp = x + (z / (a / (y - x)));
	} else if (t <= -1.3e-18) {
		tmp = t_1;
	} else if (t <= -8.2e-160) {
		tmp = x + ((z - t) * (y / a));
	} else if (t <= 1.85e-14) {
		tmp = x + ((y - x) / (a / z));
	} else if (t <= 7.5e+177) {
		tmp = t_1;
	} else {
		tmp = y + (a / (t / (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 <= (-4.1d+82)) then
        tmp = t_1
    else if (t <= (-48000000000000.0d0)) then
        tmp = x + (z / (a / (y - x)))
    else if (t <= (-1.3d-18)) then
        tmp = t_1
    else if (t <= (-8.2d-160)) then
        tmp = x + ((z - t) * (y / a))
    else if (t <= 1.85d-14) then
        tmp = x + ((y - x) / (a / z))
    else if (t <= 7.5d+177) then
        tmp = t_1
    else
        tmp = y + (a / (t / (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 <= -4.1e+82) {
		tmp = t_1;
	} else if (t <= -48000000000000.0) {
		tmp = x + (z / (a / (y - x)));
	} else if (t <= -1.3e-18) {
		tmp = t_1;
	} else if (t <= -8.2e-160) {
		tmp = x + ((z - t) * (y / a));
	} else if (t <= 1.85e-14) {
		tmp = x + ((y - x) / (a / z));
	} else if (t <= 7.5e+177) {
		tmp = t_1;
	} else {
		tmp = y + (a / (t / (y - x)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * ((z - t) / (a - t))
	tmp = 0
	if t <= -4.1e+82:
		tmp = t_1
	elif t <= -48000000000000.0:
		tmp = x + (z / (a / (y - x)))
	elif t <= -1.3e-18:
		tmp = t_1
	elif t <= -8.2e-160:
		tmp = x + ((z - t) * (y / a))
	elif t <= 1.85e-14:
		tmp = x + ((y - x) / (a / z))
	elif t <= 7.5e+177:
		tmp = t_1
	else:
		tmp = y + (a / (t / (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 <= -4.1e+82)
		tmp = t_1;
	elseif (t <= -48000000000000.0)
		tmp = Float64(x + Float64(z / Float64(a / Float64(y - x))));
	elseif (t <= -1.3e-18)
		tmp = t_1;
	elseif (t <= -8.2e-160)
		tmp = Float64(x + Float64(Float64(z - t) * Float64(y / a)));
	elseif (t <= 1.85e-14)
		tmp = Float64(x + Float64(Float64(y - x) / Float64(a / z)));
	elseif (t <= 7.5e+177)
		tmp = t_1;
	else
		tmp = Float64(y + Float64(a / Float64(t / 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 <= -4.1e+82)
		tmp = t_1;
	elseif (t <= -48000000000000.0)
		tmp = x + (z / (a / (y - x)));
	elseif (t <= -1.3e-18)
		tmp = t_1;
	elseif (t <= -8.2e-160)
		tmp = x + ((z - t) * (y / a));
	elseif (t <= 1.85e-14)
		tmp = x + ((y - x) / (a / z));
	elseif (t <= 7.5e+177)
		tmp = t_1;
	else
		tmp = y + (a / (t / (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, -4.1e+82], t$95$1, If[LessEqual[t, -48000000000000.0], N[(x + N[(z / N[(a / N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -1.3e-18], t$95$1, If[LessEqual[t, -8.2e-160], N[(x + N[(N[(z - t), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.85e-14], N[(x + N[(N[(y - x), $MachinePrecision] / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 7.5e+177], t$95$1, N[(y + N[(a / N[(t / N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -4.09999999999999995e82 or -4.8e13 < t < -1.3e-18 or 1.85000000000000001e-14 < t < 7.50000000000000039e177

   1. Initial program 51.1%

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

      1. associate-*l/ 69.6%

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

   3. Simplified 69.6%

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

   4. Taylor expanded in x around 0 52.7%

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

      1. associate-*r/ 72.3%

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

   6. Simplified 72.3%

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

   if -4.09999999999999995e82 < t < -4.8e13

   1. Initial program 77.9%

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

      1. associate-*l/ 85.0%

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

   3. Simplified 85.0%

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

   4. Taylor expanded in t around 0 57.9%

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

      1. associate-/l* 65.1%

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

   6. Simplified 65.1%

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

   if -1.3e-18 < t < -8.20000000000000003e-160

   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/ 92.5%

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

   3. Simplified 92.5%

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

   4. Taylor expanded in a around inf 70.2%

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

   5. Taylor expanded in y around inf 73.9%

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

   if -8.20000000000000003e-160 < t < 1.85000000000000001e-14

   1. Initial program 92.4%

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

      1. associate-/l* 93.6%

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

   3. Simplified 93.6%

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

   4. Taylor expanded in t around 0 77.0%

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

   if 7.50000000000000039e177 < t

   1. Initial program 15.2%

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

      1. associate-*l/ 45.8%

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

   3. Simplified 45.8%

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

   4. Taylor expanded in t around inf 46.8%

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

      1. associate--l+ 46.8%

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

      2. distribute-lft-out-- 46.8%

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

      3. div-sub 46.8%

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

      4. mul-1-neg 46.8%

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

      5. unsub-neg 46.8%

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

      6. distribute-rgt-out-- 47.0%

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

   6. Simplified 47.0%

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

   7. Taylor expanded in z around 0 47.2%

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

      1. sub-neg 47.2%

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

      2. mul-1-neg 47.2%

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

      3. remove-double-neg 47.2%

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

      4. associate-/l* 69.4%

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

   9. Simplified 69.4%

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

4. Final simplification 73.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.1 \cdot 10^{+82}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;t \leq -48000000000000:\\ \;\;\;\;x + \frac{z}{\frac{a}{y - x}}\\ \mathbf{elif}\;t \leq -1.3 \cdot 10^{-18}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;t \leq -8.2 \cdot 10^{-160}:\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;t \leq 1.85 \cdot 10^{-14}:\\ \;\;\;\;x + \frac{y - x}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 7.5 \cdot 10^{+177}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;y + \frac{a}{\frac{t}{y - x}}\\ \end{array} \]

Alternative 4: 68.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y - \frac{z}{\frac{t}{y - x}}\\ \mathbf{if}\;t \leq -4.1 \cdot 10^{+82}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -1.45 \cdot 10^{+43}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y - x}}\\ \mathbf{elif}\;t \leq -2.75 \cdot 10^{-19}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -2.5 \cdot 10^{-159}:\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;t \leq 3.9 \cdot 10^{-15}:\\ \;\;\;\;x + \frac{y - x}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 2.7 \cdot 10^{+179}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- y (/ z (/ t (- y x))))))
   (if (<= t -4.1e+82)
     t_1
     (if (<= t -1.45e+43)
       (+ x (/ z (/ a (- y x))))
       (if (<= t -2.75e-19)
         t_1
         (if (<= t -2.5e-159)
           (+ x (* (- z t) (/ y a)))
           (if (<= t 3.9e-15)
             (+ x (/ (- y x) (/ a z)))
             (if (<= t 2.7e+179) (* y (/ (- z t) (- a t))) 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 <= -4.1e+82) {
		tmp = t_1;
	} else if (t <= -1.45e+43) {
		tmp = x + (z / (a / (y - x)));
	} else if (t <= -2.75e-19) {
		tmp = t_1;
	} else if (t <= -2.5e-159) {
		tmp = x + ((z - t) * (y / a));
	} else if (t <= 3.9e-15) {
		tmp = x + ((y - x) / (a / z));
	} else if (t <= 2.7e+179) {
		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 - (z / (t / (y - x)))
    if (t <= (-4.1d+82)) then
        tmp = t_1
    else if (t <= (-1.45d+43)) then
        tmp = x + (z / (a / (y - x)))
    else if (t <= (-2.75d-19)) then
        tmp = t_1
    else if (t <= (-2.5d-159)) then
        tmp = x + ((z - t) * (y / a))
    else if (t <= 3.9d-15) then
        tmp = x + ((y - x) / (a / z))
    else if (t <= 2.7d+179) 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 - (z / (t / (y - x)));
	double tmp;
	if (t <= -4.1e+82) {
		tmp = t_1;
	} else if (t <= -1.45e+43) {
		tmp = x + (z / (a / (y - x)));
	} else if (t <= -2.75e-19) {
		tmp = t_1;
	} else if (t <= -2.5e-159) {
		tmp = x + ((z - t) * (y / a));
	} else if (t <= 3.9e-15) {
		tmp = x + ((y - x) / (a / z));
	} else if (t <= 2.7e+179) {
		tmp = y * ((z - t) / (a - t));
	} 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 <= -4.1e+82:
		tmp = t_1
	elif t <= -1.45e+43:
		tmp = x + (z / (a / (y - x)))
	elif t <= -2.75e-19:
		tmp = t_1
	elif t <= -2.5e-159:
		tmp = x + ((z - t) * (y / a))
	elif t <= 3.9e-15:
		tmp = x + ((y - x) / (a / z))
	elif t <= 2.7e+179:
		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(z / Float64(t / Float64(y - x))))
	tmp = 0.0
	if (t <= -4.1e+82)
		tmp = t_1;
	elseif (t <= -1.45e+43)
		tmp = Float64(x + Float64(z / Float64(a / Float64(y - x))));
	elseif (t <= -2.75e-19)
		tmp = t_1;
	elseif (t <= -2.5e-159)
		tmp = Float64(x + Float64(Float64(z - t) * Float64(y / a)));
	elseif (t <= 3.9e-15)
		tmp = Float64(x + Float64(Float64(y - x) / Float64(a / z)));
	elseif (t <= 2.7e+179)
		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 - (z / (t / (y - x)));
	tmp = 0.0;
	if (t <= -4.1e+82)
		tmp = t_1;
	elseif (t <= -1.45e+43)
		tmp = x + (z / (a / (y - x)));
	elseif (t <= -2.75e-19)
		tmp = t_1;
	elseif (t <= -2.5e-159)
		tmp = x + ((z - t) * (y / a));
	elseif (t <= 3.9e-15)
		tmp = x + ((y - x) / (a / z));
	elseif (t <= 2.7e+179)
		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[(z / N[(t / N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -4.1e+82], t$95$1, If[LessEqual[t, -1.45e+43], N[(x + N[(z / N[(a / N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -2.75e-19], t$95$1, If[LessEqual[t, -2.5e-159], N[(x + N[(N[(z - t), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.9e-15], N[(x + N[(N[(y - x), $MachinePrecision] / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.7e+179], N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -4.09999999999999995e82 or -1.4500000000000001e43 < t < -2.7499999999999998e-19 or 2.69999999999999982e179 < t

   1. Initial program 30.6%

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

      1. associate-*l/ 54.6%

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

   3. Simplified 54.6%

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

   4. Taylor expanded in t around inf 62.8%

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

      1. associate--l+ 62.8%

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

      2. distribute-lft-out-- 62.8%

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

      3. div-sub 62.8%

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

      4. mul-1-neg 62.8%

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

      5. unsub-neg 62.8%

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

      6. distribute-rgt-out-- 62.9%

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

   6. Simplified 62.9%

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

   7. Taylor expanded in z around inf 58.0%

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

      1. associate-/l* 70.6%

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

   9. Simplified 70.6%

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

   if -4.09999999999999995e82 < t < -1.4500000000000001e43

   1. Initial program 88.3%

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

      1. associate-*l/ 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in t around 0 68.5%

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

      1. associate-/l* 80.1%

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

   6. Simplified 80.1%

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

   if -2.7499999999999998e-19 < t < -2.50000000000000016e-159

   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/ 92.5%

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

   3. Simplified 92.5%

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

   4. Taylor expanded in a around inf 70.2%

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

   5. Taylor expanded in y around inf 73.9%

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

   if -2.50000000000000016e-159 < t < 3.90000000000000026e-15

   1. Initial program 92.4%

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

      1. associate-/l* 93.6%

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

   3. Simplified 93.6%

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

   4. Taylor expanded in t around 0 77.0%

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

   if 3.90000000000000026e-15 < t < 2.69999999999999982e179

   1. Initial program 64.8%

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

      1. associate-*l/ 79.7%

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

   3. Simplified 79.7%

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

   4. Taylor expanded in x around 0 65.7%

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

      1. associate-*r/ 78.5%

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

   6. Simplified 78.5%

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

4. Final simplification 74.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.1 \cdot 10^{+82}:\\ \;\;\;\;y - \frac{z}{\frac{t}{y - x}}\\ \mathbf{elif}\;t \leq -1.45 \cdot 10^{+43}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y - x}}\\ \mathbf{elif}\;t \leq -2.75 \cdot 10^{-19}:\\ \;\;\;\;y - \frac{z}{\frac{t}{y - x}}\\ \mathbf{elif}\;t \leq -2.5 \cdot 10^{-159}:\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;t \leq 3.9 \cdot 10^{-15}:\\ \;\;\;\;x + \frac{y - x}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 2.7 \cdot 10^{+179}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;y - \frac{z}{\frac{t}{y - x}}\\ \end{array} \]

