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

Percentage Accurate: 67.5% → 88.8%

Time: 23.5s

Alternatives: 21

Speedup: 0.9×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 67.5% 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: 88.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -6.5 \cdot 10^{+135} \lor \neg \left(t \leq 1.65 \cdot 10^{+80}\right):\\ \;\;\;\;y + \frac{x - y}{\frac{t}{z - a}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{\frac{a - t}{z - t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -6.5e+135) (not (<= t 1.65e+80)))
   (+ 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 <= -6.5e+135) || !(t <= 1.65e+80)) {
		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 <= (-6.5d+135)) .or. (.not. (t <= 1.65d+80))) 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 <= -6.5e+135) || !(t <= 1.65e+80)) {
		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 <= -6.5e+135) or not (t <= 1.65e+80):
		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 <= -6.5e+135) || !(t <= 1.65e+80))
		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 <= -6.5e+135) || ~((t <= 1.65e+80)))
		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, -6.5e+135], N[Not[LessEqual[t, 1.65e+80]], $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 < -6.5000000000000003e135 or 1.64999999999999995e80 < t

   1. Initial program 21.5%

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

      1. associate-/l* 51.5%

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

      2. clear-num 51.3%

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

      3. associate-/r/ 51.4%

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

      4. clear-num 51.4%

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

   3. Applied egg-rr 51.4%

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

   4. Taylor expanded in t around -inf 73.1%

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

      1. mul-1-neg 73.1%

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

      2. unsub-neg 73.1%

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

      3. div-sub 73.1%

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

      4. *-commutative 73.1%

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

      5. div-sub 73.1%

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

      6. distribute-rgt-out-- 73.4%

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

      7. associate-/l* 88.5%

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

   6. Simplified 88.5%

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

   if -6.5000000000000003e135 < t < 1.64999999999999995e80

   1. Initial program 83.6%

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

      1. associate-/l* 90.7%

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

   3. Simplified 90.7%

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

4. Final simplification 90.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.5 \cdot 10^{+135} \lor \neg \left(t \leq 1.65 \cdot 10^{+80}\right):\\ \;\;\;\;y + \frac{x - y}{\frac{t}{z - a}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{\frac{a - t}{z - t}}\\ \end{array} \]

Alternative 2: 66.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{z - t}{a - t}\\ \mathbf{if}\;t \leq -1.3 \cdot 10^{+134}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -7.5 \cdot 10^{+49}:\\ \;\;\;\;x - \frac{y}{\frac{a}{t} + -1}\\ \mathbf{elif}\;t \leq -4 \cdot 10^{+21}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.45 \cdot 10^{-89}:\\ \;\;\;\;x + \frac{y - x}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 10^{-23}:\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \mathbf{elif}\;t \leq 1.3 \cdot 10^{+80}:\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ (- z t) (- a t)))))
   (if (<= t -1.3e+134)
     t_1
     (if (<= t -7.5e+49)
       (- x (/ y (+ (/ a t) -1.0)))
       (if (<= t -4e+21)
         t_1
         (if (<= t 1.45e-89)
           (+ x (/ (- y x) (/ a z)))
           (if (<= t 1e-23)
             (* z (/ (- y x) (- a t)))
             (if (<= t 1.3e+80) (+ x (* (- y x) (/ z a))) 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 <= -1.3e+134) {
		tmp = t_1;
	} else if (t <= -7.5e+49) {
		tmp = x - (y / ((a / t) + -1.0));
	} else if (t <= -4e+21) {
		tmp = t_1;
	} else if (t <= 1.45e-89) {
		tmp = x + ((y - x) / (a / z));
	} else if (t <= 1e-23) {
		tmp = z * ((y - x) / (a - t));
	} else if (t <= 1.3e+80) {
		tmp = x + ((y - x) * (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 * ((z - t) / (a - t))
    if (t <= (-1.3d+134)) then
        tmp = t_1
    else if (t <= (-7.5d+49)) then
        tmp = x - (y / ((a / t) + (-1.0d0)))
    else if (t <= (-4d+21)) then
        tmp = t_1
    else if (t <= 1.45d-89) then
        tmp = x + ((y - x) / (a / z))
    else if (t <= 1d-23) then
        tmp = z * ((y - x) / (a - t))
    else if (t <= 1.3d+80) then
        tmp = x + ((y - x) * (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 * ((z - t) / (a - t));
	double tmp;
	if (t <= -1.3e+134) {
		tmp = t_1;
	} else if (t <= -7.5e+49) {
		tmp = x - (y / ((a / t) + -1.0));
	} else if (t <= -4e+21) {
		tmp = t_1;
	} else if (t <= 1.45e-89) {
		tmp = x + ((y - x) / (a / z));
	} else if (t <= 1e-23) {
		tmp = z * ((y - x) / (a - t));
	} else if (t <= 1.3e+80) {
		tmp = x + ((y - x) * (z / a));
	} 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 <= -1.3e+134:
		tmp = t_1
	elif t <= -7.5e+49:
		tmp = x - (y / ((a / t) + -1.0))
	elif t <= -4e+21:
		tmp = t_1
	elif t <= 1.45e-89:
		tmp = x + ((y - x) / (a / z))
	elif t <= 1e-23:
		tmp = z * ((y - x) / (a - t))
	elif t <= 1.3e+80:
		tmp = x + ((y - x) * (z / a))
	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 <= -1.3e+134)
		tmp = t_1;
	elseif (t <= -7.5e+49)
		tmp = Float64(x - Float64(y / Float64(Float64(a / t) + -1.0)));
	elseif (t <= -4e+21)
		tmp = t_1;
	elseif (t <= 1.45e-89)
		tmp = Float64(x + Float64(Float64(y - x) / Float64(a / z)));
	elseif (t <= 1e-23)
		tmp = Float64(z * Float64(Float64(y - x) / Float64(a - t)));
	elseif (t <= 1.3e+80)
		tmp = Float64(x + Float64(Float64(y - x) * Float64(z / a)));
	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 <= -1.3e+134)
		tmp = t_1;
	elseif (t <= -7.5e+49)
		tmp = x - (y / ((a / t) + -1.0));
	elseif (t <= -4e+21)
		tmp = t_1;
	elseif (t <= 1.45e-89)
		tmp = x + ((y - x) / (a / z));
	elseif (t <= 1e-23)
		tmp = z * ((y - x) / (a - t));
	elseif (t <= 1.3e+80)
		tmp = x + ((y - x) * (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[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.3e+134], t$95$1, If[LessEqual[t, -7.5e+49], N[(x - N[(y / N[(N[(a / t), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -4e+21], t$95$1, If[LessEqual[t, 1.45e-89], N[(x + N[(N[(y - x), $MachinePrecision] / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1e-23], N[(z * N[(N[(y - x), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.3e+80], N[(x + N[(N[(y - x), $MachinePrecision] * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -1.3000000000000001e134 or -7.4999999999999995e49 < t < -4e21 or 1.29999999999999991e80 < t

   1. Initial program 26.3%

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

      1. associate-*l/ 51.3%

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

   3. Simplified 51.3%

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

   4. Taylor expanded in x around 0 38.4%

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

      1. associate-*r/ 69.9%

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

   6. Simplified 69.9%

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

   if -1.3000000000000001e134 < t < -7.4999999999999995e49

   1. Initial program 64.2%

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

      1. associate-*l/ 82.3%

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

   3. Simplified 82.3%

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

   4. Taylor expanded in y around inf 68.6%

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

   5. Taylor expanded in z around 0 61.0%

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

      1. +-commutative 61.0%

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

      2. mul-1-neg 61.0%

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

      3. unsub-neg 61.0%

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

      4. associate-/l* 64.7%

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

      5. div-sub 64.7%

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

      6. *-inverses 64.7%

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

   7. Simplified 64.7%

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

   if -4e21 < t < 1.44999999999999996e-89

   1. Initial program 87.4%

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

      1. associate-*l/ 91.9%

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

   3. Simplified 91.9%

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

   4. Taylor expanded in t around 0 72.4%

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

      1. +-commutative 72.4%

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

      2. associate-/l* 79.2%

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

   6. Simplified 79.2%

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

   if 1.44999999999999996e-89 < t < 9.9999999999999996e-24

   1. Initial program 84.2%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   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 z around inf 68.0%

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

      1. div-sub 68.0%

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

   6. Simplified 68.0%

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

   if 9.9999999999999996e-24 < t < 1.29999999999999991e80

   1. Initial program 86.6%

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

      1. associate-/l* 90.3%

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

      2. clear-num 90.3%

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

      3. associate-/r/ 90.4%

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

      4. clear-num 90.8%

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

   3. Applied egg-rr 90.8%

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

   4. Taylor expanded in t around 0 61.6%

      \[\leadsto x + \color{blue}{\frac{z}{a}} \cdot \left(y - x\right) \]
3. Recombined 5 regimes into one program.