Alternative 5: 65.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{z}{\frac{a}{y - x}}\\ t_2 := y \cdot \frac{z - t}{a - t}\\ \mathbf{if}\;t \leq -3.7 \cdot 10^{+84}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -1.16 \cdot 10^{+17}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -1.45 \cdot 10^{-19}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -2.9 \cdot 10^{-160}:\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;t \leq 2.9 \cdot 10^{-18}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ z (/ a (- y x))))) (t_2 (* y (/ (- z t) (- a t)))))
   (if (<= t -3.7e+84)
     t_2
     (if (<= t -1.16e+17)
       t_1
       (if (<= t -1.45e-19)
         t_2
         (if (<= t -2.9e-160)
           (+ x (* (- z t) (/ y a)))
           (if (<= t 2.9e-18) t_1 t_2)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (z / (a / (y - x)));
	double t_2 = y * ((z - t) / (a - t));
	double tmp;
	if (t <= -3.7e+84) {
		tmp = t_2;
	} else if (t <= -1.16e+17) {
		tmp = t_1;
	} else if (t <= -1.45e-19) {
		tmp = t_2;
	} else if (t <= -2.9e-160) {
		tmp = x + ((z - t) * (y / a));
	} else if (t <= 2.9e-18) {
		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 = x + (z / (a / (y - x)))
    t_2 = y * ((z - t) / (a - t))
    if (t <= (-3.7d+84)) then
        tmp = t_2
    else if (t <= (-1.16d+17)) then
        tmp = t_1
    else if (t <= (-1.45d-19)) then
        tmp = t_2
    else if (t <= (-2.9d-160)) then
        tmp = x + ((z - t) * (y / a))
    else if (t <= 2.9d-18) 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 = x + (z / (a / (y - x)));
	double t_2 = y * ((z - t) / (a - t));
	double tmp;
	if (t <= -3.7e+84) {
		tmp = t_2;
	} else if (t <= -1.16e+17) {
		tmp = t_1;
	} else if (t <= -1.45e-19) {
		tmp = t_2;
	} else if (t <= -2.9e-160) {
		tmp = x + ((z - t) * (y / a));
	} else if (t <= 2.9e-18) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (z / (a / (y - x)))
	t_2 = y * ((z - t) / (a - t))
	tmp = 0
	if t <= -3.7e+84:
		tmp = t_2
	elif t <= -1.16e+17:
		tmp = t_1
	elif t <= -1.45e-19:
		tmp = t_2
	elif t <= -2.9e-160:
		tmp = x + ((z - t) * (y / a))
	elif t <= 2.9e-18:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(z / Float64(a / Float64(y - x))))
	t_2 = Float64(y * Float64(Float64(z - t) / Float64(a - t)))
	tmp = 0.0
	if (t <= -3.7e+84)
		tmp = t_2;
	elseif (t <= -1.16e+17)
		tmp = t_1;
	elseif (t <= -1.45e-19)
		tmp = t_2;
	elseif (t <= -2.9e-160)
		tmp = Float64(x + Float64(Float64(z - t) * Float64(y / a)));
	elseif (t <= 2.9e-18)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (z / (a / (y - x)));
	t_2 = y * ((z - t) / (a - t));
	tmp = 0.0;
	if (t <= -3.7e+84)
		tmp = t_2;
	elseif (t <= -1.16e+17)
		tmp = t_1;
	elseif (t <= -1.45e-19)
		tmp = t_2;
	elseif (t <= -2.9e-160)
		tmp = x + ((z - t) * (y / a));
	elseif (t <= 2.9e-18)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(z / N[(a / N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -3.7e+84], t$95$2, If[LessEqual[t, -1.16e+17], t$95$1, If[LessEqual[t, -1.45e-19], t$95$2, If[LessEqual[t, -2.9e-160], N[(x + N[(N[(z - t), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.9e-18], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -3.7e84 or -1.16e17 < t < -1.45e-19 or 2.9e-18 < t

   1. Initial program 41.2%

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

      1. associate-*l/ 63.0%

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

   3. Simplified 63.0%

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

   4. Taylor expanded in x around 0 45.7%

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

      1. associate-*r/ 67.5%

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

   6. Simplified 67.5%

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

   if -3.7e84 < t < -1.16e17 or -2.8999999999999999e-160 < t < 2.9e-18

   1. Initial program 90.6%

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

      1. associate-*l/ 91.7%

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

   3. Simplified 91.7%

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

   4. Taylor expanded in t around 0 71.8%

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

      1. associate-/l* 74.6%

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

   6. Simplified 74.6%

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

   if -1.45e-19 < t < -2.8999999999999999e-160

   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/ 92.5%

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

   3. Simplified 92.5%

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

   4. Taylor expanded in a around inf 70.2%

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

   5. Taylor expanded in y around inf 73.9%

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

4. Final simplification 71.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.7 \cdot 10^{+84}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;t \leq -1.16 \cdot 10^{+17}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y - x}}\\ \mathbf{elif}\;t \leq -1.45 \cdot 10^{-19}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;t \leq -2.9 \cdot 10^{-160}:\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;t \leq 2.9 \cdot 10^{-18}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y - x}}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \end{array} \]

Alternative 6: 66.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{z - t}{a - t}\\ \mathbf{if}\;t \leq -4.1 \cdot 10^{+82}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -8 \cdot 10^{+16}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y - x}}\\ \mathbf{elif}\;t \leq -7.6 \cdot 10^{-19}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -7.6 \cdot 10^{-159}:\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;t \leq 7 \cdot 10^{-15}:\\ \;\;\;\;x + \frac{y - x}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ (- z t) (- a t)))))
   (if (<= t -4.1e+82)
     t_1
     (if (<= t -8e+16)
       (+ x (/ z (/ a (- y x))))
       (if (<= t -7.6e-19)
         t_1
         (if (<= t -7.6e-159)
           (+ x (* (- z t) (/ y a)))
           (if (<= t 7e-15) (+ 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) / (a - t));
	double tmp;
	if (t <= -4.1e+82) {
		tmp = t_1;
	} else if (t <= -8e+16) {
		tmp = x + (z / (a / (y - x)));
	} else if (t <= -7.6e-19) {
		tmp = t_1;
	} else if (t <= -7.6e-159) {
		tmp = x + ((z - t) * (y / a));
	} else if (t <= 7e-15) {
		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) / (a - t))
    if (t <= (-4.1d+82)) then
        tmp = t_1
    else if (t <= (-8d+16)) then
        tmp = x + (z / (a / (y - x)))
    else if (t <= (-7.6d-19)) then
        tmp = t_1
    else if (t <= (-7.6d-159)) then
        tmp = x + ((z - t) * (y / a))
    else if (t <= 7d-15) 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) / (a - t));
	double tmp;
	if (t <= -4.1e+82) {
		tmp = t_1;
	} else if (t <= -8e+16) {
		tmp = x + (z / (a / (y - x)));
	} else if (t <= -7.6e-19) {
		tmp = t_1;
	} else if (t <= -7.6e-159) {
		tmp = x + ((z - t) * (y / a));
	} else if (t <= 7e-15) {
		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) / (a - t))
	tmp = 0
	if t <= -4.1e+82:
		tmp = t_1
	elif t <= -8e+16:
		tmp = x + (z / (a / (y - x)))
	elif t <= -7.6e-19:
		tmp = t_1
	elif t <= -7.6e-159:
		tmp = x + ((z - t) * (y / a))
	elif t <= 7e-15:
		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(z - t) / Float64(a - t)))
	tmp = 0.0
	if (t <= -4.1e+82)
		tmp = t_1;
	elseif (t <= -8e+16)
		tmp = Float64(x + Float64(z / Float64(a / Float64(y - x))));
	elseif (t <= -7.6e-19)
		tmp = t_1;
	elseif (t <= -7.6e-159)
		tmp = Float64(x + Float64(Float64(z - t) * Float64(y / a)));
	elseif (t <= 7e-15)
		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) / (a - t));
	tmp = 0.0;
	if (t <= -4.1e+82)
		tmp = t_1;
	elseif (t <= -8e+16)
		tmp = x + (z / (a / (y - x)));
	elseif (t <= -7.6e-19)
		tmp = t_1;
	elseif (t <= -7.6e-159)
		tmp = x + ((z - t) * (y / a));
	elseif (t <= 7e-15)
		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[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -4.1e+82], t$95$1, If[LessEqual[t, -8e+16], N[(x + N[(z / N[(a / N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -7.6e-19], t$95$1, If[LessEqual[t, -7.6e-159], N[(x + N[(N[(z - t), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 7e-15], N[(x + N[(N[(y - x), $MachinePrecision] / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -4.09999999999999995e82 or -8e16 < t < -7.6e-19 or 7.0000000000000001e-15 < t

   1. Initial program 41.2%

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

      1. associate-*l/ 63.0%

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

   3. Simplified 63.0%

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

   4. Taylor expanded in x around 0 45.7%

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

      1. associate-*r/ 67.5%

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

   6. Simplified 67.5%

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

   if -4.09999999999999995e82 < t < -8e16

   1. Initial program 77.9%

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

      1. associate-*l/ 85.0%

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

   3. Simplified 85.0%

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

   4. Taylor expanded in t around 0 57.9%

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

      1. associate-/l* 65.1%

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

   6. Simplified 65.1%

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

   if -7.6e-19 < t < -7.6000000000000002e-159

   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/ 92.5%

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

   3. Simplified 92.5%

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

   4. Taylor expanded in a around inf 70.2%

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

   5. Taylor expanded in y around inf 73.9%

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

   if -7.6000000000000002e-159 < t < 7.0000000000000001e-15

   1. Initial program 92.4%

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

      1. associate-/l* 93.6%

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

   3. Simplified 93.6%

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

   4. Taylor expanded in t around 0 77.0%

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

4. Final simplification 71.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.1 \cdot 10^{+82}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;t \leq -8 \cdot 10^{+16}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y - x}}\\ \mathbf{elif}\;t \leq -7.6 \cdot 10^{-19}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;t \leq -7.6 \cdot 10^{-159}:\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;t \leq 7 \cdot 10^{-15}:\\ \;\;\;\;x + \frac{y - x}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \end{array} \]

Alternative 7: 69.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y - \frac{z}{\frac{t}{y - x}}\\ \mathbf{if}\;t \leq -4.1 \cdot 10^{+82}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -8.6 \cdot 10^{+36}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y - x}}\\ \mathbf{elif}\;t \leq -3.2 \cdot 10^{-19}:\\ \;\;\;\;y + \frac{z \cdot \left(x - y\right)}{t}\\ \mathbf{elif}\;t \leq 9 \cdot 10^{-17}:\\ \;\;\;\;x + \frac{y - x}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 4.6 \cdot 10^{+184}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- y (/ z (/ t (- y x))))))
   (if (<= t -4.1e+82)
     t_1
     (if (<= t -8.6e+36)
       (+ x (/ z (/ a (- y x))))
       (if (<= t -3.2e-19)
         (+ y (/ (* z (- x y)) t))
         (if (<= t 9e-17)
           (+ x (/ (- y x) (/ a z)))
           (if (<= t 4.6e+184) (* y (/ (- z t) (- a t))) 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 <= -4.1e+82) {
		tmp = t_1;
	} else if (t <= -8.6e+36) {
		tmp = x + (z / (a / (y - x)));
	} else if (t <= -3.2e-19) {
		tmp = y + ((z * (x - y)) / t);
	} else if (t <= 9e-17) {
		tmp = x + ((y - x) / (a / z));
	} else if (t <= 4.6e+184) {
		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 - (z / (t / (y - x)))
    if (t <= (-4.1d+82)) then
        tmp = t_1
    else if (t <= (-8.6d+36)) then
        tmp = x + (z / (a / (y - x)))
    else if (t <= (-3.2d-19)) then
        tmp = y + ((z * (x - y)) / t)
    else if (t <= 9d-17) then
        tmp = x + ((y - x) / (a / z))
    else if (t <= 4.6d+184) 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 - (z / (t / (y - x)));
	double tmp;
	if (t <= -4.1e+82) {
		tmp = t_1;
	} else if (t <= -8.6e+36) {
		tmp = x + (z / (a / (y - x)));
	} else if (t <= -3.2e-19) {
		tmp = y + ((z * (x - y)) / t);
	} else if (t <= 9e-17) {
		tmp = x + ((y - x) / (a / z));
	} else if (t <= 4.6e+184) {
		tmp = y * ((z - t) / (a - t));
	} 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 <= -4.1e+82:
		tmp = t_1
	elif t <= -8.6e+36:
		tmp = x + (z / (a / (y - x)))
	elif t <= -3.2e-19:
		tmp = y + ((z * (x - y)) / t)
	elif t <= 9e-17:
		tmp = x + ((y - x) / (a / z))
	elif t <= 4.6e+184:
		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(z / Float64(t / Float64(y - x))))
	tmp = 0.0
	if (t <= -4.1e+82)
		tmp = t_1;
	elseif (t <= -8.6e+36)
		tmp = Float64(x + Float64(z / Float64(a / Float64(y - x))));
	elseif (t <= -3.2e-19)
		tmp = Float64(y + Float64(Float64(z * Float64(x - y)) / t));
	elseif (t <= 9e-17)
		tmp = Float64(x + Float64(Float64(y - x) / Float64(a / z)));
	elseif (t <= 4.6e+184)
		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 - (z / (t / (y - x)));
	tmp = 0.0;
	if (t <= -4.1e+82)
		tmp = t_1;
	elseif (t <= -8.6e+36)
		tmp = x + (z / (a / (y - x)));
	elseif (t <= -3.2e-19)
		tmp = y + ((z * (x - y)) / t);
	elseif (t <= 9e-17)
		tmp = x + ((y - x) / (a / z));
	elseif (t <= 4.6e+184)
		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[(z / N[(t / N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -4.1e+82], t$95$1, If[LessEqual[t, -8.6e+36], N[(x + N[(z / N[(a / N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -3.2e-19], N[(y + N[(N[(z * N[(x - y), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 9e-17], N[(x + N[(N[(y - x), $MachinePrecision] / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4.6e+184], N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -4.09999999999999995e82 or 4.6e184 < t

   1. Initial program 24.2%

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

      1. associate-*l/ 52.6%

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

   3. Simplified 52.6%

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

   4. Taylor expanded in t around inf 61.2%

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

      1. associate--l+ 61.2%

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

      2. distribute-lft-out-- 61.2%

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

      3. div-sub 61.2%

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

      4. mul-1-neg 61.2%

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

      5. unsub-neg 61.2%

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

      6. distribute-rgt-out-- 61.3%

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

   6. Simplified 61.3%

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

   7. Taylor expanded in z around inf 57.5%

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

      1. associate-/l* 72.9%

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

   9. Simplified 72.9%

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

   if -4.09999999999999995e82 < t < -8.6000000000000001e36

   1. Initial program 88.3%

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

      1. associate-*l/ 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in t around 0 68.5%

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

      1. associate-/l* 80.1%

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

   6. Simplified 80.1%

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

   if -8.6000000000000001e36 < t < -3.19999999999999982e-19

   1. Initial program 79.2%

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

      1. associate-*l/ 70.2%

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

   3. Simplified 70.2%

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

   4. Taylor expanded in t around inf 75.2%

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

      1. associate--l+ 75.2%

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

      2. distribute-lft-out-- 75.2%

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

      3. div-sub 75.2%

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

      4. mul-1-neg 75.2%

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

      5. unsub-neg 75.2%

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

      6. distribute-rgt-out-- 75.2%

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

   6. Simplified 75.2%

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

   7. Taylor expanded in z around inf 61.5%

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

   if -3.19999999999999982e-19 < t < 8.99999999999999957e-17

   1. Initial program 92.5%

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

      1. associate-/l* 94.2%

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

   3. Simplified 94.2%

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

   4. Taylor expanded in t around 0 73.9%

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

   if 8.99999999999999957e-17 < t < 4.6e184

   1. Initial program 64.8%

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

      1. associate-*l/ 79.7%

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

   3. Simplified 79.7%

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

   4. Taylor expanded in x around 0 65.7%

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

      1. associate-*r/ 78.5%

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

   6. Simplified 78.5%

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

4. Final simplification 74.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.1 \cdot 10^{+82}:\\ \;\;\;\;y - \frac{z}{\frac{t}{y - x}}\\ \mathbf{elif}\;t \leq -8.6 \cdot 10^{+36}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y - x}}\\ \mathbf{elif}\;t \leq -3.2 \cdot 10^{-19}:\\ \;\;\;\;y + \frac{z \cdot \left(x - y\right)}{t}\\ \mathbf{elif}\;t \leq 9 \cdot 10^{-17}:\\ \;\;\;\;x + \frac{y - x}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 4.6 \cdot 10^{+184}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;y - \frac{z}{\frac{t}{y - x}}\\ \end{array} \]

Alternative 8: 68.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y - \frac{z}{\frac{t}{y - x}}\\ \mathbf{if}\;t \leq -2.2 \cdot 10^{+90}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -90000:\\ \;\;\;\;x \cdot \left(\frac{t - z}{a - t} + 1\right)\\ \mathbf{elif}\;t \leq -1.6 \cdot 10^{-18}:\\ \;\;\;\;y \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{elif}\;t \leq 3.2 \cdot 10^{-14}:\\ \;\;\;\;x + \frac{y - x}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 3.05 \cdot 10^{+184}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- y (/ z (/ t (- y x))))))
   (if (<= t -2.2e+90)
     t_1
     (if (<= t -90000.0)
       (* x (+ (/ (- t z) (- a t)) 1.0))
       (if (<= t -1.6e-18)
         (* y (- 1.0 (/ z t)))
         (if (<= t 3.2e-14)
           (+ x (/ (- y x) (/ a z)))
           (if (<= t 3.05e+184) (* y (/ (- z t) (- a t))) 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 <= -2.2e+90) {
		tmp = t_1;
	} else if (t <= -90000.0) {
		tmp = x * (((t - z) / (a - t)) + 1.0);
	} else if (t <= -1.6e-18) {
		tmp = y * (1.0 - (z / t));
	} else if (t <= 3.2e-14) {
		tmp = x + ((y - x) / (a / z));
	} else if (t <= 3.05e+184) {
		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 - (z / (t / (y - x)))
    if (t <= (-2.2d+90)) then
        tmp = t_1
    else if (t <= (-90000.0d0)) then
        tmp = x * (((t - z) / (a - t)) + 1.0d0)
    else if (t <= (-1.6d-18)) then
        tmp = y * (1.0d0 - (z / t))
    else if (t <= 3.2d-14) then
        tmp = x + ((y - x) / (a / z))
    else if (t <= 3.05d+184) 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 - (z / (t / (y - x)));
	double tmp;
	if (t <= -2.2e+90) {
		tmp = t_1;
	} else if (t <= -90000.0) {
		tmp = x * (((t - z) / (a - t)) + 1.0);
	} else if (t <= -1.6e-18) {
		tmp = y * (1.0 - (z / t));
	} else if (t <= 3.2e-14) {
		tmp = x + ((y - x) / (a / z));
	} else if (t <= 3.05e+184) {
		tmp = y * ((z - t) / (a - t));
	} 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 <= -2.2e+90:
		tmp = t_1
	elif t <= -90000.0:
		tmp = x * (((t - z) / (a - t)) + 1.0)
	elif t <= -1.6e-18:
		tmp = y * (1.0 - (z / t))
	elif t <= 3.2e-14:
		tmp = x + ((y - x) / (a / z))
	elif t <= 3.05e+184:
		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(z / Float64(t / Float64(y - x))))
	tmp = 0.0
	if (t <= -2.2e+90)
		tmp = t_1;
	elseif (t <= -90000.0)
		tmp = Float64(x * Float64(Float64(Float64(t - z) / Float64(a - t)) + 1.0));
	elseif (t <= -1.6e-18)
		tmp = Float64(y * Float64(1.0 - Float64(z / t)));
	elseif (t <= 3.2e-14)
		tmp = Float64(x + Float64(Float64(y - x) / Float64(a / z)));
	elseif (t <= 3.05e+184)
		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 - (z / (t / (y - x)));
	tmp = 0.0;
	if (t <= -2.2e+90)
		tmp = t_1;
	elseif (t <= -90000.0)
		tmp = x * (((t - z) / (a - t)) + 1.0);
	elseif (t <= -1.6e-18)
		tmp = y * (1.0 - (z / t));
	elseif (t <= 3.2e-14)
		tmp = x + ((y - x) / (a / z));
	elseif (t <= 3.05e+184)
		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[(z / N[(t / N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.2e+90], t$95$1, If[LessEqual[t, -90000.0], N[(x * N[(N[(N[(t - z), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -1.6e-18], N[(y * N[(1.0 - N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.2e-14], N[(x + N[(N[(y - x), $MachinePrecision] / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.05e+184], N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -2.1999999999999999e90 or 3.05000000000000004e184 < t

   1. Initial program 23.2%

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

      1. associate-*l/ 51.9%

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

   3. Simplified 51.9%

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

   4. Taylor expanded in t around inf 60.7%

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

      1. associate--l+ 60.7%

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

      2. distribute-lft-out-- 60.7%

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

      3. div-sub 60.7%

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

      4. mul-1-neg 60.7%

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

      5. unsub-neg 60.7%

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

      6. distribute-rgt-out-- 60.8%

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

   6. Simplified 60.8%

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

   7. Taylor expanded in z around inf 57.0%

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

      1. associate-/l* 72.6%

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

   9. Simplified 72.6%

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

   if -2.1999999999999999e90 < t < -9e4

   1. Initial program 81.2%

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

      1. associate-*l/ 86.5%

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

   3. Simplified 86.5%

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

      1. associate-/r/ 86.5%

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

      2. div-inv 86.3%

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

      3. associate-/r* 86.6%

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

   5. Applied egg-rr 86.6%

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

   6. Taylor expanded in x around inf 69.0%

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

      1. mul-1-neg 69.0%

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

      2. unsub-neg 69.0%

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

   8. Simplified 69.0%

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

   if -9e4 < t < -1.6e-18

   1. Initial program 100.0%

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

      1. associate-*l/ 72.1%

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

   3. Simplified 72.1%

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

   4. Taylor expanded in y around inf 100.0%

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

   5. Taylor expanded in a around 0 100.0%

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

      1. mul-1-neg 100.0%

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

      2. unsub-neg 100.0%

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

   7. Simplified 100.0%

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

   if -1.6e-18 < t < 3.2000000000000002e-14

   1. Initial program 92.5%

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

      1. associate-/l* 94.2%

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

   3. Simplified 94.2%

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

   4. Taylor expanded in t around 0 73.9%

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

   if 3.2000000000000002e-14 < t < 3.05000000000000004e184

   1. Initial program 64.8%

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

      1. associate-*l/ 79.7%

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

   3. Simplified 79.7%

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

   4. Taylor expanded in x around 0 65.7%

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

      1. associate-*r/ 78.5%

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

   6. Simplified 78.5%

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

4. Final simplification 74.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.2 \cdot 10^{+90}:\\ \;\;\;\;y - \frac{z}{\frac{t}{y - x}}\\ \mathbf{elif}\;t \leq -90000:\\ \;\;\;\;x \cdot \left(\frac{t - z}{a - t} + 1\right)\\ \mathbf{elif}\;t \leq -1.6 \cdot 10^{-18}:\\ \;\;\;\;y \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{elif}\;t \leq 3.2 \cdot 10^{-14}:\\ \;\;\;\;x + \frac{y - x}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 3.05 \cdot 10^{+184}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;y - \frac{z}{\frac{t}{y - x}}\\ \end{array} \]

Alternative 9: 69.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y - \frac{z}{\frac{t}{y - x}}\\ \mathbf{if}\;t \leq -2.2 \cdot 10^{+90}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -370000:\\ \;\;\;\;x \cdot \left(\frac{t - z}{a - t} + 1\right)\\ \mathbf{elif}\;t \leq -6.5 \cdot 10^{-19}:\\ \;\;\;\;y \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{elif}\;t \leq 5 \cdot 10^{-17}:\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y - x}{a}\\ \mathbf{elif}\;t \leq 6.8 \cdot 10^{+185}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- y (/ z (/ t (- y x))))))
   (if (<= t -2.2e+90)
     t_1
     (if (<= t -370000.0)
       (* x (+ (/ (- t z) (- a t)) 1.0))
       (if (<= t -6.5e-19)
         (* y (- 1.0 (/ z t)))
         (if (<= t 5e-17)
           (+ x (* (- z t) (/ (- y x) a)))
           (if (<= t 6.8e+185) (* y (/ (- z t) (- a t))) 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 <= -2.2e+90) {
		tmp = t_1;
	} else if (t <= -370000.0) {
		tmp = x * (((t - z) / (a - t)) + 1.0);
	} else if (t <= -6.5e-19) {
		tmp = y * (1.0 - (z / t));
	} else if (t <= 5e-17) {
		tmp = x + ((z - t) * ((y - x) / a));
	} else if (t <= 6.8e+185) {
		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 - (z / (t / (y - x)))
    if (t <= (-2.2d+90)) then
        tmp = t_1
    else if (t <= (-370000.0d0)) then
        tmp = x * (((t - z) / (a - t)) + 1.0d0)
    else if (t <= (-6.5d-19)) then
        tmp = y * (1.0d0 - (z / t))
    else if (t <= 5d-17) then
        tmp = x + ((z - t) * ((y - x) / a))
    else if (t <= 6.8d+185) 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 - (z / (t / (y - x)));
	double tmp;
	if (t <= -2.2e+90) {
		tmp = t_1;
	} else if (t <= -370000.0) {
		tmp = x * (((t - z) / (a - t)) + 1.0);
	} else if (t <= -6.5e-19) {
		tmp = y * (1.0 - (z / t));
	} else if (t <= 5e-17) {
		tmp = x + ((z - t) * ((y - x) / a));
	} else if (t <= 6.8e+185) {
		tmp = y * ((z - t) / (a - t));
	} 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 <= -2.2e+90:
		tmp = t_1
	elif t <= -370000.0:
		tmp = x * (((t - z) / (a - t)) + 1.0)
	elif t <= -6.5e-19:
		tmp = y * (1.0 - (z / t))
	elif t <= 5e-17:
		tmp = x + ((z - t) * ((y - x) / a))
	elif t <= 6.8e+185:
		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(z / Float64(t / Float64(y - x))))
	tmp = 0.0
	if (t <= -2.2e+90)
		tmp = t_1;
	elseif (t <= -370000.0)
		tmp = Float64(x * Float64(Float64(Float64(t - z) / Float64(a - t)) + 1.0));
	elseif (t <= -6.5e-19)
		tmp = Float64(y * Float64(1.0 - Float64(z / t)));
	elseif (t <= 5e-17)
		tmp = Float64(x + Float64(Float64(z - t) * Float64(Float64(y - x) / a)));
	elseif (t <= 6.8e+185)
		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 - (z / (t / (y - x)));
	tmp = 0.0;
	if (t <= -2.2e+90)
		tmp = t_1;
	elseif (t <= -370000.0)
		tmp = x * (((t - z) / (a - t)) + 1.0);
	elseif (t <= -6.5e-19)
		tmp = y * (1.0 - (z / t));
	elseif (t <= 5e-17)
		tmp = x + ((z - t) * ((y - x) / a));
	elseif (t <= 6.8e+185)
		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[(z / N[(t / N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.2e+90], t$95$1, If[LessEqual[t, -370000.0], N[(x * N[(N[(N[(t - z), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -6.5e-19], N[(y * N[(1.0 - N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 5e-17], N[(x + N[(N[(z - t), $MachinePrecision] * N[(N[(y - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 6.8e+185], N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -2.1999999999999999e90 or 6.80000000000000034e185 < t