4. Final simplification 72.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.3 \cdot 10^{+134}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;t \leq -7.5 \cdot 10^{+49}:\\ \;\;\;\;x - \frac{y}{\frac{a}{t} + -1}\\ \mathbf{elif}\;t \leq -4 \cdot 10^{+21}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;t \leq 1.45 \cdot 10^{-89}:\\ \;\;\;\;x + \frac{y - x}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 10^{-23}:\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \mathbf{elif}\;t \leq 1.3 \cdot 10^{+80}:\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \end{array} \]

Alternative 3: 66.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{z - t}{a - t}\\ \mathbf{if}\;t \leq -2.7 \cdot 10^{+132}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -6.6 \cdot 10^{+49}:\\ \;\;\;\;x - \frac{y}{\frac{a}{t} + -1}\\ \mathbf{elif}\;t \leq -7.2 \cdot 10^{+23}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 6 \cdot 10^{-90}:\\ \;\;\;\;x + \frac{y - x}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 3.3 \cdot 10^{-23}:\\ \;\;\;\;\frac{z}{\frac{a - t}{y - x}}\\ \mathbf{elif}\;t \leq 1.2 \cdot 10^{+80}:\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ (- z t) (- a t)))))
   (if (<= t -2.7e+132)
     t_1
     (if (<= t -6.6e+49)
       (- x (/ y (+ (/ a t) -1.0)))
       (if (<= t -7.2e+23)
         t_1
         (if (<= t 6e-90)
           (+ x (/ (- y x) (/ a z)))
           (if (<= t 3.3e-23)
             (/ z (/ (- a t) (- y x)))
             (if (<= t 1.2e+80) (+ x (* (- y x) (/ z a))) 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 <= -2.7e+132) {
		tmp = t_1;
	} else if (t <= -6.6e+49) {
		tmp = x - (y / ((a / t) + -1.0));
	} else if (t <= -7.2e+23) {
		tmp = t_1;
	} else if (t <= 6e-90) {
		tmp = x + ((y - x) / (a / z));
	} else if (t <= 3.3e-23) {
		tmp = z / ((a - t) / (y - x));
	} else if (t <= 1.2e+80) {
		tmp = x + ((y - x) * (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 * ((z - t) / (a - t))
    if (t <= (-2.7d+132)) then
        tmp = t_1
    else if (t <= (-6.6d+49)) then
        tmp = x - (y / ((a / t) + (-1.0d0)))
    else if (t <= (-7.2d+23)) then
        tmp = t_1
    else if (t <= 6d-90) then
        tmp = x + ((y - x) / (a / z))
    else if (t <= 3.3d-23) then
        tmp = z / ((a - t) / (y - x))
    else if (t <= 1.2d+80) then
        tmp = x + ((y - x) * (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 * ((z - t) / (a - t));
	double tmp;
	if (t <= -2.7e+132) {
		tmp = t_1;
	} else if (t <= -6.6e+49) {
		tmp = x - (y / ((a / t) + -1.0));
	} else if (t <= -7.2e+23) {
		tmp = t_1;
	} else if (t <= 6e-90) {
		tmp = x + ((y - x) / (a / z));
	} else if (t <= 3.3e-23) {
		tmp = z / ((a - t) / (y - x));
	} else if (t <= 1.2e+80) {
		tmp = x + ((y - x) * (z / a));
	} 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 <= -2.7e+132:
		tmp = t_1
	elif t <= -6.6e+49:
		tmp = x - (y / ((a / t) + -1.0))
	elif t <= -7.2e+23:
		tmp = t_1
	elif t <= 6e-90:
		tmp = x + ((y - x) / (a / z))
	elif t <= 3.3e-23:
		tmp = z / ((a - t) / (y - x))
	elif t <= 1.2e+80:
		tmp = x + ((y - x) * (z / a))
	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 <= -2.7e+132)
		tmp = t_1;
	elseif (t <= -6.6e+49)
		tmp = Float64(x - Float64(y / Float64(Float64(a / t) + -1.0)));
	elseif (t <= -7.2e+23)
		tmp = t_1;
	elseif (t <= 6e-90)
		tmp = Float64(x + Float64(Float64(y - x) / Float64(a / z)));
	elseif (t <= 3.3e-23)
		tmp = Float64(z / Float64(Float64(a - t) / Float64(y - x)));
	elseif (t <= 1.2e+80)
		tmp = Float64(x + Float64(Float64(y - x) * Float64(z / a)));
	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 <= -2.7e+132)
		tmp = t_1;
	elseif (t <= -6.6e+49)
		tmp = x - (y / ((a / t) + -1.0));
	elseif (t <= -7.2e+23)
		tmp = t_1;
	elseif (t <= 6e-90)
		tmp = x + ((y - x) / (a / z));
	elseif (t <= 3.3e-23)
		tmp = z / ((a - t) / (y - x));
	elseif (t <= 1.2e+80)
		tmp = x + ((y - x) * (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[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.7e+132], t$95$1, If[LessEqual[t, -6.6e+49], N[(x - N[(y / N[(N[(a / t), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -7.2e+23], t$95$1, If[LessEqual[t, 6e-90], N[(x + N[(N[(y - x), $MachinePrecision] / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.3e-23], N[(z / N[(N[(a - t), $MachinePrecision] / N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.2e+80], N[(x + N[(N[(y - x), $MachinePrecision] * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -2.7e132 or -6.5999999999999997e49 < t < -7.1999999999999997e23 or 1.1999999999999999e80 < t

   1. Initial program 26.3%

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

      1. associate-*l/ 51.3%

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

   3. Simplified 51.3%

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

   4. Taylor expanded in x around 0 38.4%

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

      1. associate-*r/ 69.9%

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

   6. Simplified 69.9%

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

   if -2.7e132 < t < -6.5999999999999997e49

   1. Initial program 64.2%

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

      1. associate-*l/ 82.3%

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

   3. Simplified 82.3%

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

   4. Taylor expanded in y around inf 68.6%

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

   5. Taylor expanded in z around 0 61.0%

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

      1. +-commutative 61.0%

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

      2. mul-1-neg 61.0%

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

      3. unsub-neg 61.0%

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

      4. associate-/l* 64.7%

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

      5. div-sub 64.7%

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

      6. *-inverses 64.7%

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

   7. Simplified 64.7%

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

   if -7.1999999999999997e23 < t < 6.00000000000000041e-90

   1. Initial program 87.4%

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

      1. associate-*l/ 91.9%

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

   3. Simplified 91.9%

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

   4. Taylor expanded in t around 0 72.4%

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

      1. +-commutative 72.4%

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

      2. associate-/l* 79.2%

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

   6. Simplified 79.2%

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

   if 6.00000000000000041e-90 < t < 3.30000000000000021e-23

   1. Initial program 84.2%

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

      1. associate-/l* 91.6%

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

      2. clear-num 91.6%

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

      3. associate-/r/ 91.4%

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

      4. clear-num 91.4%

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

   3. Applied egg-rr 91.4%

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

      1. div-inv 91.6%

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

   5. Applied egg-rr 91.6%

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

   6. Taylor expanded in z around -inf 76.1%

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

      1. associate-/l* 68.2%

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

   8. Simplified 68.2%

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

   if 3.30000000000000021e-23 < t < 1.1999999999999999e80

   1. Initial program 86.6%

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

      1. associate-/l* 90.3%

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

      2. clear-num 90.3%

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

      3. associate-/r/ 90.4%

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

      4. clear-num 90.8%

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

   3. Applied egg-rr 90.8%

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

   4. Taylor expanded in t around 0 61.6%

      \[\leadsto x + \color{blue}{\frac{z}{a}} \cdot \left(y - x\right) \]
3. Recombined 5 regimes into one program.

4. Final simplification 72.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.7 \cdot 10^{+132}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;t \leq -6.6 \cdot 10^{+49}:\\ \;\;\;\;x - \frac{y}{\frac{a}{t} + -1}\\ \mathbf{elif}\;t \leq -7.2 \cdot 10^{+23}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;t \leq 6 \cdot 10^{-90}:\\ \;\;\;\;x + \frac{y - x}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 3.3 \cdot 10^{-23}:\\ \;\;\;\;\frac{z}{\frac{a - t}{y - x}}\\ \mathbf{elif}\;t \leq 1.2 \cdot 10^{+80}:\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \end{array} \]

Alternative 4: 53.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{if}\;t \leq -1.45 \cdot 10^{+133}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -5.5 \cdot 10^{+23}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;t \leq -4.8 \cdot 10^{-18}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -2.15 \cdot 10^{-36}:\\ \;\;\;\;\frac{y}{\frac{a - t}{z}}\\ \mathbf{elif}\;t \leq -3.7 \cdot 10^{-51}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 2 \cdot 10^{+80}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (- 1.0 (/ z a)))))
   (if (<= t -1.45e+133)
     y
     (if (<= t -5.5e+23)
       (+ y x)
       (if (<= t -4.8e-18)
         t_1
         (if (<= t -2.15e-36)
           (/ y (/ (- a t) z))
           (if (<= t -3.7e-51)
             t_1
             (if (<= t 2e+80) (+ x (/ y (/ a z))) 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 <= -1.45e+133) {
		tmp = y;
	} else if (t <= -5.5e+23) {
		tmp = y + x;
	} else if (t <= -4.8e-18) {
		tmp = t_1;
	} else if (t <= -2.15e-36) {
		tmp = y / ((a - t) / z);
	} else if (t <= -3.7e-51) {
		tmp = t_1;
	} else if (t <= 2e+80) {
		tmp = x + (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) :: t_1
    real(8) :: tmp
    t_1 = x * (1.0d0 - (z / a))
    if (t <= (-1.45d+133)) then
        tmp = y
    else if (t <= (-5.5d+23)) then
        tmp = y + x
    else if (t <= (-4.8d-18)) then
        tmp = t_1
    else if (t <= (-2.15d-36)) then
        tmp = y / ((a - t) / z)
    else if (t <= (-3.7d-51)) then
        tmp = t_1
    else if (t <= 2d+80) then
        tmp = x + (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 t_1 = x * (1.0 - (z / a));
	double tmp;
	if (t <= -1.45e+133) {
		tmp = y;
	} else if (t <= -5.5e+23) {
		tmp = y + x;
	} else if (t <= -4.8e-18) {
		tmp = t_1;
	} else if (t <= -2.15e-36) {
		tmp = y / ((a - t) / z);
	} else if (t <= -3.7e-51) {
		tmp = t_1;
	} else if (t <= 2e+80) {
		tmp = x + (y / (a / z));
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x * (1.0 - (z / a))
	tmp = 0
	if t <= -1.45e+133:
		tmp = y
	elif t <= -5.5e+23:
		tmp = y + x
	elif t <= -4.8e-18:
		tmp = t_1
	elif t <= -2.15e-36:
		tmp = y / ((a - t) / z)
	elif t <= -3.7e-51:
		tmp = t_1
	elif t <= 2e+80:
		tmp = x + (y / (a / z))
	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 <= -1.45e+133)
		tmp = y;
	elseif (t <= -5.5e+23)
		tmp = Float64(y + x);
	elseif (t <= -4.8e-18)
		tmp = t_1;
	elseif (t <= -2.15e-36)
		tmp = Float64(y / Float64(Float64(a - t) / z));
	elseif (t <= -3.7e-51)
		tmp = t_1;
	elseif (t <= 2e+80)
		tmp = Float64(x + Float64(y / Float64(a / z)));
	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 <= -1.45e+133)
		tmp = y;
	elseif (t <= -5.5e+23)
		tmp = y + x;
	elseif (t <= -4.8e-18)
		tmp = t_1;
	elseif (t <= -2.15e-36)
		tmp = y / ((a - t) / z);
	elseif (t <= -3.7e-51)
		tmp = t_1;
	elseif (t <= 2e+80)
		tmp = x + (y / (a / z));
	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, -1.45e+133], y, If[LessEqual[t, -5.5e+23], N[(y + x), $MachinePrecision], If[LessEqual[t, -4.8e-18], t$95$1, If[LessEqual[t, -2.15e-36], N[(y / N[(N[(a - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -3.7e-51], t$95$1, If[LessEqual[t, 2e+80], N[(x + N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], y]]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -1.4500000000000001e133 or 2e80 < t

   1. Initial program 21.5%

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

      1. associate-*l/ 48.6%

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

   3. Simplified 48.6%

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

   4. Taylor expanded in t around inf 59.7%

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

   if -1.4500000000000001e133 < t < -5.50000000000000004e23

   1. Initial program 67.8%

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

      1. associate-*l/ 82.4%

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

   3. Simplified 82.4%

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

   4. Taylor expanded in y around inf 68.4%

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

   5. Taylor expanded in t around inf 43.5%

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

   if -5.50000000000000004e23 < t < -4.79999999999999988e-18 or -2.1500000000000001e-36 < t < -3.69999999999999973e-51

   1. Initial program 61.8%

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

      1. associate-*l/ 75.8%

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

   3. Simplified 75.8%

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

   4. Taylor expanded in t around 0 46.2%

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

   5. Taylor expanded in x around inf 59.8%

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

      1. *-commutative 59.8%

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

      2. mul-1-neg 59.8%

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

      3. unsub-neg 59.8%

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

   7. Simplified 59.8%

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

   if -4.79999999999999988e-18 < t < -2.1500000000000001e-36

   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/ 99.6%

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

   3. Simplified 99.6%

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

   4. Taylor expanded in x around 0 100.0%

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

   5. Taylor expanded in z around inf 76.2%

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

      1. associate-/l* 76.2%

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

   7. Simplified 76.2%

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

   if -3.69999999999999973e-51 < t < 2e80

   1. Initial program 89.7%

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

      1. associate-*l/ 93.5%

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

   3. Simplified 93.5%

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

   4. Taylor expanded in t around 0 69.2%

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

   5. Taylor expanded in y around inf 58.9%

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

      1. associate-/l* 64.3%

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

   7. Simplified 64.3%

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

4. Final simplification 60.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.45 \cdot 10^{+133}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -5.5 \cdot 10^{+23}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;t \leq -4.8 \cdot 10^{-18}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{elif}\;t \leq -2.15 \cdot 10^{-36}:\\ \;\;\;\;\frac{y}{\frac{a - t}{z}}\\ \mathbf{elif}\;t \leq -3.7 \cdot 10^{-51}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{elif}\;t \leq 2 \cdot 10^{+80}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 5: 66.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{z - t}{a - t}\\ \mathbf{if}\;t \leq -7.5 \cdot 10^{+133}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -3.9 \cdot 10^{+49}:\\ \;\;\;\;x - \frac{y}{\frac{a}{t} + -1}\\ \mathbf{elif}\;t \leq -4.4 \cdot 10^{+21}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.6 \cdot 10^{-89}:\\ \;\;\;\;x + \frac{y - x}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 1.15 \cdot 10^{+33}:\\ \;\;\;\;\frac{\left(y - x\right) \cdot z}{a - t}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ (- z t) (- a t)))))
   (if (<= t -7.5e+133)
     t_1
     (if (<= t -3.9e+49)
       (- x (/ y (+ (/ a t) -1.0)))
       (if (<= t -4.4e+21)
         t_1
         (if (<= t 1.6e-89)
           (+ x (/ (- y x) (/ a z)))
           (if (<= t 1.15e+33) (/ (* (- y x) z) (- a t)) 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 <= -7.5e+133) {
		tmp = t_1;
	} else if (t <= -3.9e+49) {
		tmp = x - (y / ((a / t) + -1.0));
	} else if (t <= -4.4e+21) {
		tmp = t_1;
	} else if (t <= 1.6e-89) {
		tmp = x + ((y - x) / (a / z));
	} else if (t <= 1.15e+33) {
		tmp = ((y - x) * z) / (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) / (a - t))
    if (t <= (-7.5d+133)) then
        tmp = t_1
    else if (t <= (-3.9d+49)) then
        tmp = x - (y / ((a / t) + (-1.0d0)))
    else if (t <= (-4.4d+21)) then
        tmp = t_1
    else if (t <= 1.6d-89) then
        tmp = x + ((y - x) / (a / z))
    else if (t <= 1.15d+33) then
        tmp = ((y - x) * z) / (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) / (a - t));
	double tmp;
	if (t <= -7.5e+133) {
		tmp = t_1;
	} else if (t <= -3.9e+49) {
		tmp = x - (y / ((a / t) + -1.0));
	} else if (t <= -4.4e+21) {
		tmp = t_1;
	} else if (t <= 1.6e-89) {
		tmp = x + ((y - x) / (a / z));
	} else if (t <= 1.15e+33) {
		tmp = ((y - x) * z) / (a - t);
	} 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 <= -7.5e+133:
		tmp = t_1
	elif t <= -3.9e+49:
		tmp = x - (y / ((a / t) + -1.0))
	elif t <= -4.4e+21:
		tmp = t_1
	elif t <= 1.6e-89:
		tmp = x + ((y - x) / (a / z))
	elif t <= 1.15e+33:
		tmp = ((y - x) * z) / (a - t)
	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 <= -7.5e+133)
		tmp = t_1;
	elseif (t <= -3.9e+49)
		tmp = Float64(x - Float64(y / Float64(Float64(a / t) + -1.0)));
	elseif (t <= -4.4e+21)
		tmp = t_1;
	elseif (t <= 1.6e-89)
		tmp = Float64(x + Float64(Float64(y - x) / Float64(a / z)));
	elseif (t <= 1.15e+33)
		tmp = Float64(Float64(Float64(y - x) * z) / 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) / (a - t));
	tmp = 0.0;
	if (t <= -7.5e+133)
		tmp = t_1;
	elseif (t <= -3.9e+49)
		tmp = x - (y / ((a / t) + -1.0));
	elseif (t <= -4.4e+21)
		tmp = t_1;
	elseif (t <= 1.6e-89)
		tmp = x + ((y - x) / (a / z));
	elseif (t <= 1.15e+33)
		tmp = ((y - x) * z) / (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[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -7.5e+133], t$95$1, If[LessEqual[t, -3.9e+49], N[(x - N[(y / N[(N[(a / t), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -4.4e+21], t$95$1, If[LessEqual[t, 1.6e-89], N[(x + N[(N[(y - x), $MachinePrecision] / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.15e+33], N[(N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -7.49999999999999992e133 or -3.9000000000000001e49 < t < -4.4e21 or 1.15000000000000005e33 < t

   1. Initial program 31.0%

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

      1. associate-*l/ 54.7%

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

   3. Simplified 54.7%

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

   4. Taylor expanded in x around 0 39.6%

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

      1. associate-*r/ 68.2%

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

   6. Simplified 68.2%

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

   if -7.49999999999999992e133 < t < -3.9000000000000001e49

   1. Initial program 64.2%

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

      1. associate-*l/ 82.3%

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

   3. Simplified 82.3%

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

   4. Taylor expanded in y around inf 68.6%

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

   5. Taylor expanded in z around 0 61.0%

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

      1. +-commutative 61.0%

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

      2. mul-1-neg 61.0%

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

      3. unsub-neg 61.0%

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

      4. associate-/l* 64.7%

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

      5. div-sub 64.7%

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

      6. *-inverses 64.7%

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

   7. Simplified 64.7%

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

   if -4.4e21 < t < 1.59999999999999999e-89

   1. Initial program 87.4%

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

      1. associate-*l/ 91.9%

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

   3. Simplified 91.9%

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

   4. Taylor expanded in t around 0 72.4%

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

      1. +-commutative 72.4%

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

      2. associate-/l* 79.2%

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

   6. Simplified 79.2%

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

   if 1.59999999999999999e-89 < t < 1.15000000000000005e33

   1. Initial program 88.6%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   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 z around -inf 64.7%