   1. Initial program 23.2%

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

      1. associate-*l/ 51.9%

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

   3. Simplified 51.9%

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

   4. Taylor expanded in t around inf 60.7%

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

      1. associate--l+ 60.7%

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

      2. distribute-lft-out-- 60.7%

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

      3. div-sub 60.7%

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

      4. mul-1-neg 60.7%

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

      5. unsub-neg 60.7%

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

      6. distribute-rgt-out-- 60.8%

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

   6. Simplified 60.8%

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

   7. Taylor expanded in z around inf 57.0%

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

      1. associate-/l* 72.6%

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

   9. Simplified 72.6%

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

   if -2.1999999999999999e90 < t < -3.7e5

   1. Initial program 81.2%

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

      1. associate-*l/ 86.5%

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

   3. Simplified 86.5%

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

      1. associate-/r/ 86.5%

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

      2. div-inv 86.3%

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

      3. associate-/r* 86.6%

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

   5. Applied egg-rr 86.6%

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

   6. Taylor expanded in x around inf 69.0%

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

      1. mul-1-neg 69.0%

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

      2. unsub-neg 69.0%

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

   8. Simplified 69.0%

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

   if -3.7e5 < t < -6.5000000000000001e-19

   1. Initial program 100.0%

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

      1. associate-*l/ 72.1%

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

   3. Simplified 72.1%

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

   4. Taylor expanded in y around inf 100.0%

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

   5. Taylor expanded in a around 0 100.0%

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

      1. mul-1-neg 100.0%

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

      2. unsub-neg 100.0%

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

   7. Simplified 100.0%

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

   if -6.5000000000000001e-19 < t < 4.9999999999999999e-17

   1. Initial program 92.5%

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

      1. associate-*l/ 92.6%

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

   3. Simplified 92.6%

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

   4. Taylor expanded in a around inf 80.3%

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

   if 4.9999999999999999e-17 < t < 6.80000000000000034e185

   1. Initial program 64.8%

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

      1. associate-*l/ 79.7%

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

   3. Simplified 79.7%

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

   4. Taylor expanded in x around 0 65.7%

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

      1. associate-*r/ 78.5%

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

   6. Simplified 78.5%

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

4. Final simplification 77.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.2 \cdot 10^{+90}:\\ \;\;\;\;y - \frac{z}{\frac{t}{y - x}}\\ \mathbf{elif}\;t \leq -370000:\\ \;\;\;\;x \cdot \left(\frac{t - z}{a - t} + 1\right)\\ \mathbf{elif}\;t \leq -6.5 \cdot 10^{-19}:\\ \;\;\;\;y \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{elif}\;t \leq 5 \cdot 10^{-17}:\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y - x}{a}\\ \mathbf{elif}\;t \leq 6.8 \cdot 10^{+185}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;y - \frac{z}{\frac{t}{y - x}}\\ \end{array} \]

Alternative 10: 69.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y - \frac{z}{\frac{t}{y - x}}\\ \mathbf{if}\;t \leq -5.6 \cdot 10^{+91}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -520000:\\ \;\;\;\;x + x \cdot \frac{t - z}{a - t}\\ \mathbf{elif}\;t \leq -1.6 \cdot 10^{-18}:\\ \;\;\;\;y \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{elif}\;t \leq 8.5 \cdot 10^{-16}:\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y - x}{a}\\ \mathbf{elif}\;t \leq 6.2 \cdot 10^{+180}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- y (/ z (/ t (- y x))))))
   (if (<= t -5.6e+91)
     t_1
     (if (<= t -520000.0)
       (+ x (* x (/ (- t z) (- a t))))
       (if (<= t -1.6e-18)
         (* y (- 1.0 (/ z t)))
         (if (<= t 8.5e-16)
           (+ x (* (- z t) (/ (- y x) a)))
           (if (<= t 6.2e+180) (* y (/ (- z t) (- a t))) 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 <= -5.6e+91) {
		tmp = t_1;
	} else if (t <= -520000.0) {
		tmp = x + (x * ((t - z) / (a - t)));
	} else if (t <= -1.6e-18) {
		tmp = y * (1.0 - (z / t));
	} else if (t <= 8.5e-16) {
		tmp = x + ((z - t) * ((y - x) / a));
	} else if (t <= 6.2e+180) {
		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 - (z / (t / (y - x)))
    if (t <= (-5.6d+91)) then
        tmp = t_1
    else if (t <= (-520000.0d0)) then
        tmp = x + (x * ((t - z) / (a - t)))
    else if (t <= (-1.6d-18)) then
        tmp = y * (1.0d0 - (z / t))
    else if (t <= 8.5d-16) then
        tmp = x + ((z - t) * ((y - x) / a))
    else if (t <= 6.2d+180) 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 - (z / (t / (y - x)));
	double tmp;
	if (t <= -5.6e+91) {
		tmp = t_1;
	} else if (t <= -520000.0) {
		tmp = x + (x * ((t - z) / (a - t)));
	} else if (t <= -1.6e-18) {
		tmp = y * (1.0 - (z / t));
	} else if (t <= 8.5e-16) {
		tmp = x + ((z - t) * ((y - x) / a));
	} else if (t <= 6.2e+180) {
		tmp = y * ((z - t) / (a - t));
	} 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 <= -5.6e+91:
		tmp = t_1
	elif t <= -520000.0:
		tmp = x + (x * ((t - z) / (a - t)))
	elif t <= -1.6e-18:
		tmp = y * (1.0 - (z / t))
	elif t <= 8.5e-16:
		tmp = x + ((z - t) * ((y - x) / a))
	elif t <= 6.2e+180:
		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(z / Float64(t / Float64(y - x))))
	tmp = 0.0
	if (t <= -5.6e+91)
		tmp = t_1;
	elseif (t <= -520000.0)
		tmp = Float64(x + Float64(x * Float64(Float64(t - z) / Float64(a - t))));
	elseif (t <= -1.6e-18)
		tmp = Float64(y * Float64(1.0 - Float64(z / t)));
	elseif (t <= 8.5e-16)
		tmp = Float64(x + Float64(Float64(z - t) * Float64(Float64(y - x) / a)));
	elseif (t <= 6.2e+180)
		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 - (z / (t / (y - x)));
	tmp = 0.0;
	if (t <= -5.6e+91)
		tmp = t_1;
	elseif (t <= -520000.0)
		tmp = x + (x * ((t - z) / (a - t)));
	elseif (t <= -1.6e-18)
		tmp = y * (1.0 - (z / t));
	elseif (t <= 8.5e-16)
		tmp = x + ((z - t) * ((y - x) / a));
	elseif (t <= 6.2e+180)
		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[(z / N[(t / N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -5.6e+91], t$95$1, If[LessEqual[t, -520000.0], N[(x + N[(x * N[(N[(t - z), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -1.6e-18], N[(y * N[(1.0 - N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 8.5e-16], N[(x + N[(N[(z - t), $MachinePrecision] * N[(N[(y - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 6.2e+180], N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -5.5999999999999997e91 or 6.19999999999999997e180 < t

   1. Initial program 23.2%

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

      1. associate-*l/ 51.9%

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

   3. Simplified 51.9%

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

   4. Taylor expanded in t around inf 60.7%

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

      1. associate--l+ 60.7%

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

      2. distribute-lft-out-- 60.7%

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

      3. div-sub 60.7%

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

      4. mul-1-neg 60.7%

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

      5. unsub-neg 60.7%

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

      6. distribute-rgt-out-- 60.8%

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

   6. Simplified 60.8%

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

   7. Taylor expanded in z around inf 57.0%

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

      1. associate-/l* 72.6%

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

   9. Simplified 72.6%

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

   if -5.5999999999999997e91 < t < -5.2e5

   1. Initial program 81.2%

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

      1. associate-*l/ 86.5%

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

   3. Simplified 86.5%

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

   4. Taylor expanded in x around inf 69.0%

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

      1. distribute-lft-in 69.0%

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

      2. mul-1-neg 69.0%

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

      3. distribute-rgt-neg-in 69.0%

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

      4. unsub-neg 69.0%

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

      5. *-rgt-identity 69.0%

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

   6. Simplified 69.0%

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

   if -5.2e5 < t < -1.6e-18

   1. Initial program 100.0%

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

      1. associate-*l/ 72.1%

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

   3. Simplified 72.1%

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

   4. Taylor expanded in y around inf 100.0%

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

   5. Taylor expanded in a around 0 100.0%

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

      1. mul-1-neg 100.0%

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

      2. unsub-neg 100.0%

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

   7. Simplified 100.0%

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

   if -1.6e-18 < t < 8.5000000000000001e-16

   1. Initial program 92.5%

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

      1. associate-*l/ 92.6%

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

   3. Simplified 92.6%

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

   4. Taylor expanded in a around inf 80.3%

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

   if 8.5000000000000001e-16 < t < 6.19999999999999997e180

   1. Initial program 64.8%

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

      1. associate-*l/ 79.7%

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

   3. Simplified 79.7%

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

   4. Taylor expanded in x around 0 65.7%

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

      1. associate-*r/ 78.5%

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

   6. Simplified 78.5%

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

4. Final simplification 77.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.6 \cdot 10^{+91}:\\ \;\;\;\;y - \frac{z}{\frac{t}{y - x}}\\ \mathbf{elif}\;t \leq -520000:\\ \;\;\;\;x + x \cdot \frac{t - z}{a - t}\\ \mathbf{elif}\;t \leq -1.6 \cdot 10^{-18}:\\ \;\;\;\;y \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{elif}\;t \leq 8.5 \cdot 10^{-16}:\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y - x}{a}\\ \mathbf{elif}\;t \leq 6.2 \cdot 10^{+180}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;y - \frac{z}{\frac{t}{y - x}}\\ \end{array} \]

Alternative 11: 68.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(z - t\right) \cdot \frac{y - x}{a}\\ t_2 := y + \frac{\left(y - x\right) \cdot \left(a - z\right)}{t}\\ \mathbf{if}\;t \leq -9.5 \cdot 10^{+62}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -1.1 \cdot 10^{+43}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -7.5 \cdot 10^{-19}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 1.15 \cdot 10^{-15}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 4.9 \cdot 10^{+178}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;y - \frac{z}{\frac{t}{y - x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- z t) (/ (- y x) a))))
        (t_2 (+ y (/ (* (- y x) (- a z)) t))))
   (if (<= t -9.5e+62)
     t_2
     (if (<= t -1.1e+43)
       t_1
       (if (<= t -7.5e-19)
         t_2
         (if (<= t 1.15e-15)
           t_1
           (if (<= t 4.9e+178)
             (* y (/ (- z t) (- a t)))
             (- y (/ z (/ t (- y x)))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((z - t) * ((y - x) / a));
	double t_2 = y + (((y - x) * (a - z)) / t);
	double tmp;
	if (t <= -9.5e+62) {
		tmp = t_2;
	} else if (t <= -1.1e+43) {
		tmp = t_1;
	} else if (t <= -7.5e-19) {
		tmp = t_2;
	} else if (t <= 1.15e-15) {
		tmp = t_1;
	} else if (t <= 4.9e+178) {
		tmp = y * ((z - t) / (a - t));
	} else {
		tmp = y - (z / (t / (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) :: t_2
    real(8) :: tmp
    t_1 = x + ((z - t) * ((y - x) / a))
    t_2 = y + (((y - x) * (a - z)) / t)
    if (t <= (-9.5d+62)) then
        tmp = t_2
    else if (t <= (-1.1d+43)) then
        tmp = t_1
    else if (t <= (-7.5d-19)) then
        tmp = t_2
    else if (t <= 1.15d-15) then
        tmp = t_1
    else if (t <= 4.9d+178) then
        tmp = y * ((z - t) / (a - t))
    else
        tmp = y - (z / (t / (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 = x + ((z - t) * ((y - x) / a));
	double t_2 = y + (((y - x) * (a - z)) / t);
	double tmp;
	if (t <= -9.5e+62) {
		tmp = t_2;
	} else if (t <= -1.1e+43) {
		tmp = t_1;
	} else if (t <= -7.5e-19) {
		tmp = t_2;
	} else if (t <= 1.15e-15) {
		tmp = t_1;
	} else if (t <= 4.9e+178) {
		tmp = y * ((z - t) / (a - t));
	} else {
		tmp = y - (z / (t / (y - x)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((z - t) * ((y - x) / a))
	t_2 = y + (((y - x) * (a - z)) / t)
	tmp = 0
	if t <= -9.5e+62:
		tmp = t_2
	elif t <= -1.1e+43:
		tmp = t_1
	elif t <= -7.5e-19:
		tmp = t_2
	elif t <= 1.15e-15:
		tmp = t_1
	elif t <= 4.9e+178:
		tmp = y * ((z - t) / (a - t))
	else:
		tmp = y - (z / (t / (y - x)))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(z - t) * Float64(Float64(y - x) / a)))
	t_2 = Float64(y + Float64(Float64(Float64(y - x) * Float64(a - z)) / t))
	tmp = 0.0
	if (t <= -9.5e+62)
		tmp = t_2;
	elseif (t <= -1.1e+43)
		tmp = t_1;
	elseif (t <= -7.5e-19)
		tmp = t_2;
	elseif (t <= 1.15e-15)
		tmp = t_1;
	elseif (t <= 4.9e+178)
		tmp = Float64(y * Float64(Float64(z - t) / Float64(a - t)));
	else
		tmp = Float64(y - Float64(z / Float64(t / Float64(y - x))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((z - t) * ((y - x) / a));
	t_2 = y + (((y - x) * (a - z)) / t);
	tmp = 0.0;
	if (t <= -9.5e+62)
		tmp = t_2;
	elseif (t <= -1.1e+43)
		tmp = t_1;
	elseif (t <= -7.5e-19)
		tmp = t_2;
	elseif (t <= 1.15e-15)
		tmp = t_1;
	elseif (t <= 4.9e+178)
		tmp = y * ((z - t) / (a - t));
	else
		tmp = y - (z / (t / (y - x)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(z - t), $MachinePrecision] * N[(N[(y - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y + N[(N[(N[(y - x), $MachinePrecision] * N[(a - z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -9.5e+62], t$95$2, If[LessEqual[t, -1.1e+43], t$95$1, If[LessEqual[t, -7.5e-19], t$95$2, If[LessEqual[t, 1.15e-15], t$95$1, If[LessEqual[t, 4.9e+178], N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y - N[(z / N[(t / N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -9.5000000000000003e62 or -1.1e43 < t < -7.49999999999999957e-19