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

4. Final simplification 72.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7.5 \cdot 10^{+133}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;t \leq -3.9 \cdot 10^{+49}:\\ \;\;\;\;x - \frac{y}{\frac{a}{t} + -1}\\ \mathbf{elif}\;t \leq -4.4 \cdot 10^{+21}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;t \leq 1.6 \cdot 10^{-89}:\\ \;\;\;\;x + \frac{y - x}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 1.15 \cdot 10^{+33}:\\ \;\;\;\;\frac{\left(y - x\right) \cdot z}{a - t}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \end{array} \]

Alternative 6: 71.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(z - t\right) \cdot \frac{y}{a - t}\\ t_2 := y \cdot \frac{z - t}{a - t}\\ \mathbf{if}\;t \leq -1.15 \cdot 10^{+135}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -3.5 \cdot 10^{+24}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 5.7 \cdot 10^{-111}:\\ \;\;\;\;x + \frac{y - x}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 2.2 \cdot 10^{+80}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- z t) (/ y (- a t))))) (t_2 (* y (/ (- z t) (- a t)))))
   (if (<= t -1.15e+135)
     t_2
     (if (<= t -3.5e+24)
       t_1
       (if (<= t 5.7e-111)
         (+ x (/ (- y x) (/ a z)))
         (if (<= t 2.2e+80) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((z - t) * (y / (a - t)));
	double t_2 = y * ((z - t) / (a - t));
	double tmp;
	if (t <= -1.15e+135) {
		tmp = t_2;
	} else if (t <= -3.5e+24) {
		tmp = t_1;
	} else if (t <= 5.7e-111) {
		tmp = x + ((y - x) / (a / z));
	} else if (t <= 2.2e+80) {
		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 / (a - t)))
    t_2 = y * ((z - t) / (a - t))
    if (t <= (-1.15d+135)) then
        tmp = t_2
    else if (t <= (-3.5d+24)) then
        tmp = t_1
    else if (t <= 5.7d-111) then
        tmp = x + ((y - x) / (a / z))
    else if (t <= 2.2d+80) 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 / (a - t)));
	double t_2 = y * ((z - t) / (a - t));
	double tmp;
	if (t <= -1.15e+135) {
		tmp = t_2;
	} else if (t <= -3.5e+24) {
		tmp = t_1;
	} else if (t <= 5.7e-111) {
		tmp = x + ((y - x) / (a / z));
	} else if (t <= 2.2e+80) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((z - t) * (y / (a - t)))
	t_2 = y * ((z - t) / (a - t))
	tmp = 0
	if t <= -1.15e+135:
		tmp = t_2
	elif t <= -3.5e+24:
		tmp = t_1
	elif t <= 5.7e-111:
		tmp = x + ((y - x) / (a / z))
	elif t <= 2.2e+80:
		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(y / Float64(a - t))))
	t_2 = Float64(y * Float64(Float64(z - t) / Float64(a - t)))
	tmp = 0.0
	if (t <= -1.15e+135)
		tmp = t_2;
	elseif (t <= -3.5e+24)
		tmp = t_1;
	elseif (t <= 5.7e-111)
		tmp = Float64(x + Float64(Float64(y - x) / Float64(a / z)));
	elseif (t <= 2.2e+80)
		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 / (a - t)));
	t_2 = y * ((z - t) / (a - t));
	tmp = 0.0;
	if (t <= -1.15e+135)
		tmp = t_2;
	elseif (t <= -3.5e+24)
		tmp = t_1;
	elseif (t <= 5.7e-111)
		tmp = x + ((y - x) / (a / z));
	elseif (t <= 2.2e+80)
		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[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.15e+135], t$95$2, If[LessEqual[t, -3.5e+24], t$95$1, If[LessEqual[t, 5.7e-111], N[(x + N[(N[(y - x), $MachinePrecision] / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.2e+80], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.1500000000000001e135 or 2.20000000000000003e80 < t

   1. Initial program 21.5%

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

      1. associate-*l/ 48.6%

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

   3. Simplified 48.6%

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

   4. Taylor expanded in x around 0 34.6%

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

      1. associate-*r/ 68.7%

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

   6. Simplified 68.7%

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

   if -1.1500000000000001e135 < t < -3.5000000000000002e24 or 5.7e-111 < t < 2.20000000000000003e80

   1. Initial program 77.6%

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

      1. associate-*l/ 86.4%

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

   3. Simplified 86.4%

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

   4. Taylor expanded in y around inf 67.4%

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

   if -3.5000000000000002e24 < t < 5.7e-111

   1. Initial program 87.9%

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

      1. associate-*l/ 92.8%

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

   3. Simplified 92.8%

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

   4. Taylor expanded in t around 0 73.3%

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

      1. +-commutative 73.3%

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

      2. associate-/l* 80.7%

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

   6. Simplified 80.7%

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

4. Final simplification 73.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.15 \cdot 10^{+135}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;t \leq -3.5 \cdot 10^{+24}:\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y}{a - t}\\ \mathbf{elif}\;t \leq 5.7 \cdot 10^{-111}:\\ \;\;\;\;x + \frac{y - x}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 2.2 \cdot 10^{+80}:\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y}{a - t}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \end{array} \]

Alternative 7: 49.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{if}\;t \leq -1.55 \cdot 10^{+135}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -2.9 \cdot 10^{+24}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;t \leq -3.2 \cdot 10^{-20}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -9 \cdot 10^{-37}:\\ \;\;\;\;y \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq 1.2 \cdot 10^{+80}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (- 1.0 (/ z a)))))
   (if (<= t -1.55e+135)
     y
     (if (<= t -2.9e+24)
       (+ y x)
       (if (<= t -3.2e-20)
         t_1
         (if (<= t -9e-37) (* y (/ z a)) (if (<= t 1.2e+80) 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 <= -1.55e+135) {
		tmp = y;
	} else if (t <= -2.9e+24) {
		tmp = y + x;
	} else if (t <= -3.2e-20) {
		tmp = t_1;
	} else if (t <= -9e-37) {
		tmp = y * (z / a);
	} else if (t <= 1.2e+80) {
		tmp = t_1;
	} else {
		tmp = y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (1.0d0 - (z / a))
    if (t <= (-1.55d+135)) then
        tmp = y
    else if (t <= (-2.9d+24)) then
        tmp = y + x
    else if (t <= (-3.2d-20)) then
        tmp = t_1
    else if (t <= (-9d-37)) then
        tmp = y * (z / a)
    else if (t <= 1.2d+80) then
        tmp = t_1
    else
        tmp = y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (1.0 - (z / a));
	double tmp;
	if (t <= -1.55e+135) {
		tmp = y;
	} else if (t <= -2.9e+24) {
		tmp = y + x;
	} else if (t <= -3.2e-20) {
		tmp = t_1;
	} else if (t <= -9e-37) {
		tmp = y * (z / a);
	} else if (t <= 1.2e+80) {
		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 <= -1.55e+135:
		tmp = y
	elif t <= -2.9e+24:
		tmp = y + x
	elif t <= -3.2e-20:
		tmp = t_1
	elif t <= -9e-37:
		tmp = y * (z / a)
	elif t <= 1.2e+80:
		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 <= -1.55e+135)
		tmp = y;
	elseif (t <= -2.9e+24)
		tmp = Float64(y + x);
	elseif (t <= -3.2e-20)
		tmp = t_1;
	elseif (t <= -9e-37)
		tmp = Float64(y * Float64(z / a));
	elseif (t <= 1.2e+80)
		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 <= -1.55e+135)
		tmp = y;
	elseif (t <= -2.9e+24)
		tmp = y + x;
	elseif (t <= -3.2e-20)
		tmp = t_1;
	elseif (t <= -9e-37)
		tmp = y * (z / a);
	elseif (t <= 1.2e+80)
		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, -1.55e+135], y, If[LessEqual[t, -2.9e+24], N[(y + x), $MachinePrecision], If[LessEqual[t, -3.2e-20], t$95$1, If[LessEqual[t, -9e-37], N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.2e+80], t$95$1, y]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -1.55000000000000011e135 or 1.1999999999999999e80 < t

   1. Initial program 21.5%

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

      1. associate-*l/ 48.6%

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

   3. Simplified 48.6%

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

   4. Taylor expanded in t around inf 59.7%

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

   if -1.55000000000000011e135 < t < -2.89999999999999979e24

   1. Initial program 67.8%

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

      1. associate-*l/ 82.4%

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

   3. Simplified 82.4%

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

   4. Taylor expanded in y around inf 68.4%

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

   5. Taylor expanded in t around inf 43.5%

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

   if -2.89999999999999979e24 < t < -3.1999999999999997e-20 or -9.00000000000000081e-37 < t < 1.1999999999999999e80

   1. Initial program 86.7%

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

      1. associate-*l/ 91.6%

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

   3. Simplified 91.6%

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

   4. Taylor expanded in t around 0 66.7%

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

   5. Taylor expanded in x around inf 55.6%

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

      1. *-commutative 55.6%

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

      2. mul-1-neg 55.6%

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

      3. unsub-neg 55.6%

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

   7. Simplified 55.6%

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

   if -3.1999999999999997e-20 < t < -9.00000000000000081e-37

   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/ 99.6%

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

   3. Simplified 99.6%

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

   4. Taylor expanded in x around 0 100.0%

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

   5. Taylor expanded in t around 0 51.6%

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

      1. associate-/l* 51.6%

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

   7. Simplified 51.6%

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

      1. div-inv 51.6%

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

      2. clear-num 51.6%

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

   9. Applied egg-rr 51.6%

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

4. Final simplification 55.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.55 \cdot 10^{+135}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -2.9 \cdot 10^{+24}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;t \leq -3.2 \cdot 10^{-20}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{elif}\;t \leq -9 \cdot 10^{-37}:\\ \;\;\;\;y \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq 1.2 \cdot 10^{+80}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 8: 49.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{if}\;t \leq -1.35 \cdot 10^{+136}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -1.05 \cdot 10^{+22}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;t \leq -3.2 \cdot 10^{-20}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -3.85 \cdot 10^{-84}:\\ \;\;\;\;z \cdot \frac{y - x}{a}\\ \mathbf{elif}\;t \leq 1.7 \cdot 10^{+80}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (- 1.0 (/ z a)))))
   (if (<= t -1.35e+136)
     y
     (if (<= t -1.05e+22)
       (+ y x)
       (if (<= t -3.2e-20)
         t_1
         (if (<= t -3.85e-84)
           (* z (/ (- y x) a))
           (if (<= t 1.7e+80) 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 <= -1.35e+136) {
		tmp = y;
	} else if (t <= -1.05e+22) {
		tmp = y + x;
	} else if (t <= -3.2e-20) {
		tmp = t_1;
	} else if (t <= -3.85e-84) {
		tmp = z * ((y - x) / a);
	} else if (t <= 1.7e+80) {
		tmp = t_1;
	} else {
		tmp = y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (1.0d0 - (z / a))
    if (t <= (-1.35d+136)) then
        tmp = y
    else if (t <= (-1.05d+22)) then
        tmp = y + x
    else if (t <= (-3.2d-20)) then
        tmp = t_1
    else if (t <= (-3.85d-84)) then
        tmp = z * ((y - x) / a)
    else if (t <= 1.7d+80) then
        tmp = t_1
    else
        tmp = y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (1.0 - (z / a));
	double tmp;
	if (t <= -1.35e+136) {
		tmp = y;
	} else if (t <= -1.05e+22) {
		tmp = y + x;
	} else if (t <= -3.2e-20) {
		tmp = t_1;
	} else if (t <= -3.85e-84) {
		tmp = z * ((y - x) / a);
	} else if (t <= 1.7e+80) {
		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 <= -1.35e+136:
		tmp = y
	elif t <= -1.05e+22:
		tmp = y + x
	elif t <= -3.2e-20:
		tmp = t_1
	elif t <= -3.85e-84:
		tmp = z * ((y - x) / a)
	elif t <= 1.7e+80:
		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 <= -1.35e+136)
		tmp = y;
	elseif (t <= -1.05e+22)
		tmp = Float64(y + x);
	elseif (t <= -3.2e-20)
		tmp = t_1;
	elseif (t <= -3.85e-84)
		tmp = Float64(z * Float64(Float64(y - x) / a));
	elseif (t <= 1.7e+80)
		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 <= -1.35e+136)
		tmp = y;
	elseif (t <= -1.05e+22)
		tmp = y + x;
	elseif (t <= -3.2e-20)
		tmp = t_1;
	elseif (t <= -3.85e-84)
		tmp = z * ((y - x) / a);
	elseif (t <= 1.7e+80)
		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, -1.35e+136], y, If[LessEqual[t, -1.05e+22], N[(y + x), $MachinePrecision], If[LessEqual[t, -3.2e-20], t$95$1, If[LessEqual[t, -3.85e-84], N[(z * N[(N[(y - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.7e+80], t$95$1, y]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -1.3500000000000001e136 or 1.69999999999999996e80 < t

   1. Initial program 21.5%

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

      1. associate-*l/ 48.6%

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

   3. Simplified 48.6%

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

   4. Taylor expanded in t around inf 59.7%

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

   if -1.3500000000000001e136 < t < -1.0499999999999999e22

   1. Initial program 67.8%

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

      1. associate-*l/ 82.4%

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

   3. Simplified 82.4%

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

   4. Taylor expanded in y around inf 68.4%

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

   5. Taylor expanded in t around inf 43.5%

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

   if -1.0499999999999999e22 < t < -3.1999999999999997e-20 or -3.85e-84 < t < 1.69999999999999996e80

   1. Initial program 87.0%

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

      1. associate-*l/ 90.9%

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

   3. Simplified 90.9%

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

   4. Taylor expanded in t around 0 68.0%

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

   5. Taylor expanded in x around inf 56.0%

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

      1. *-commutative 56.0%

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

      2. mul-1-neg 56.0%

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

      3. unsub-neg 56.0%

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

   7. Simplified 56.0%

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

   if -3.1999999999999997e-20 < t < -3.85e-84

   1. Initial program 87.1%

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

      1. associate-*l/ 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in t around 0 50.9%

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

   5. Taylor expanded in z around inf 54.9%

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

      1. div-sub 54.9%

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

   7. Simplified 54.9%

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

4. Final simplification 55.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.35 \cdot 10^{+136}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -1.05 \cdot 10^{+22}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;t \leq -3.2 \cdot 10^{-20}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{elif}\;t \leq -3.85 \cdot 10^{-84}:\\ \;\;\;\;z \cdot \frac{y - x}{a}\\ \mathbf{elif}\;t \leq 1.7 \cdot 10^{+80}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 9: 66.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(y - x\right) \cdot \frac{z}{a}\\ t_2 := y \cdot \frac{z - t}{a - t}\\ \mathbf{if}\;t \leq -3.2 \cdot 10^{+23}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 1.4 \cdot 10^{-89}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 2.4 \cdot 10^{-24}:\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \mathbf{elif}\;t \leq 1.16 \cdot 10^{+80}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- y x) (/ z a)))) (t_2 (* y (/ (- z t) (- a t)))))
   (if (<= t -3.2e+23)
     t_2
     (if (<= t 1.4e-89)
       t_1
       (if (<= t 2.4e-24)
         (* z (/ (- y x) (- a t)))
         (if (<= t 1.16e+80) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - x) * (z / a));
	double t_2 = y * ((z - t) / (a - t));
	double tmp;
	if (t <= -3.2e+23) {
		tmp = t_2;
	} else if (t <= 1.4e-89) {
		tmp = t_1;
	} else if (t <= 2.4e-24) {
		tmp = z * ((y - x) / (a - t));
	} else if (t <= 1.16e+80) {
		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 + ((y - x) * (z / a))
    t_2 = y * ((z - t) / (a - t))
    if (t <= (-3.2d+23)) then
        tmp = t_2
    else if (t <= 1.4d-89) then
        tmp = t_1
    else if (t <= 2.4d-24) then
        tmp = z * ((y - x) / (a - t))
    else if (t <= 1.16d+80) 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 + ((y - x) * (z / a));
	double t_2 = y * ((z - t) / (a - t));
	double tmp;
	if (t <= -3.2e+23) {
		tmp = t_2;
	} else if (t <= 1.4e-89) {
		tmp = t_1;
	} else if (t <= 2.4e-24) {
		tmp = z * ((y - x) / (a - t));
	} else if (t <= 1.16e+80) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((y - x) * (z / a))
	t_2 = y * ((z - t) / (a - t))
	tmp = 0
	if t <= -3.2e+23:
		tmp = t_2
	elif t <= 1.4e-89:
		tmp = t_1
	elif t <= 2.4e-24:
		tmp = z * ((y - x) / (a - t))
	elif t <= 1.16e+80:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(y - x) * Float64(z / a)))
	t_2 = Float64(y * Float64(Float64(z - t) / Float64(a - t)))
	tmp = 0.0
	if (t <= -3.2e+23)
		tmp = t_2;
	elseif (t <= 1.4e-89)
		tmp = t_1;
	elseif (t <= 2.4e-24)
		tmp = Float64(z * Float64(Float64(y - x) / Float64(a - t)));
	elseif (t <= 1.16e+80)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((y - x) * (z / a));
	t_2 = y * ((z - t) / (a - t));
	tmp = 0.0;
	if (t <= -3.2e+23)
		tmp = t_2;
	elseif (t <= 1.4e-89)
		tmp = t_1;
	elseif (t <= 2.4e-24)
		tmp = z * ((y - x) / (a - t));
	elseif (t <= 1.16e+80)
		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[(y - x), $MachinePrecision] * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -3.2e+23], t$95$2, If[LessEqual[t, 1.4e-89], t$95$1, If[LessEqual[t, 2.4e-24], N[(z * N[(N[(y - x), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.16e+80], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -3.2e23 or 1.15999999999999997e80 < t

   1. Initial program 36.1%

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

      1. associate-*l/ 59.3%

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

   3. Simplified 59.3%

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

   4. Taylor expanded in x around 0 40.3%

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

      1. associate-*r/ 63.9%

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

   6. Simplified 63.9%

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

   if -3.2e23 < t < 1.3999999999999999e-89 or 2.3999999999999998e-24 < t < 1.15999999999999997e80