   1. Initial program 42.1%

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

      1. associate-*l/ 60.8%

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

   3. Simplified 60.8%

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

   4. Taylor expanded in t around inf 71.1%

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

      1. associate--l+ 71.1%

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

      2. distribute-lft-out-- 71.1%

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

      3. div-sub 71.1%

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

      4. mul-1-neg 71.1%

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

      5. unsub-neg 71.1%

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

      6. distribute-rgt-out-- 71.2%

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

   6. Simplified 71.2%

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

   if -9.5000000000000003e62 < t < -1.1e43 or -7.49999999999999957e-19 < t < 1.14999999999999995e-15

   1. Initial program 92.1%

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

      1. associate-*l/ 93.0%

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

   3. Simplified 93.0%

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

   4. Taylor expanded in a around inf 80.8%

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

   if 1.14999999999999995e-15 < t < 4.9000000000000001e178

   1. Initial program 64.8%

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

      1. associate-*l/ 79.7%

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

   3. Simplified 79.7%

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

   4. Taylor expanded in x around 0 65.7%

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

      1. associate-*r/ 78.5%

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

   6. Simplified 78.5%

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

   if 4.9000000000000001e178 < t

   1. Initial program 15.7%

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

      1. associate-*l/ 47.1%

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

   3. Simplified 47.1%

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

   4. Taylor expanded in t around inf 48.2%

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

      1. associate--l+ 48.2%

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

      2. distribute-lft-out-- 48.2%

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

      3. div-sub 48.2%

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

      4. mul-1-neg 48.2%

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

      5. unsub-neg 48.2%

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

      6. distribute-rgt-out-- 48.2%

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

   6. Simplified 48.2%

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

   7. Taylor expanded in z around inf 51.5%

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

      1. associate-/l* 75.5%

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

   9. Simplified 75.5%

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

4. Final simplification 77.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -9.5 \cdot 10^{+62}:\\ \;\;\;\;y + \frac{\left(y - x\right) \cdot \left(a - z\right)}{t}\\ \mathbf{elif}\;t \leq -1.1 \cdot 10^{+43}:\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y - x}{a}\\ \mathbf{elif}\;t \leq -7.5 \cdot 10^{-19}:\\ \;\;\;\;y + \frac{\left(y - x\right) \cdot \left(a - z\right)}{t}\\ \mathbf{elif}\;t \leq 1.15 \cdot 10^{-15}:\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y - x}{a}\\ \mathbf{elif}\;t \leq 4.9 \cdot 10^{+178}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;y - \frac{z}{\frac{t}{y - x}}\\ \end{array} \]

Alternative 12: 75.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(z - t\right) \cdot \frac{y - x}{a}\\ t_2 := y + \frac{x - y}{\frac{t}{z - a}}\\ \mathbf{if}\;t \leq -5.2 \cdot 10^{+58}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -1.62 \cdot 10^{+41}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -6.5 \cdot 10^{-20}:\\ \;\;\;\;y + \frac{\left(y - x\right) \cdot \left(a - z\right)}{t}\\ \mathbf{elif}\;t \leq 1.12 \cdot 10^{-9}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- z t) (/ (- y x) a))))
        (t_2 (+ y (/ (- x y) (/ t (- z a))))))
   (if (<= t -5.2e+58)
     t_2
     (if (<= t -1.62e+41)
       t_1
       (if (<= t -6.5e-20)
         (+ y (/ (* (- y x) (- a z)) t))
         (if (<= t 1.12e-9) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((z - t) * ((y - x) / a));
	double t_2 = y + ((x - y) / (t / (z - a)));
	double tmp;
	if (t <= -5.2e+58) {
		tmp = t_2;
	} else if (t <= -1.62e+41) {
		tmp = t_1;
	} else if (t <= -6.5e-20) {
		tmp = y + (((y - x) * (a - z)) / t);
	} else if (t <= 1.12e-9) {
		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 = x + ((z - t) * ((y - x) / a))
    t_2 = y + ((x - y) / (t / (z - a)))
    if (t <= (-5.2d+58)) then
        tmp = t_2
    else if (t <= (-1.62d+41)) then
        tmp = t_1
    else if (t <= (-6.5d-20)) then
        tmp = y + (((y - x) * (a - z)) / t)
    else if (t <= 1.12d-9) 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 = x + ((z - t) * ((y - x) / a));
	double t_2 = y + ((x - y) / (t / (z - a)));
	double tmp;
	if (t <= -5.2e+58) {
		tmp = t_2;
	} else if (t <= -1.62e+41) {
		tmp = t_1;
	} else if (t <= -6.5e-20) {
		tmp = y + (((y - x) * (a - z)) / t);
	} else if (t <= 1.12e-9) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((z - t) * ((y - x) / a))
	t_2 = y + ((x - y) / (t / (z - a)))
	tmp = 0
	if t <= -5.2e+58:
		tmp = t_2
	elif t <= -1.62e+41:
		tmp = t_1
	elif t <= -6.5e-20:
		tmp = y + (((y - x) * (a - z)) / t)
	elif t <= 1.12e-9:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(z - t) * Float64(Float64(y - x) / a)))
	t_2 = Float64(y + Float64(Float64(x - y) / Float64(t / Float64(z - a))))
	tmp = 0.0
	if (t <= -5.2e+58)
		tmp = t_2;
	elseif (t <= -1.62e+41)
		tmp = t_1;
	elseif (t <= -6.5e-20)
		tmp = Float64(y + Float64(Float64(Float64(y - x) * Float64(a - z)) / t));
	elseif (t <= 1.12e-9)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((z - t) * ((y - x) / a));
	t_2 = y + ((x - y) / (t / (z - a)));
	tmp = 0.0;
	if (t <= -5.2e+58)
		tmp = t_2;
	elseif (t <= -1.62e+41)
		tmp = t_1;
	elseif (t <= -6.5e-20)
		tmp = y + (((y - x) * (a - z)) / t);
	elseif (t <= 1.12e-9)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(z - t), $MachinePrecision] * N[(N[(y - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y + N[(N[(x - y), $MachinePrecision] / N[(t / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -5.2e+58], t$95$2, If[LessEqual[t, -1.62e+41], t$95$1, If[LessEqual[t, -6.5e-20], N[(y + N[(N[(N[(y - x), $MachinePrecision] * N[(a - z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.12e-9], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -5.19999999999999976e58 or 1.12000000000000006e-9 < t

   1. Initial program 39.4%

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

      1. associate-*l/ 62.7%

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

   3. Simplified 62.7%

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

   4. Taylor expanded in t around inf 62.4%

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

      1. associate--l+ 62.4%

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

      2. distribute-lft-out-- 62.4%

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

      3. div-sub 62.4%

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

      4. mul-1-neg 62.4%

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

      5. unsub-neg 62.4%

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

      6. distribute-rgt-out-- 62.6%

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

   6. Simplified 62.6%

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

      1. sub-neg 62.6%

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

      2. associate-/l* 84.2%

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

   8. Applied egg-rr 84.2%

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

   if -5.19999999999999976e58 < t < -1.61999999999999996e41 or -6.50000000000000032e-20 < t < 1.12000000000000006e-9

   1. Initial program 92.1%

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

      1. associate-*l/ 93.0%

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

   3. Simplified 93.0%

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

   4. Taylor expanded in a around inf 81.0%

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

   if -1.61999999999999996e41 < t < -6.50000000000000032e-20

   1. Initial program 79.2%

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

      1. associate-*l/ 70.2%

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

   3. Simplified 70.2%

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

   4. Taylor expanded in t around inf 75.2%

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

      1. associate--l+ 75.2%

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

      2. distribute-lft-out-- 75.2%

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

      3. div-sub 75.2%

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

      4. mul-1-neg 75.2%

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

      5. unsub-neg 75.2%

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

      6. distribute-rgt-out-- 75.2%

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

   6. Simplified 75.2%

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

4. Final simplification 82.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.2 \cdot 10^{+58}:\\ \;\;\;\;y + \frac{x - y}{\frac{t}{z - a}}\\ \mathbf{elif}\;t \leq -1.62 \cdot 10^{+41}:\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y - x}{a}\\ \mathbf{elif}\;t \leq -6.5 \cdot 10^{-20}:\\ \;\;\;\;y + \frac{\left(y - x\right) \cdot \left(a - z\right)}{t}\\ \mathbf{elif}\;t \leq 1.12 \cdot 10^{-9}:\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y - x}{a}\\ \mathbf{else}:\\ \;\;\;\;y + \frac{x - y}{\frac{t}{z - a}}\\ \end{array} \]

Alternative 13: 56.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{z - t}{a - t}\\ t_2 := \frac{x}{\frac{t}{z - a}}\\ \mathbf{if}\;x \leq -5.5 \cdot 10^{+133}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 3.9 \cdot 10^{+160}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 3.3 \cdot 10^{+211}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 1.35 \cdot 10^{+250}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 2.15 \cdot 10^{+281}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ (- z t) (- a t)))) (t_2 (/ x (/ t (- z a)))))
   (if (<= x -5.5e+133)
     t_2
     (if (<= x 3.9e+160)
       t_1
       (if (<= x 3.3e+211)
         t_2
         (if (<= x 1.35e+250)
           t_1
           (if (<= x 2.15e+281) t_2 (* x (- 1.0 (/ z a))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((z - t) / (a - t));
	double t_2 = x / (t / (z - a));
	double tmp;
	if (x <= -5.5e+133) {
		tmp = t_2;
	} else if (x <= 3.9e+160) {
		tmp = t_1;
	} else if (x <= 3.3e+211) {
		tmp = t_2;
	} else if (x <= 1.35e+250) {
		tmp = t_1;
	} else if (x <= 2.15e+281) {
		tmp = t_2;
	} else {
		tmp = x * (1.0 - (z / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = y * ((z - t) / (a - t))
    t_2 = x / (t / (z - a))
    if (x <= (-5.5d+133)) then
        tmp = t_2
    else if (x <= 3.9d+160) then
        tmp = t_1
    else if (x <= 3.3d+211) then
        tmp = t_2
    else if (x <= 1.35d+250) then
        tmp = t_1
    else if (x <= 2.15d+281) then
        tmp = t_2
    else
        tmp = x * (1.0d0 - (z / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((z - t) / (a - t));
	double t_2 = x / (t / (z - a));
	double tmp;
	if (x <= -5.5e+133) {
		tmp = t_2;
	} else if (x <= 3.9e+160) {
		tmp = t_1;
	} else if (x <= 3.3e+211) {
		tmp = t_2;
	} else if (x <= 1.35e+250) {
		tmp = t_1;
	} else if (x <= 2.15e+281) {
		tmp = t_2;
	} else {
		tmp = x * (1.0 - (z / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * ((z - t) / (a - t))
	t_2 = x / (t / (z - a))
	tmp = 0
	if x <= -5.5e+133:
		tmp = t_2
	elif x <= 3.9e+160:
		tmp = t_1
	elif x <= 3.3e+211:
		tmp = t_2
	elif x <= 1.35e+250:
		tmp = t_1
	elif x <= 2.15e+281:
		tmp = t_2
	else:
		tmp = x * (1.0 - (z / a))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(Float64(z - t) / Float64(a - t)))
	t_2 = Float64(x / Float64(t / Float64(z - a)))
	tmp = 0.0
	if (x <= -5.5e+133)
		tmp = t_2;
	elseif (x <= 3.9e+160)
		tmp = t_1;
	elseif (x <= 3.3e+211)
		tmp = t_2;
	elseif (x <= 1.35e+250)
		tmp = t_1;
	elseif (x <= 2.15e+281)
		tmp = t_2;
	else
		tmp = Float64(x * Float64(1.0 - Float64(z / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * ((z - t) / (a - t));
	t_2 = x / (t / (z - a));
	tmp = 0.0;
	if (x <= -5.5e+133)
		tmp = t_2;
	elseif (x <= 3.9e+160)
		tmp = t_1;
	elseif (x <= 3.3e+211)
		tmp = t_2;
	elseif (x <= 1.35e+250)
		tmp = t_1;
	elseif (x <= 2.15e+281)
		tmp = t_2;
	else
		tmp = x * (1.0 - (z / a));
	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]}, Block[{t$95$2 = N[(x / N[(t / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -5.5e+133], t$95$2, If[LessEqual[x, 3.9e+160], t$95$1, If[LessEqual[x, 3.3e+211], t$95$2, If[LessEqual[x, 1.35e+250], t$95$1, If[LessEqual[x, 2.15e+281], t$95$2, N[(x * N[(1.0 - N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -5.5e133 or 3.90000000000000007e160 < x < 3.29999999999999983e211 or 1.35e250 < x < 2.1499999999999999e281

   1. Initial program 53.0%

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

      1. associate-*l/ 61.8%

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

   3. Simplified 61.8%

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

   4. Taylor expanded in t around inf 45.6%

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

      1. associate--l+ 45.6%

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

      2. distribute-lft-out-- 45.6%

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

      3. div-sub 47.3%

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

      4. mul-1-neg 47.3%

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

      5. unsub-neg 47.3%

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

      6. distribute-rgt-out-- 49.2%

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

   6. Simplified 49.2%

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

   7. Taylor expanded in y around 0 46.0%

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

      1. associate-/l* 63.5%

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

   9. Simplified 63.5%

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

   if -5.5e133 < x < 3.90000000000000007e160 or 3.29999999999999983e211 < x < 1.35e250

   1. Initial program 72.4%

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

      1. associate-*l/ 83.6%

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

   3. Simplified 83.6%

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

   4. Taylor expanded in x around 0 57.8%

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

      1. associate-*r/ 71.7%

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

   6. Simplified 71.7%

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

   if 2.1499999999999999e281 < x

   1. Initial program 45.9%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   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. Taylor expanded in t around 0 47.6%

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

      1. associate-/l* 68.7%

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

   6. Simplified 68.7%

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

   7. Taylor expanded in x around inf 68.7%

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

      1. mul-1-neg 68.7%

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

      2. unsub-neg 68.7%

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

   9. Simplified 68.7%

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

4. Final simplification 69.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.5 \cdot 10^{+133}:\\ \;\;\;\;\frac{x}{\frac{t}{z - a}}\\ \mathbf{elif}\;x \leq 3.9 \cdot 10^{+160}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;x \leq 3.3 \cdot 10^{+211}:\\ \;\;\;\;\frac{x}{\frac{t}{z - a}}\\ \mathbf{elif}\;x \leq 1.35 \cdot 10^{+250}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;x \leq 2.15 \cdot 10^{+281}:\\ \;\;\;\;\frac{x}{\frac{t}{z - a}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \end{array} \]

Alternative 14: 87.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -6.3 \cdot 10^{+94} \lor \neg \left(t \leq 10^{+176}\right):\\ \;\;\;\;y + \frac{x - y}{\frac{t}{z - a}}\\ \mathbf{else}:\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y - x}{a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -6.3e+94) (not (<= t 1e+176)))
   (+ y (/ (- x y) (/ t (- z a))))
   (+ x (* (- z t) (/ (- y x) (- a t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -6.3e+94) || !(t <= 1e+176)) {
		tmp = y + ((x - y) / (t / (z - a)));
	} 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 <= (-6.3d+94)) .or. (.not. (t <= 1d+176))) then
        tmp = y + ((x - y) / (t / (z - a)))
    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 <= -6.3e+94) || !(t <= 1e+176)) {
		tmp = y + ((x - y) / (t / (z - a)));
	} else {
		tmp = x + ((z - t) * ((y - x) / (a - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -6.3e+94) or not (t <= 1e+176):
		tmp = y + ((x - y) / (t / (z - a)))
	else:
		tmp = x + ((z - t) * ((y - x) / (a - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -6.3e+94) || !(t <= 1e+176))
		tmp = Float64(y + Float64(Float64(x - y) / Float64(t / Float64(z - a))));
	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 <= -6.3e+94) || ~((t <= 1e+176)))
		tmp = y + ((x - y) / (t / (z - a)));
	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, -6.3e+94], N[Not[LessEqual[t, 1e+176]], $MachinePrecision]], N[(y + N[(N[(x - y), $MachinePrecision] / N[(t / N[(z - a), $MachinePrecision]), $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 < -6.3000000000000001e94 or 1e176 < t

   1. Initial program 23.9%

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

      1. associate-*l/ 51.9%

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

   3. Simplified 51.9%

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

   4. Taylor expanded in t around inf 60.4%

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

      1. associate--l+ 60.4%

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

      2. distribute-lft-out-- 60.4%

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

      3. div-sub 60.4%

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

      4. mul-1-neg 60.4%

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

      5. unsub-neg 60.4%

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

      6. distribute-rgt-out-- 60.6%

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

   6. Simplified 60.6%

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

      1. sub-neg 60.6%

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

      2. associate-/l* 89.3%

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

   8. Applied egg-rr 89.3%

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

   if -6.3000000000000001e94 < t < 1e176

   1. Initial program 85.4%

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

      1. associate-*l/ 89.1%

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

   3. Simplified 89.1%

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

4. Final simplification 89.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.3 \cdot 10^{+94} \lor \neg \left(t \leq 10^{+176}\right):\\ \;\;\;\;y + \frac{x - y}{\frac{t}{z - a}}\\ \mathbf{else}:\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y - x}{a - t}\\ \end{array} \]

Alternative 15: 48.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{if}\;t \leq -1.12 \cdot 10^{+85}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 2.7 \cdot 10^{-242}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.1 \cdot 10^{-203}:\\ \;\;\;\;z \cdot \frac{y}{a}\\ \mathbf{elif}\;t \leq 3.3 \cdot 10^{-16}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (- 1.0 (/ z a)))))
   (if (<= t -1.12e+85)
     y
     (if (<= t 2.7e-242)
       t_1
       (if (<= t 1.1e-203) (* z (/ y a)) (if (<= t 3.3e-16) t_1 y))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (1.0 - (z / a));
	double tmp;
	if (t <= -1.12e+85) {
		tmp = y;
	} else if (t <= 2.7e-242) {
		tmp = t_1;
	} else if (t <= 1.1e-203) {
		tmp = z * (y / a);
	} else if (t <= 3.3e-16) {
		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 = x * (1.0d0 - (z / a))
    if (t <= (-1.12d+85)) then
        tmp = y
    else if (t <= 2.7d-242) then
        tmp = t_1
    else if (t <= 1.1d-203) then
        tmp = z * (y / a)
    else if (t <= 3.3d-16) 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 = x * (1.0 - (z / a));
	double tmp;
	if (t <= -1.12e+85) {
		tmp = y;
	} else if (t <= 2.7e-242) {
		tmp = t_1;
	} else if (t <= 1.1e-203) {
		tmp = z * (y / a);
	} else if (t <= 3.3e-16) {
		tmp = t_1;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x * (1.0 - (z / a))
	tmp = 0
	if t <= -1.12e+85:
		tmp = y
	elif t <= 2.7e-242:
		tmp = t_1
	elif t <= 1.1e-203:
		tmp = z * (y / a)
	elif t <= 3.3e-16:
		tmp = t_1
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x * Float64(1.0 - Float64(z / a)))
	tmp = 0.0
	if (t <= -1.12e+85)
		tmp = y;
	elseif (t <= 2.7e-242)
		tmp = t_1;
	elseif (t <= 1.1e-203)
		tmp = Float64(z * Float64(y / a));
	elseif (t <= 3.3e-16)
		tmp = t_1;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x * (1.0 - (z / a));
	tmp = 0.0;
	if (t <= -1.12e+85)
		tmp = y;
	elseif (t <= 2.7e-242)
		tmp = t_1;
	elseif (t <= 1.1e-203)
		tmp = z * (y / a);
	elseif (t <= 3.3e-16)
		tmp = t_1;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x * N[(1.0 - N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.12e+85], y, If[LessEqual[t, 2.7e-242], t$95$1, If[LessEqual[t, 1.1e-203], N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.3e-16], t$95$1, y]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.11999999999999993e85 or 3.29999999999999988e-16 < t

   1. Initial program 38.9%

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

      1. associate-*l/ 62.4%

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

   3. Simplified 62.4%

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

   4. Taylor expanded in t around inf 48.5%

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

   if -1.11999999999999993e85 < t < 2.7e-242 or 1.1e-203 < t < 3.29999999999999988e-16

   1. Initial program 90.6%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   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. Taylor expanded in t around 0 65.0%

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

      1. associate-/l* 68.1%

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

   6. Simplified 68.1%

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

   7. Taylor expanded in x around inf 51.5%

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

      1. mul-1-neg 51.5%

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

      2. unsub-neg 51.5%

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

   9. Simplified 51.5%

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

   if 2.7e-242 < t < 1.1e-203

   1. Initial program 100.0%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   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. Taylor expanded in y around inf 70.6%

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

   5. Taylor expanded in t around 0 61.5%

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

      1. associate-/l* 61.7%

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

   7. Simplified 61.7%

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

      1. associate-/r/ 62.0%

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

   9. Applied egg-rr 62.0%

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

4. Final simplification 50.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.12 \cdot 10^{+85}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 2.7 \cdot 10^{-242}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{elif}\;t \leq 1.1 \cdot 10^{-203}:\\ \;\;\;\;z \cdot \frac{y}{a}\\ \mathbf{elif}\;t \leq 3.3 \cdot 10^{-16}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 16: 52.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(1 - \frac{z}{a}\right)\\ t_2 := y \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{if}\;t \leq -4 \cdot 10^{+86}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 2.4 \cdot 10^{-242}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.1 \cdot 10^{-203}:\\ \;\;\;\;z \cdot \frac{y}{a}\\ \mathbf{elif}\;t \leq 4.8 \cdot 10^{-18}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (- 1.0 (/ z a)))) (t_2 (* y (- 1.0 (/ z t)))))
   (if (<= t -4e+86)
     t_2
     (if (<= t 2.4e-242)
       t_1
       (if (<= t 1.1e-203) (* z (/ y a)) (if (<= t 4.8e-18) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (1.0 - (z / a));
	double t_2 = y * (1.0 - (z / t));
	double tmp;
	if (t <= -4e+86) {
		tmp = t_2;
	} else if (t <= 2.4e-242) {
		tmp = t_1;
	} else if (t <= 1.1e-203) {
		tmp = z * (y / a);
	} else if (t <= 4.8e-18) {
		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 = x * (1.0d0 - (z / a))
    t_2 = y * (1.0d0 - (z / t))
    if (t <= (-4d+86)) then
        tmp = t_2
    else if (t <= 2.4d-242) then
        tmp = t_1
    else if (t <= 1.1d-203) then
        tmp = z * (y / a)
    else if (t <= 4.8d-18) 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 = x * (1.0 - (z / a));
	double t_2 = y * (1.0 - (z / t));
	double tmp;
	if (t <= -4e+86) {
		tmp = t_2;
	} else if (t <= 2.4e-242) {
		tmp = t_1;
	} else if (t <= 1.1e-203) {
		tmp = z * (y / a);
	} else if (t <= 4.8e-18) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x * (1.0 - (z / a))
	t_2 = y * (1.0 - (z / t))
	tmp = 0
	if t <= -4e+86:
		tmp = t_2
	elif t <= 2.4e-242:
		tmp = t_1
	elif t <= 1.1e-203:
		tmp = z * (y / a)
	elif t <= 4.8e-18:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x * Float64(1.0 - Float64(z / a)))
	t_2 = Float64(y * Float64(1.0 - Float64(z / t)))
	tmp = 0.0
	if (t <= -4e+86)
		tmp = t_2;
	elseif (t <= 2.4e-242)
		tmp = t_1;
	elseif (t <= 1.1e-203)
		tmp = Float64(z * Float64(y / a));
	elseif (t <= 4.8e-18)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x * (1.0 - (z / a));
	t_2 = y * (1.0 - (z / t));
	tmp = 0.0;
	if (t <= -4e+86)
		tmp = t_2;
	elseif (t <= 2.4e-242)
		tmp = t_1;
	elseif (t <= 1.1e-203)
		tmp = z * (y / a);
	elseif (t <= 4.8e-18)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x * N[(1.0 - N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(1.0 - N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -4e+86], t$95$2, If[LessEqual[t, 2.4e-242], t$95$1, If[LessEqual[t, 1.1e-203], N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4.8e-18], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -4.0000000000000001e86 or 4.79999999999999988e-18 < t

   1. Initial program 38.9%

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

      1. associate-*l/ 62.4%

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

   3. Simplified 62.4%

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

   4. Taylor expanded in y around inf 67.8%

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

   5. Taylor expanded in a around 0 57.9%

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

      1. mul-1-neg 57.9%

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

      2. unsub-neg 57.9%

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

   7. Simplified 57.9%

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

   if -4.0000000000000001e86 < t < 2.4000000000000001e-242 or 1.1e-203 < t < 4.79999999999999988e-18

   1. Initial program 90.6%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   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. Taylor expanded in t around 0 65.0%

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

      1. associate-/l* 68.1%

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

   6. Simplified 68.1%

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

   7. Taylor expanded in x around inf 51.5%

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

      1. mul-1-neg 51.5%

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

      2. unsub-neg 51.5%

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

   9. Simplified 51.5%

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

   if 2.4000000000000001e-242 < t < 1.1e-203

   1. Initial program 100.0%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   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. Taylor expanded in y around inf 70.6%

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

   5. Taylor expanded in t around 0 61.5%

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

      1. associate-/l* 61.7%

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

   7. Simplified 61.7%

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

      1. associate-/r/ 62.0%

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

   9. Applied egg-rr 62.0%

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

4. Final simplification 54.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4 \cdot 10^{+86}:\\ \;\;\;\;y \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{elif}\;t \leq 2.4 \cdot 10^{-242}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{elif}\;t \leq 1.1 \cdot 10^{-203}:\\ \;\;\;\;z \cdot \frac{y}{a}\\ \mathbf{elif}\;t \leq 4.8 \cdot 10^{-18}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(1 - \frac{z}{t}\right)\\ \end{array} \]

Alternative 17: 52.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - \frac{x}{\frac{a}{z}}\\ t_2 := y \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{if}\;t \leq -3.8 \cdot 10^{+83}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 2.35 \cdot 10^{-242}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.1 \cdot 10^{-203}:\\ \;\;\;\;z \cdot \frac{y}{a}\\ \mathbf{elif}\;t \leq 4.8 \cdot 10^{-18}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (/ x (/ a z)))) (t_2 (* y (- 1.0 (/ z t)))))
   (if (<= t -3.8e+83)
     t_2
     (if (<= t 2.35e-242)
       t_1
       (if (<= t 1.1e-203) (* z (/ y a)) (if (<= t 4.8e-18) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (x / (a / z));
	double t_2 = y * (1.0 - (z / t));
	double tmp;
	if (t <= -3.8e+83) {
		tmp = t_2;
	} else if (t <= 2.35e-242) {
		tmp = t_1;
	} else if (t <= 1.1e-203) {
		tmp = z * (y / a);
	} else if (t <= 4.8e-18) {
		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 = x - (x / (a / z))
    t_2 = y * (1.0d0 - (z / t))
    if (t <= (-3.8d+83)) then
        tmp = t_2
    else if (t <= 2.35d-242) then
        tmp = t_1
    else if (t <= 1.1d-203) then
        tmp = z * (y / a)
    else if (t <= 4.8d-18) 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 = x - (x / (a / z));
	double t_2 = y * (1.0 - (z / t));
	double tmp;
	if (t <= -3.8e+83) {
		tmp = t_2;
	} else if (t <= 2.35e-242) {
		tmp = t_1;
	} else if (t <= 1.1e-203) {
		tmp = z * (y / a);
	} else if (t <= 4.8e-18) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - (x / (a / z))
	t_2 = y * (1.0 - (z / t))
	tmp = 0
	if t <= -3.8e+83:
		tmp = t_2
	elif t <= 2.35e-242:
		tmp = t_1
	elif t <= 1.1e-203:
		tmp = z * (y / a)
	elif t <= 4.8e-18:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(x / Float64(a / z)))
	t_2 = Float64(y * Float64(1.0 - Float64(z / t)))
	tmp = 0.0
	if (t <= -3.8e+83)
		tmp = t_2;
	elseif (t <= 2.35e-242)
		tmp = t_1;
	elseif (t <= 1.1e-203)
		tmp = Float64(z * Float64(y / a));
	elseif (t <= 4.8e-18)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - (x / (a / z));
	t_2 = y * (1.0 - (z / t));
	tmp = 0.0;
	if (t <= -3.8e+83)
		tmp = t_2;
	elseif (t <= 2.35e-242)
		tmp = t_1;
	elseif (t <= 1.1e-203)
		tmp = z * (y / a);
	elseif (t <= 4.8e-18)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x - N[(x / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(1.0 - N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -3.8e+83], t$95$2, If[LessEqual[t, 2.35e-242], t$95$1, If[LessEqual[t, 1.1e-203], N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4.8e-18], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -3.8000000000000002e83 or 4.79999999999999988e-18 < t