   1. Initial program 87.3%

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

      1. associate-/l* 91.8%

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

      2. clear-num 91.9%

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

      3. associate-/r/ 91.3%

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

      4. clear-num 91.4%

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

   3. Applied egg-rr 91.4%

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

   4. Taylor expanded in t around 0 75.8%

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

   if 1.3999999999999999e-89 < t < 2.3999999999999998e-24

   1. Initial program 84.2%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   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 z around inf 68.0%

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

      1. div-sub 68.0%

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

   6. Simplified 68.0%

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

4. Final simplification 70.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.2 \cdot 10^{+23}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;t \leq 1.4 \cdot 10^{-89}:\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq 2.4 \cdot 10^{-24}:\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \mathbf{elif}\;t \leq 1.16 \cdot 10^{+80}:\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \end{array} \]

Alternative 10: 66.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{z - t}{a - t}\\ \mathbf{if}\;t \leq -1.3 \cdot 10^{+22}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.05 \cdot 10^{-89}:\\ \;\;\;\;x + \frac{y - x}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 1.7 \cdot 10^{-24}:\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \mathbf{elif}\;t \leq 1.16 \cdot 10^{+80}:\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ (- z t) (- a t)))))
   (if (<= t -1.3e+22)
     t_1
     (if (<= t 1.05e-89)
       (+ x (/ (- y x) (/ a z)))
       (if (<= t 1.7e-24)
         (* z (/ (- y x) (- a t)))
         (if (<= t 1.16e+80) (+ x (* (- y x) (/ z a))) 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 <= -1.3e+22) {
		tmp = t_1;
	} else if (t <= 1.05e-89) {
		tmp = x + ((y - x) / (a / z));
	} else if (t <= 1.7e-24) {
		tmp = z * ((y - x) / (a - t));
	} else if (t <= 1.16e+80) {
		tmp = x + ((y - x) * (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 * ((z - t) / (a - t))
    if (t <= (-1.3d+22)) then
        tmp = t_1
    else if (t <= 1.05d-89) then
        tmp = x + ((y - x) / (a / z))
    else if (t <= 1.7d-24) then
        tmp = z * ((y - x) / (a - t))
    else if (t <= 1.16d+80) then
        tmp = x + ((y - x) * (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 * ((z - t) / (a - t));
	double tmp;
	if (t <= -1.3e+22) {
		tmp = t_1;
	} else if (t <= 1.05e-89) {
		tmp = x + ((y - x) / (a / z));
	} else if (t <= 1.7e-24) {
		tmp = z * ((y - x) / (a - t));
	} else if (t <= 1.16e+80) {
		tmp = x + ((y - x) * (z / a));
	} 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 <= -1.3e+22:
		tmp = t_1
	elif t <= 1.05e-89:
		tmp = x + ((y - x) / (a / z))
	elif t <= 1.7e-24:
		tmp = z * ((y - x) / (a - t))
	elif t <= 1.16e+80:
		tmp = x + ((y - x) * (z / a))
	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 <= -1.3e+22)
		tmp = t_1;
	elseif (t <= 1.05e-89)
		tmp = Float64(x + Float64(Float64(y - x) / Float64(a / z)));
	elseif (t <= 1.7e-24)
		tmp = Float64(z * Float64(Float64(y - x) / Float64(a - t)));
	elseif (t <= 1.16e+80)
		tmp = Float64(x + Float64(Float64(y - x) * Float64(z / a)));
	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 <= -1.3e+22)
		tmp = t_1;
	elseif (t <= 1.05e-89)
		tmp = x + ((y - x) / (a / z));
	elseif (t <= 1.7e-24)
		tmp = z * ((y - x) / (a - t));
	elseif (t <= 1.16e+80)
		tmp = x + ((y - x) * (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[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.3e+22], t$95$1, If[LessEqual[t, 1.05e-89], N[(x + N[(N[(y - x), $MachinePrecision] / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.7e-24], N[(z * N[(N[(y - x), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.16e+80], N[(x + N[(N[(y - x), $MachinePrecision] * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -1.3e22 or 1.15999999999999997e80 < t

   1. Initial program 36.1%

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

      1. associate-*l/ 59.3%

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

   3. Simplified 59.3%

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

   4. Taylor expanded in x around 0 40.3%

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

      1. associate-*r/ 63.9%

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

   6. Simplified 63.9%

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

   if -1.3e22 < t < 1.05e-89

   1. Initial program 87.4%

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

      1. associate-*l/ 91.9%

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

   3. Simplified 91.9%

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

   4. Taylor expanded in t around 0 72.4%

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

      1. +-commutative 72.4%

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

      2. associate-/l* 79.2%

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

   6. Simplified 79.2%

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

   if 1.05e-89 < t < 1.69999999999999996e-24

   1. Initial program 84.2%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   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 z around inf 68.0%

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

      1. div-sub 68.0%

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

   6. Simplified 68.0%

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

   if 1.69999999999999996e-24 < t < 1.15999999999999997e80

   1. Initial program 86.6%

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

      1. associate-/l* 90.3%

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

      2. clear-num 90.3%

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

      3. associate-/r/ 90.4%

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

      4. clear-num 90.8%

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

   3. Applied egg-rr 90.8%

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

   4. Taylor expanded in t around 0 61.6%

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

4. Final simplification 70.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.3 \cdot 10^{+22}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;t \leq 1.05 \cdot 10^{-89}:\\ \;\;\;\;x + \frac{y - x}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 1.7 \cdot 10^{-24}:\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \mathbf{elif}\;t \leq 1.16 \cdot 10^{+80}:\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \end{array} \]

Alternative 11: 87.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -6.5 \cdot 10^{+135} \lor \neg \left(t \leq 2.2 \cdot 10^{+80}\right):\\ \;\;\;\;y + \frac{x - y}{\frac{t}{z - a}}\\ \mathbf{else}:\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y - x}{a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -6.5e+135) (not (<= t 2.2e+80)))
   (+ 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 <= -6.5e+135) || !(t <= 2.2e+80)) {
		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 <= (-6.5d+135)) .or. (.not. (t <= 2.2d+80))) 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 <= -6.5e+135) || !(t <= 2.2e+80)) {
		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 <= -6.5e+135) or not (t <= 2.2e+80):
		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 <= -6.5e+135) || !(t <= 2.2e+80))
		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 <= -6.5e+135) || ~((t <= 2.2e+80)))
		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, -6.5e+135], N[Not[LessEqual[t, 2.2e+80]], $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 < -6.5000000000000003e135 or 2.20000000000000003e80 < t

   1. Initial program 21.5%

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

      1. associate-/l* 51.5%

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

      2. clear-num 51.3%

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

      3. associate-/r/ 51.4%

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

      4. clear-num 51.4%

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

   3. Applied egg-rr 51.4%

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

   4. Taylor expanded in t around -inf 73.1%

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

      1. mul-1-neg 73.1%

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

      2. unsub-neg 73.1%

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

      3. div-sub 73.1%

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

      4. *-commutative 73.1%

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

      5. div-sub 73.1%

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

      6. distribute-rgt-out-- 73.4%

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

      7. associate-/l* 88.5%

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

   6. Simplified 88.5%

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

   if -6.5000000000000003e135 < t < 2.20000000000000003e80

   1. Initial program 83.6%

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

      1. associate-*l/ 90.1%

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

   3. Simplified 90.1%

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

4. Final simplification 89.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.5 \cdot 10^{+135} \lor \neg \left(t \leq 2.2 \cdot 10^{+80}\right):\\ \;\;\;\;y + \frac{x - y}{\frac{t}{z - a}}\\ \mathbf{else}:\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y - x}{a - t}\\ \end{array} \]

Alternative 12: 88.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4.5 \cdot 10^{+132} \lor \neg \left(t \leq 2.2 \cdot 10^{+80}\right):\\ \;\;\;\;y + \frac{x - y}{\frac{t}{z - a}}\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z - t}{a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -4.5e+132) (not (<= t 2.2e+80)))
   (+ y (/ (- x y) (/ t (- z a))))
   (+ x (* (- y x) (/ (- z t) (- a t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -4.5e+132) || !(t <= 2.2e+80)) {
		tmp = y + ((x - y) / (t / (z - a)));
	} else {
		tmp = x + ((y - x) * ((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 ((t <= (-4.5d+132)) .or. (.not. (t <= 2.2d+80))) then
        tmp = y + ((x - y) / (t / (z - a)))
    else
        tmp = x + ((y - x) * ((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 ((t <= -4.5e+132) || !(t <= 2.2e+80)) {
		tmp = y + ((x - y) / (t / (z - a)));
	} else {
		tmp = x + ((y - x) * ((z - t) / (a - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -4.5e+132) or not (t <= 2.2e+80):
		tmp = y + ((x - y) / (t / (z - a)))
	else:
		tmp = x + ((y - x) * ((z - t) / (a - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -4.5e+132) || !(t <= 2.2e+80))
		tmp = Float64(y + Float64(Float64(x - y) / Float64(t / Float64(z - a))));
	else
		tmp = Float64(x + Float64(Float64(y - x) * 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 ((t <= -4.5e+132) || ~((t <= 2.2e+80)))
		tmp = y + ((x - y) / (t / (z - a)));
	else
		tmp = x + ((y - x) * ((z - t) / (a - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -4.5e+132], N[Not[LessEqual[t, 2.2e+80]], $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[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -4.49999999999999972e132 or 2.20000000000000003e80 < t