   1. Initial program 38.9%

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

      1. associate-*l/ 62.4%

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

   3. Simplified 62.4%

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

   4. Taylor expanded in y around inf 67.8%

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

   5. Taylor expanded in a around 0 57.9%

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

      1. mul-1-neg 57.9%

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

      2. unsub-neg 57.9%

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

   7. Simplified 57.9%

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

   if -3.8000000000000002e83 < t < 2.35000000000000018e-242 or 1.1e-203 < t < 4.79999999999999988e-18

   1. Initial program 90.6%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   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. Taylor expanded in t around 0 65.0%

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

      1. associate-/l* 68.1%

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

   6. Simplified 68.1%

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

   7. Taylor expanded in y around 0 48.5%

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

      1. mul-1-neg 48.5%

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

      2. unsub-neg 48.5%

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

      3. associate-/l* 51.5%

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

   9. Simplified 51.5%

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

   if 2.35000000000000018e-242 < t < 1.1e-203

   1. Initial program 100.0%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   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. Taylor expanded in y around inf 70.6%

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

   5. Taylor expanded in t around 0 61.5%

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

      1. associate-/l* 61.7%

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

   7. Simplified 61.7%

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

      1. associate-/r/ 62.0%

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

   9. Applied egg-rr 62.0%

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

4. Final simplification 54.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.8 \cdot 10^{+83}:\\ \;\;\;\;y \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{elif}\;t \leq 2.35 \cdot 10^{-242}:\\ \;\;\;\;x - \frac{x}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 1.1 \cdot 10^{-203}:\\ \;\;\;\;z \cdot \frac{y}{a}\\ \mathbf{elif}\;t \leq 4.8 \cdot 10^{-18}:\\ \;\;\;\;x - \frac{x}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(1 - \frac{z}{t}\right)\\ \end{array} \]

Alternative 18: 52.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{if}\;t \leq -3.8 \cdot 10^{+83}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 2.35 \cdot 10^{-242}:\\ \;\;\;\;x - \frac{x}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 4.2 \cdot 10^{-208}:\\ \;\;\;\;\frac{y}{\frac{a - t}{z}}\\ \mathbf{elif}\;t \leq 1.5 \cdot 10^{-16}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (- 1.0 (/ z t)))))
   (if (<= t -3.8e+83)
     t_1
     (if (<= t 2.35e-242)
       (- x (/ x (/ a z)))
       (if (<= t 4.2e-208)
         (/ y (/ (- a t) z))
         (if (<= t 1.5e-16) (* x (- 1.0 (/ z a))) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * (1.0 - (z / t));
	double tmp;
	if (t <= -3.8e+83) {
		tmp = t_1;
	} else if (t <= 2.35e-242) {
		tmp = x - (x / (a / z));
	} else if (t <= 4.2e-208) {
		tmp = y / ((a - t) / z);
	} else if (t <= 1.5e-16) {
		tmp = x * (1.0 - (z / a));
	} 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 * (1.0d0 - (z / t))
    if (t <= (-3.8d+83)) then
        tmp = t_1
    else if (t <= 2.35d-242) then
        tmp = x - (x / (a / z))
    else if (t <= 4.2d-208) then
        tmp = y / ((a - t) / z)
    else if (t <= 1.5d-16) then
        tmp = x * (1.0d0 - (z / a))
    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 * (1.0 - (z / t));
	double tmp;
	if (t <= -3.8e+83) {
		tmp = t_1;
	} else if (t <= 2.35e-242) {
		tmp = x - (x / (a / z));
	} else if (t <= 4.2e-208) {
		tmp = y / ((a - t) / z);
	} else if (t <= 1.5e-16) {
		tmp = x * (1.0 - (z / a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * (1.0 - (z / t))
	tmp = 0
	if t <= -3.8e+83:
		tmp = t_1
	elif t <= 2.35e-242:
		tmp = x - (x / (a / z))
	elif t <= 4.2e-208:
		tmp = y / ((a - t) / z)
	elif t <= 1.5e-16:
		tmp = x * (1.0 - (z / a))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(1.0 - Float64(z / t)))
	tmp = 0.0
	if (t <= -3.8e+83)
		tmp = t_1;
	elseif (t <= 2.35e-242)
		tmp = Float64(x - Float64(x / Float64(a / z)));
	elseif (t <= 4.2e-208)
		tmp = Float64(y / Float64(Float64(a - t) / z));
	elseif (t <= 1.5e-16)
		tmp = Float64(x * Float64(1.0 - Float64(z / a)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * (1.0 - (z / t));
	tmp = 0.0;
	if (t <= -3.8e+83)
		tmp = t_1;
	elseif (t <= 2.35e-242)
		tmp = x - (x / (a / z));
	elseif (t <= 4.2e-208)
		tmp = y / ((a - t) / z);
	elseif (t <= 1.5e-16)
		tmp = x * (1.0 - (z / a));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(1.0 - N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -3.8e+83], t$95$1, If[LessEqual[t, 2.35e-242], N[(x - N[(x / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4.2e-208], N[(y / N[(N[(a - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.5e-16], N[(x * N[(1.0 - N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -3.8000000000000002e83 or 1.49999999999999997e-16 < t

   1. Initial program 38.9%

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

      1. associate-*l/ 62.4%

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

   3. Simplified 62.4%

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

   4. Taylor expanded in y around inf 67.8%

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

   5. Taylor expanded in a around 0 57.9%

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

      1. mul-1-neg 57.9%

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

      2. unsub-neg 57.9%

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

   7. Simplified 57.9%

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

   if -3.8000000000000002e83 < t < 2.35000000000000018e-242

   1. Initial program 93.2%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   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. Taylor expanded in t around 0 68.7%

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

      1. associate-/l* 70.7%

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

   6. Simplified 70.7%

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

   7. Taylor expanded in y around 0 51.0%

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

      1. mul-1-neg 51.0%

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

      2. unsub-neg 51.0%

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

      3. associate-/l* 53.1%

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

   9. Simplified 53.1%

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

   if 2.35000000000000018e-242 < t < 4.20000000000000024e-208

   1. Initial program 100.0%

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

      1. associate-*l/ 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in y around inf 86.0%

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

   5. Taylor expanded in z around inf 86.1%

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

      1. associate-/l* 86.1%

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

   7. Simplified 86.1%

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

   if 4.20000000000000024e-208 < t < 1.49999999999999997e-16

   1. Initial program 85.8%

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

      1. associate-*l/ 88.6%

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

   3. Simplified 88.6%

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

   4. Taylor expanded in t around 0 57.7%

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

      1. associate-/l* 62.6%

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

   6. Simplified 62.6%

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

   7. Taylor expanded in x around inf 47.2%

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

      1. mul-1-neg 47.2%

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

      2. unsub-neg 47.2%

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

   9. Simplified 47.2%

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

4. Final simplification 55.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.8 \cdot 10^{+83}:\\ \;\;\;\;y \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{elif}\;t \leq 2.35 \cdot 10^{-242}:\\ \;\;\;\;x - \frac{x}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 4.2 \cdot 10^{-208}:\\ \;\;\;\;\frac{y}{\frac{a - t}{z}}\\ \mathbf{elif}\;t \leq 1.5 \cdot 10^{-16}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(1 - \frac{z}{t}\right)\\ \end{array} \]

Alternative 19: 52.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - \frac{x}{\frac{a}{z}}\\ t_2 := y \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{if}\;t \leq -3.9 \cdot 10^{+84}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 5.2 \cdot 10^{-244}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.85 \cdot 10^{-203}:\\ \;\;\;\;\frac{y \cdot z}{a - t}\\ \mathbf{elif}\;t \leq 1.5 \cdot 10^{-16}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (/ x (/ a z)))) (t_2 (* y (- 1.0 (/ z t)))))
   (if (<= t -3.9e+84)
     t_2
     (if (<= t 5.2e-244)
       t_1
       (if (<= t 1.85e-203)
         (/ (* y z) (- a t))
         (if (<= t 1.5e-16) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (x / (a / z));
	double t_2 = y * (1.0 - (z / t));
	double tmp;
	if (t <= -3.9e+84) {
		tmp = t_2;
	} else if (t <= 5.2e-244) {
		tmp = t_1;
	} else if (t <= 1.85e-203) {
		tmp = (y * z) / (a - t);
	} else if (t <= 1.5e-16) {
		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 = x - (x / (a / z))
    t_2 = y * (1.0d0 - (z / t))
    if (t <= (-3.9d+84)) then
        tmp = t_2
    else if (t <= 5.2d-244) then
        tmp = t_1
    else if (t <= 1.85d-203) then
        tmp = (y * z) / (a - t)
    else if (t <= 1.5d-16) 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 = x - (x / (a / z));
	double t_2 = y * (1.0 - (z / t));
	double tmp;
	if (t <= -3.9e+84) {
		tmp = t_2;
	} else if (t <= 5.2e-244) {
		tmp = t_1;
	} else if (t <= 1.85e-203) {
		tmp = (y * z) / (a - t);
	} else if (t <= 1.5e-16) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - (x / (a / z))
	t_2 = y * (1.0 - (z / t))
	tmp = 0
	if t <= -3.9e+84:
		tmp = t_2
	elif t <= 5.2e-244:
		tmp = t_1
	elif t <= 1.85e-203:
		tmp = (y * z) / (a - t)
	elif t <= 1.5e-16:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(x / Float64(a / z)))
	t_2 = Float64(y * Float64(1.0 - Float64(z / t)))
	tmp = 0.0
	if (t <= -3.9e+84)
		tmp = t_2;
	elseif (t <= 5.2e-244)
		tmp = t_1;
	elseif (t <= 1.85e-203)
		tmp = Float64(Float64(y * z) / Float64(a - t));
	elseif (t <= 1.5e-16)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - (x / (a / z));
	t_2 = y * (1.0 - (z / t));
	tmp = 0.0;
	if (t <= -3.9e+84)
		tmp = t_2;
	elseif (t <= 5.2e-244)
		tmp = t_1;
	elseif (t <= 1.85e-203)
		tmp = (y * z) / (a - t);
	elseif (t <= 1.5e-16)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x - N[(x / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(1.0 - N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -3.9e+84], t$95$2, If[LessEqual[t, 5.2e-244], t$95$1, If[LessEqual[t, 1.85e-203], N[(N[(y * z), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.5e-16], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -3.90000000000000016e84 or 1.49999999999999997e-16 < t

   1. Initial program 38.9%

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

      1. associate-*l/ 62.4%

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

   3. Simplified 62.4%

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

   4. Taylor expanded in y around inf 67.8%

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

   5. Taylor expanded in a around 0 57.9%

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

      1. mul-1-neg 57.9%

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

      2. unsub-neg 57.9%

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

   7. Simplified 57.9%

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

   if -3.90000000000000016e84 < t < 5.2000000000000003e-244 or 1.85000000000000001e-203 < t < 1.49999999999999997e-16

   1. Initial program 90.6%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   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. Taylor expanded in t around 0 65.0%

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

      1. associate-/l* 68.1%

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

   6. Simplified 68.1%

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

   7. Taylor expanded in y around 0 48.5%

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

      1. mul-1-neg 48.5%

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

      2. unsub-neg 48.5%

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

      3. associate-/l* 51.5%

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

   9. Simplified 51.5%

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

   if 5.2000000000000003e-244 < t < 1.85000000000000001e-203

   1. Initial program 100.0%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   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. Taylor expanded in y around inf 70.6%

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

   5. Taylor expanded in z around inf 70.8%

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

4. Final simplification 55.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.9 \cdot 10^{+84}:\\ \;\;\;\;y \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{elif}\;t \leq 5.2 \cdot 10^{-244}:\\ \;\;\;\;x - \frac{x}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 1.85 \cdot 10^{-203}:\\ \;\;\;\;\frac{y \cdot z}{a - t}\\ \mathbf{elif}\;t \leq 1.5 \cdot 10^{-16}:\\ \;\;\;\;x - \frac{x}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(1 - \frac{z}{t}\right)\\ \end{array} \]