   1. Initial program 21.5%

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

      1. associate-/l* 51.5%

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

      2. clear-num 51.3%

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

      3. associate-/r/ 51.4%

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

      4. clear-num 51.4%

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

   3. Applied egg-rr 51.4%

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

   4. Taylor expanded in t around -inf 73.1%

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

      1. mul-1-neg 73.1%

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

      2. unsub-neg 73.1%

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

      3. div-sub 73.1%

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

      4. *-commutative 73.1%

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

      5. div-sub 73.1%

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

      6. distribute-rgt-out-- 73.4%

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

      7. associate-/l* 88.5%

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

   6. Simplified 88.5%

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

   if -4.49999999999999972e132 < t < 2.20000000000000003e80

   1. Initial program 83.6%

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

      1. associate-/l* 90.7%

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

      2. clear-num 90.6%

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

      3. associate-/r/ 90.3%

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

      4. clear-num 90.4%

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

   3. Applied egg-rr 90.4%

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

4. Final simplification 89.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.5 \cdot 10^{+132} \lor \neg \left(t \leq 2.2 \cdot 10^{+80}\right):\\ \;\;\;\;y + \frac{x - y}{\frac{t}{z - a}}\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z - t}{a - t}\\ \end{array} \]

Alternative 13: 60.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{z - t}{a - t}\\ \mathbf{if}\;t \leq -5 \cdot 10^{-97}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.05 \cdot 10^{-89}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 1.9 \cdot 10^{+36}:\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ (- z t) (- a t)))))
   (if (<= t -5e-97)
     t_1
     (if (<= t 1.05e-89)
       (+ x (/ y (/ a z)))
       (if (<= t 1.9e+36) (* z (/ (- y x) (- a t))) 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 <= -5e-97) {
		tmp = t_1;
	} else if (t <= 1.05e-89) {
		tmp = x + (y / (a / z));
	} else if (t <= 1.9e+36) {
		tmp = z * ((y - x) / (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) / (a - t))
    if (t <= (-5d-97)) then
        tmp = t_1
    else if (t <= 1.05d-89) then
        tmp = x + (y / (a / z))
    else if (t <= 1.9d+36) then
        tmp = z * ((y - x) / (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) / (a - t));
	double tmp;
	if (t <= -5e-97) {
		tmp = t_1;
	} else if (t <= 1.05e-89) {
		tmp = x + (y / (a / z));
	} else if (t <= 1.9e+36) {
		tmp = z * ((y - x) / (a - t));
	} 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 <= -5e-97:
		tmp = t_1
	elif t <= 1.05e-89:
		tmp = x + (y / (a / z))
	elif t <= 1.9e+36:
		tmp = z * ((y - x) / (a - t))
	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 <= -5e-97)
		tmp = t_1;
	elseif (t <= 1.05e-89)
		tmp = Float64(x + Float64(y / Float64(a / z)));
	elseif (t <= 1.9e+36)
		tmp = Float64(z * Float64(Float64(y - x) / 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) / (a - t));
	tmp = 0.0;
	if (t <= -5e-97)
		tmp = t_1;
	elseif (t <= 1.05e-89)
		tmp = x + (y / (a / z));
	elseif (t <= 1.9e+36)
		tmp = z * ((y - x) / (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[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -5e-97], t$95$1, If[LessEqual[t, 1.05e-89], N[(x + N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.9e+36], N[(z * N[(N[(y - x), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -4.9999999999999995e-97 or 1.90000000000000012e36 < t

   1. Initial program 47.0%

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

      1. associate-*l/ 65.8%

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

   3. Simplified 65.8%

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

   4. Taylor expanded in x around 0 42.5%

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

      1. associate-*r/ 59.9%

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

   6. Simplified 59.9%

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

   if -4.9999999999999995e-97 < t < 1.05e-89

   1. Initial program 90.3%

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

      1. associate-*l/ 94.8%

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

   3. Simplified 94.8%

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

   4. Taylor expanded in t around 0 79.3%

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

   5. Taylor expanded in y around inf 66.3%

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

      1. associate-/l* 74.4%

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

   7. Simplified 74.4%

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

   if 1.05e-89 < t < 1.90000000000000012e36

   1. Initial program 88.6%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   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 z around inf 61.0%

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

      1. div-sub 61.0%

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

   6. Simplified 61.0%

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

4. Final simplification 65.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5 \cdot 10^{-97}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;t \leq 1.05 \cdot 10^{-89}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 1.9 \cdot 10^{+36}:\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \end{array} \]

Alternative 14: 75.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -4.4 \cdot 10^{-18} \lor \neg \left(a \leq 4 \cdot 10^{-51}\right):\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y}{a - t}\\ \mathbf{else}:\\ \;\;\;\;y + \frac{\left(y - x\right) \cdot \left(a - z\right)}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -4.4e-18) (not (<= a 4e-51)))
   (+ x (* (- z t) (/ y (- a t))))
   (+ y (/ (* (- y x) (- a z)) t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -4.4e-18) || !(a <= 4e-51)) {
		tmp = x + ((z - t) * (y / (a - t)));
	} else {
		tmp = y + (((y - x) * (a - 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 ((a <= (-4.4d-18)) .or. (.not. (a <= 4d-51))) then
        tmp = x + ((z - t) * (y / (a - t)))
    else
        tmp = y + (((y - x) * (a - 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 ((a <= -4.4e-18) || !(a <= 4e-51)) {
		tmp = x + ((z - t) * (y / (a - t)));
	} else {
		tmp = y + (((y - x) * (a - z)) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -4.4e-18) or not (a <= 4e-51):
		tmp = x + ((z - t) * (y / (a - t)))
	else:
		tmp = y + (((y - x) * (a - z)) / t)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -4.4e-18) || !(a <= 4e-51))
		tmp = Float64(x + Float64(Float64(z - t) * Float64(y / Float64(a - t))));
	else
		tmp = Float64(y + Float64(Float64(Float64(y - x) * Float64(a - z)) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -4.4e-18) || ~((a <= 4e-51)))
		tmp = x + ((z - t) * (y / (a - t)));
	else
		tmp = y + (((y - x) * (a - z)) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -4.4e-18], N[Not[LessEqual[a, 4e-51]], $MachinePrecision]], N[(x + N[(N[(z - t), $MachinePrecision] * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y + N[(N[(N[(y - x), $MachinePrecision] * N[(a - z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -4.3999999999999997e-18 or 4e-51 < a

   1. Initial program 70.3%

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

      1. associate-*l/ 87.2%

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

   3. Simplified 87.2%

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

   4. Taylor expanded in y around inf 76.5%

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

   if -4.3999999999999997e-18 < a < 4e-51

   1. Initial program 60.6%

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

      1. associate-*l/ 66.8%

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

   3. Simplified 66.8%

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

   4. Taylor expanded in t around -inf 82.1%

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

      1. mul-1-neg 82.1%

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

      2. unsub-neg 82.1%

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

      3. div-sub 81.2%

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

      4. *-commutative 81.2%

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

      5. div-sub 82.1%

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

      6. distribute-rgt-out-- 82.1%

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

   6. Simplified 82.1%

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

4. Final simplification 78.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4.4 \cdot 10^{-18} \lor \neg \left(a \leq 4 \cdot 10^{-51}\right):\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y}{a - t}\\ \mathbf{else}:\\ \;\;\;\;y + \frac{\left(y - x\right) \cdot \left(a - z\right)}{t}\\ \end{array} \]

Alternative 15: 77.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.15 \cdot 10^{+22} \lor \neg \left(a \leq 1.05 \cdot 10^{-50}\right):\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y}{a - t}\\ \mathbf{else}:\\ \;\;\;\;y + \frac{x - y}{\frac{t}{z - a}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -2.15e+22) (not (<= a 1.05e-50)))
   (+ x (* (- z t) (/ y (- a t))))
   (+ y (/ (- x y) (/ t (- z a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -2.15e+22) || !(a <= 1.05e-50)) {
		tmp = x + ((z - t) * (y / (a - t)));
	} else {
		tmp = y + ((x - y) / (t / (z - a)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a <= (-2.15d+22)) .or. (.not. (a <= 1.05d-50))) then
        tmp = x + ((z - t) * (y / (a - t)))
    else
        tmp = y + ((x - y) / (t / (z - a)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -2.15e+22) || !(a <= 1.05e-50)) {
		tmp = x + ((z - t) * (y / (a - t)));
	} else {
		tmp = y + ((x - y) / (t / (z - a)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -2.15e+22) or not (a <= 1.05e-50):
		tmp = x + ((z - t) * (y / (a - t)))
	else:
		tmp = y + ((x - y) / (t / (z - a)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -2.15e+22) || !(a <= 1.05e-50))
		tmp = Float64(x + Float64(Float64(z - t) * Float64(y / Float64(a - t))));
	else
		tmp = Float64(y + Float64(Float64(x - y) / Float64(t / Float64(z - a))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -2.15e+22) || ~((a <= 1.05e-50)))
		tmp = x + ((z - t) * (y / (a - t)));
	else
		tmp = y + ((x - y) / (t / (z - a)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -2.15e+22], N[Not[LessEqual[a, 1.05e-50]], $MachinePrecision]], N[(x + N[(N[(z - t), $MachinePrecision] * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y + N[(N[(x - y), $MachinePrecision] / N[(t / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -2.1500000000000001e22 or 1.05e-50 < a

   1. Initial program 70.6%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   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 y around inf 78.0%