Alternative 20: 52.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - \frac{x}{\frac{a}{z}}\\ \mathbf{if}\;t \leq -5.4 \cdot 10^{+82}:\\ \;\;\;\;y \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{elif}\;t \leq 1.6 \cdot 10^{-242}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.1 \cdot 10^{-203}:\\ \;\;\;\;\frac{y \cdot z}{a - t}\\ \mathbf{elif}\;t \leq 6 \cdot 10^{-15}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;y - y \cdot \frac{z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (/ x (/ a z)))))
   (if (<= t -5.4e+82)
     (* y (- 1.0 (/ z t)))
     (if (<= t 1.6e-242)
       t_1
       (if (<= t 1.1e-203)
         (/ (* y z) (- a t))
         (if (<= t 6e-15) t_1 (- y (* y (/ z t)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (x / (a / z));
	double tmp;
	if (t <= -5.4e+82) {
		tmp = y * (1.0 - (z / t));
	} else if (t <= 1.6e-242) {
		tmp = t_1;
	} else if (t <= 1.1e-203) {
		tmp = (y * z) / (a - t);
	} else if (t <= 6e-15) {
		tmp = t_1;
	} else {
		tmp = y - (y * (z / t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x - (x / (a / z))
    if (t <= (-5.4d+82)) then
        tmp = y * (1.0d0 - (z / t))
    else if (t <= 1.6d-242) then
        tmp = t_1
    else if (t <= 1.1d-203) then
        tmp = (y * z) / (a - t)
    else if (t <= 6d-15) then
        tmp = t_1
    else
        tmp = y - (y * (z / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (x / (a / z));
	double tmp;
	if (t <= -5.4e+82) {
		tmp = y * (1.0 - (z / t));
	} else if (t <= 1.6e-242) {
		tmp = t_1;
	} else if (t <= 1.1e-203) {
		tmp = (y * z) / (a - t);
	} else if (t <= 6e-15) {
		tmp = t_1;
	} else {
		tmp = y - (y * (z / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - (x / (a / z))
	tmp = 0
	if t <= -5.4e+82:
		tmp = y * (1.0 - (z / t))
	elif t <= 1.6e-242:
		tmp = t_1
	elif t <= 1.1e-203:
		tmp = (y * z) / (a - t)
	elif t <= 6e-15:
		tmp = t_1
	else:
		tmp = y - (y * (z / t))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(x / Float64(a / z)))
	tmp = 0.0
	if (t <= -5.4e+82)
		tmp = Float64(y * Float64(1.0 - Float64(z / t)));
	elseif (t <= 1.6e-242)
		tmp = t_1;
	elseif (t <= 1.1e-203)
		tmp = Float64(Float64(y * z) / Float64(a - t));
	elseif (t <= 6e-15)
		tmp = t_1;
	else
		tmp = Float64(y - Float64(y * Float64(z / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - (x / (a / z));
	tmp = 0.0;
	if (t <= -5.4e+82)
		tmp = y * (1.0 - (z / t));
	elseif (t <= 1.6e-242)
		tmp = t_1;
	elseif (t <= 1.1e-203)
		tmp = (y * z) / (a - t);
	elseif (t <= 6e-15)
		tmp = t_1;
	else
		tmp = y - (y * (z / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x - N[(x / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -5.4e+82], N[(y * N[(1.0 - N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.6e-242], t$95$1, If[LessEqual[t, 1.1e-203], N[(N[(y * z), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 6e-15], t$95$1, N[(y - N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -5.3999999999999999e82

   1. Initial program 30.8%

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

      1. associate-*l/ 56.7%

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

   3. Simplified 56.7%

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

   4. Taylor expanded in y around inf 65.8%

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

   5. Taylor expanded in a around 0 61.2%

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

      1. mul-1-neg 61.2%

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

      2. unsub-neg 61.2%

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

   7. Simplified 61.2%

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

   if -5.3999999999999999e82 < t < 1.59999999999999999e-242 or 1.1e-203 < t < 6e-15

   1. Initial program 90.6%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   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. Taylor expanded in t around 0 65.0%

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

      1. associate-/l* 68.1%

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

   6. Simplified 68.1%

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

   7. Taylor expanded in y around 0 48.5%

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

      1. mul-1-neg 48.5%

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

      2. unsub-neg 48.5%

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

      3. associate-/l* 51.5%

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

   9. Simplified 51.5%

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

   if 1.59999999999999999e-242 < t < 1.1e-203

   1. Initial program 100.0%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   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. Taylor expanded in y around inf 70.6%

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

   5. Taylor expanded in z around inf 70.8%

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

   if 6e-15 < t

   1. Initial program 43.4%

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

      1. associate-*l/ 65.5%

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

   3. Simplified 65.5%

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

   4. Taylor expanded in y around inf 68.9%

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

   5. Taylor expanded in a around 0 56.0%

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

      1. distribute-lft-in 56.0%

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

      2. *-commutative 56.0%

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

      3. *-lft-identity 56.0%

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

      4. associate-*r/ 56.0%

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

      5. mul-1-neg 56.0%

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

   7. Simplified 56.0%

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

4. Final simplification 55.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.4 \cdot 10^{+82}:\\ \;\;\;\;y \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{elif}\;t \leq 1.6 \cdot 10^{-242}:\\ \;\;\;\;x - \frac{x}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 1.1 \cdot 10^{-203}:\\ \;\;\;\;\frac{y \cdot z}{a - t}\\ \mathbf{elif}\;t \leq 6 \cdot 10^{-15}:\\ \;\;\;\;x - \frac{x}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;y - y \cdot \frac{z}{t}\\ \end{array} \]

Alternative 21: 64.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -3.3 \cdot 10^{+26} \lor \neg \left(a \leq 1.3 \cdot 10^{+48}\right):\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -3.3e+26) (not (<= a 1.3e+48)))
   (+ x (* (- z t) (/ y a)))
   (* y (/ (- z t) (- a t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -3.3e+26) || !(a <= 1.3e+48)) {
		tmp = x + ((z - t) * (y / a));
	} 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 ((a <= (-3.3d+26)) .or. (.not. (a <= 1.3d+48))) then
        tmp = x + ((z - t) * (y / a))
    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 ((a <= -3.3e+26) || !(a <= 1.3e+48)) {
		tmp = x + ((z - t) * (y / a));
	} else {
		tmp = y * ((z - t) / (a - t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -3.3e+26) or not (a <= 1.3e+48):
		tmp = x + ((z - t) * (y / a))
	else:
		tmp = y * ((z - t) / (a - t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -3.3e+26) || !(a <= 1.3e+48))
		tmp = Float64(x + Float64(Float64(z - t) * Float64(y / a)));
	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 ((a <= -3.3e+26) || ~((a <= 1.3e+48)))
		tmp = x + ((z - t) * (y / a));
	else
		tmp = y * ((z - t) / (a - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -3.3e+26], N[Not[LessEqual[a, 1.3e+48]], $MachinePrecision]], N[(x + N[(N[(z - t), $MachinePrecision] * N[(y / a), $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 a < -3.29999999999999993e26 or 1.29999999999999998e48 < a

   1. Initial program 66.2%

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

      1. associate-*l/ 84.8%

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

   3. Simplified 84.8%

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

   4. Taylor expanded in a around inf 73.3%

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

   5. Taylor expanded in y around inf 67.1%

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

   if -3.29999999999999993e26 < a < 1.29999999999999998e48

   1. Initial program 67.4%

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

      1. associate-*l/ 73.1%

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

   3. Simplified 73.1%

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

   4. Taylor expanded in x around 0 53.7%

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

      1. associate-*r/ 63.0%

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

   6. Simplified 63.0%

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

4. Final simplification 64.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.3 \cdot 10^{+26} \lor \neg \left(a \leq 1.3 \cdot 10^{+48}\right):\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \end{array} \]

Alternative 22: 36.9% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.2 \cdot 10^{+58}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -8 \cdot 10^{-230}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 1.3 \cdot 10^{-10}:\\ \;\;\;\;z \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -2.2e+58)
   y
   (if (<= t -8e-230) x (if (<= t 1.3e-10) (* z (/ y a)) y))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -2.2e+58) {
		tmp = y;
	} else if (t <= -8e-230) {
		tmp = x;
	} else if (t <= 1.3e-10) {
		tmp = z * (y / a);
	} 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 <= (-2.2d+58)) then
        tmp = y
    else if (t <= (-8d-230)) then
        tmp = x
    else if (t <= 1.3d-10) then
        tmp = z * (y / a)
    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 <= -2.2e+58) {
		tmp = y;
	} else if (t <= -8e-230) {
		tmp = x;
	} else if (t <= 1.3e-10) {
		tmp = z * (y / a);
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -2.2e+58:
		tmp = y
	elif t <= -8e-230:
		tmp = x
	elif t <= 1.3e-10:
		tmp = z * (y / a)
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -2.2e+58)
		tmp = y;
	elseif (t <= -8e-230)
		tmp = x;
	elseif (t <= 1.3e-10)
		tmp = Float64(z * Float64(y / a));
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -2.2e+58)
		tmp = y;
	elseif (t <= -8e-230)
		tmp = x;
	elseif (t <= 1.3e-10)
		tmp = z * (y / a);
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -2.2e+58], y, If[LessEqual[t, -8e-230], x, If[LessEqual[t, 1.3e-10], N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision], y]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.2000000000000001e58 or 1.29999999999999991e-10 < t

   1. Initial program 39.4%

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

      1. associate-*l/ 62.7%

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

   3. Simplified 62.7%

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

   4. Taylor expanded in t around inf 48.9%

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

   if -2.2000000000000001e58 < t < -8.00000000000000037e-230

   1. Initial program 91.5%

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

      1. associate-*l/ 90.0%

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

   3. Simplified 90.0%

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

   4. Taylor expanded in a around inf 36.9%

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

   if -8.00000000000000037e-230 < t < 1.29999999999999991e-10

   1. Initial program 90.9%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   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. Taylor expanded in y around inf 45.5%

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

   5. Taylor expanded in t around 0 33.3%

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

      1. associate-/l* 34.5%

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

   7. Simplified 34.5%

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

      1. associate-/r/ 32.2%

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

   9. Applied egg-rr 32.2%

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

4. Final simplification 41.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.2 \cdot 10^{+58}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -8 \cdot 10^{-230}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 1.3 \cdot 10^{-10}:\\ \;\;\;\;z \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 23: 37.5% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.6 \cdot 10^{+61}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -5.6 \cdot 10^{-228}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 8.2 \cdot 10^{-8}:\\ \;\;\;\;\frac{y}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -2.6e+61)
   y
   (if (<= t -5.6e-228) x (if (<= t 8.2e-8) (/ y (/ a z)) y))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -2.6e+61) {
		tmp = y;
	} else if (t <= -5.6e-228) {
		tmp = x;
	} else if (t <= 8.2e-8) {
		tmp = y / (a / z);
	} 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 <= (-2.6d+61)) then
        tmp = y
    else if (t <= (-5.6d-228)) then
        tmp = x
    else if (t <= 8.2d-8) then
        tmp = y / (a / z)
    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 <= -2.6e+61) {
		tmp = y;
	} else if (t <= -5.6e-228) {
		tmp = x;
	} else if (t <= 8.2e-8) {
		tmp = y / (a / z);
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -2.6e+61:
		tmp = y
	elif t <= -5.6e-228:
		tmp = x
	elif t <= 8.2e-8:
		tmp = y / (a / z)
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -2.6e+61)
		tmp = y;
	elseif (t <= -5.6e-228)
		tmp = x;
	elseif (t <= 8.2e-8)
		tmp = Float64(y / Float64(a / z));
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -2.6e+61)
		tmp = y;
	elseif (t <= -5.6e-228)
		tmp = x;
	elseif (t <= 8.2e-8)
		tmp = y / (a / z);
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -2.6e+61], y, If[LessEqual[t, -5.6e-228], x, If[LessEqual[t, 8.2e-8], N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision], y]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.59999999999999973e61 or 8.20000000000000063e-8 < t

   1. Initial program 39.4%

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

      1. associate-*l/ 62.7%

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

   3. Simplified 62.7%

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

   4. Taylor expanded in t around inf 48.9%

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

   if -2.59999999999999973e61 < t < -5.6000000000000005e-228

   1. Initial program 91.5%

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

      1. associate-*l/ 90.0%

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

   3. Simplified 90.0%

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

   4. Taylor expanded in a around inf 36.9%

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

   if -5.6000000000000005e-228 < t < 8.20000000000000063e-8

   1. Initial program 90.9%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   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. Taylor expanded in y around inf 45.5%

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

   5. Taylor expanded in t around 0 33.3%

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

      1. associate-/l* 34.5%

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

   7. Simplified 34.5%

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

4. Final simplification 41.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.6 \cdot 10^{+61}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -5.6 \cdot 10^{-228}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 8.2 \cdot 10^{-8}:\\ \;\;\;\;\frac{y}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 24: 39.0% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.45 \cdot 10^{+64}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 2.5 \cdot 10^{-10}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -1.45e+64) y (if (<= t 2.5e-10) x y)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.45e+64) {
		tmp = y;
	} else if (t <= 2.5e-10) {
		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 <= (-1.45d+64)) then
        tmp = y
    else if (t <= 2.5d-10) 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 <= -1.45e+64) {
		tmp = y;
	} else if (t <= 2.5e-10) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -1.45e+64:
		tmp = y
	elif t <= 2.5e-10:
		tmp = x
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -1.45e+64)
		tmp = y;
	elseif (t <= 2.5e-10)
		tmp = x;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -1.45e+64)
		tmp = y;
	elseif (t <= 2.5e-10)
		tmp = x;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -1.45e+64], y, If[LessEqual[t, 2.5e-10], x, y]]

Derivation

1. Split input into 2 regimes

2. if t < -1.44999999999999997e64 or 2.50000000000000016e-10 < t

   1. Initial program 39.4%

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

      1. associate-*l/ 62.7%

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

   3. Simplified 62.7%

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

   4. Taylor expanded in t around inf 48.9%

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

   if -1.44999999999999997e64 < t < 2.50000000000000016e-10

   1. Initial program 91.2%

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

      1. associate-*l/ 91.4%

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

   3. Simplified 91.4%

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

   4. Taylor expanded in a around inf 30.5%

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

4. Final simplification 39.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.45 \cdot 10^{+64}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 2.5 \cdot 10^{-10}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 25: 24.9% 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 66.9%

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

   1. associate-*l/ 77.9%

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

3. Simplified 77.9%

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

4. Taylor expanded in a around inf 19.6%

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

5. Final simplification 19.6%

   \[\leadsto x \]

Developer target: 87.0% 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 2023275 
(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))))