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

   if -2.1500000000000001e22 < a < 1.05e-50

   1. Initial program 60.8%

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

      1. associate-/l* 67.9%

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

      2. clear-num 67.8%

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

      3. associate-/r/ 67.3%

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

      4. clear-num 67.4%

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

   3. Applied egg-rr 67.4%

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

   4. Taylor expanded in t around -inf 79.3%

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

      1. mul-1-neg 79.3%

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

      2. unsub-neg 79.3%

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

      3. div-sub 78.4%

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

      4. *-commutative 78.4%

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

      5. div-sub 79.3%

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

      6. distribute-rgt-out-- 79.3%

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

      7. associate-/l* 82.6%

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

   6. Simplified 82.6%

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

4. Final simplification 80.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.15 \cdot 10^{+22} \lor \neg \left(a \leq 1.05 \cdot 10^{-50}\right):\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y}{a - t}\\ \mathbf{else}:\\ \;\;\;\;y + \frac{x - y}{\frac{t}{z - a}}\\ \end{array} \]

Alternative 16: 77.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -9.2 \cdot 10^{+20}:\\ \;\;\;\;x + \left(y - x\right) \cdot \left(\left(t - z\right) \cdot \frac{-1}{a}\right)\\ \mathbf{elif}\;a \leq 8 \cdot 10^{-51}:\\ \;\;\;\;y + \frac{x - y}{\frac{t}{z - a}}\\ \mathbf{else}:\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y}{a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -9.2e+20)
   (+ x (* (- y x) (* (- t z) (/ -1.0 a))))
   (if (<= a 8e-51)
     (+ y (/ (- x y) (/ t (- z a))))
     (+ x (* (- z t) (/ y (- a t)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -9.2e+20) {
		tmp = x + ((y - x) * ((t - z) * (-1.0 / a)));
	} else if (a <= 8e-51) {
		tmp = y + ((x - y) / (t / (z - a)));
	} else {
		tmp = x + ((z - t) * (y / (a - t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-9.2d+20)) then
        tmp = x + ((y - x) * ((t - z) * ((-1.0d0) / a)))
    else if (a <= 8d-51) then
        tmp = y + ((x - y) / (t / (z - a)))
    else
        tmp = x + ((z - t) * (y / (a - t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -9.2e+20) {
		tmp = x + ((y - x) * ((t - z) * (-1.0 / a)));
	} else if (a <= 8e-51) {
		tmp = y + ((x - y) / (t / (z - a)));
	} else {
		tmp = x + ((z - t) * (y / (a - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -9.2e+20:
		tmp = x + ((y - x) * ((t - z) * (-1.0 / a)))
	elif a <= 8e-51:
		tmp = y + ((x - y) / (t / (z - a)))
	else:
		tmp = x + ((z - t) * (y / (a - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -9.2e+20)
		tmp = Float64(x + Float64(Float64(y - x) * Float64(Float64(t - z) * Float64(-1.0 / a))));
	elseif (a <= 8e-51)
		tmp = Float64(y + Float64(Float64(x - y) / Float64(t / Float64(z - a))));
	else
		tmp = Float64(x + Float64(Float64(z - t) * Float64(y / Float64(a - t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -9.2e+20)
		tmp = x + ((y - x) * ((t - z) * (-1.0 / a)));
	elseif (a <= 8e-51)
		tmp = y + ((x - y) / (t / (z - a)));
	else
		tmp = x + ((z - t) * (y / (a - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -9.2e+20], N[(x + N[(N[(y - x), $MachinePrecision] * N[(N[(t - z), $MachinePrecision] * N[(-1.0 / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 8e-51], N[(y + N[(N[(x - y), $MachinePrecision] / N[(t / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(z - t), $MachinePrecision] * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < -9.2e20

   1. Initial program 73.4%

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

      1. associate-/l* 90.1%

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

      2. clear-num 90.0%

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

      3. associate-/r/ 90.1%

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

      4. clear-num 90.1%

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

   3. Applied egg-rr 90.1%

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

      1. div-inv 90.1%

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

   5. Applied egg-rr 90.1%

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

   6. Taylor expanded in a around inf 81.3%

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

   if -9.2e20 < a < 8.0000000000000001e-51

   1. Initial program 60.8%

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

      1. associate-/l* 67.9%

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

      2. clear-num 67.8%

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

      3. associate-/r/ 67.3%

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

      4. clear-num 67.4%

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

   3. Applied egg-rr 67.4%

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

   4. Taylor expanded in t around -inf 79.3%

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

      1. mul-1-neg 79.3%

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

      2. unsub-neg 79.3%

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

      3. div-sub 78.4%

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

      4. *-commutative 78.4%

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

      5. div-sub 79.3%

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

      6. distribute-rgt-out-- 79.3%

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

      7. associate-/l* 82.6%

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

   6. Simplified 82.6%

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

   if 8.0000000000000001e-51 < a

   1. Initial program 68.0%

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

      1. associate-*l/ 89.4%

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

   3. Simplified 89.4%

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

   4. Taylor expanded in y around inf 75.9%

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

4. Final simplification 80.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -9.2 \cdot 10^{+20}:\\ \;\;\;\;x + \left(y - x\right) \cdot \left(\left(t - z\right) \cdot \frac{-1}{a}\right)\\ \mathbf{elif}\;a \leq 8 \cdot 10^{-51}:\\ \;\;\;\;y + \frac{x - y}{\frac{t}{z - a}}\\ \mathbf{else}:\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y}{a - t}\\ \end{array} \]

Alternative 17: 54.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4.1 \cdot 10^{+132}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -3.3 \cdot 10^{+24}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;t \leq 2.1 \cdot 10^{+80}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -4.1e+132)
   y
   (if (<= t -3.3e+24) (+ y x) (if (<= t 2.1e+80) (+ x (/ y (/ a z))) y))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -4.1e+132) {
		tmp = y;
	} else if (t <= -3.3e+24) {
		tmp = y + x;
	} else if (t <= 2.1e+80) {
		tmp = x + (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 <= (-4.1d+132)) then
        tmp = y
    else if (t <= (-3.3d+24)) then
        tmp = y + x
    else if (t <= 2.1d+80) then
        tmp = x + (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 <= -4.1e+132) {
		tmp = y;
	} else if (t <= -3.3e+24) {
		tmp = y + x;
	} else if (t <= 2.1e+80) {
		tmp = x + (y / (a / z));
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -4.1e+132:
		tmp = y
	elif t <= -3.3e+24:
		tmp = y + x
	elif t <= 2.1e+80:
		tmp = x + (y / (a / z))
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -4.1e+132)
		tmp = y;
	elseif (t <= -3.3e+24)
		tmp = Float64(y + x);
	elseif (t <= 2.1e+80)
		tmp = Float64(x + 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 <= -4.1e+132)
		tmp = y;
	elseif (t <= -3.3e+24)
		tmp = y + x;
	elseif (t <= 2.1e+80)
		tmp = x + (y / (a / z));
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -4.1e+132], y, If[LessEqual[t, -3.3e+24], N[(y + x), $MachinePrecision], If[LessEqual[t, 2.1e+80], N[(x + N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], y]]]

Derivation

1. Split input into 3 regimes

2. if t < -4.09999999999999992e132 or 2.10000000000000001e80 < t

   1. Initial program 21.5%

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

      1. associate-*l/ 48.6%

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

   3. Simplified 48.6%

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

   4. Taylor expanded in t around inf 59.7%

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

   if -4.09999999999999992e132 < t < -3.2999999999999999e24

   1. Initial program 67.8%

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

      1. associate-*l/ 82.4%

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

   3. Simplified 82.4%

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

   4. Taylor expanded in y around inf 68.4%

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

   5. Taylor expanded in t around inf 43.5%

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

   if -3.2999999999999999e24 < t < 2.10000000000000001e80

   1. Initial program 87.0%

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

      1. associate-*l/ 91.8%

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

   3. Simplified 91.8%

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

   4. Taylor expanded in t around 0 66.3%

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

   5. Taylor expanded in y around inf 56.2%

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

      1. associate-/l* 60.8%

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

   7. Simplified 60.8%

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

4. Final simplification 58.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.1 \cdot 10^{+132}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -3.3 \cdot 10^{+24}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;t \leq 2.1 \cdot 10^{+80}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 18: 52.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y}{\frac{a}{z}}\\ \mathbf{if}\;a \leq -5.2 \cdot 10^{+47}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -2.8 \cdot 10^{-38}:\\ \;\;\;\;x - \frac{z}{\frac{a}{x}}\\ \mathbf{elif}\;a \leq 4.8 \cdot 10^{-41}:\\ \;\;\;\;\frac{t - z}{\frac{t}{y}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ y (/ a z)))))
   (if (<= a -5.2e+47)
     t_1
     (if (<= a -2.8e-38)
       (- x (/ z (/ a x)))
       (if (<= a 4.8e-41) (/ (- t z) (/ t y)) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y / (a / z));
	double tmp;
	if (a <= -5.2e+47) {
		tmp = t_1;
	} else if (a <= -2.8e-38) {
		tmp = x - (z / (a / x));
	} else if (a <= 4.8e-41) {
		tmp = (t - z) / (t / y);
	} 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 / (a / z))
    if (a <= (-5.2d+47)) then
        tmp = t_1
    else if (a <= (-2.8d-38)) then
        tmp = x - (z / (a / x))
    else if (a <= 4.8d-41) then
        tmp = (t - z) / (t / y)
    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 / (a / z));
	double tmp;
	if (a <= -5.2e+47) {
		tmp = t_1;
	} else if (a <= -2.8e-38) {
		tmp = x - (z / (a / x));
	} else if (a <= 4.8e-41) {
		tmp = (t - z) / (t / y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (y / (a / z))
	tmp = 0
	if a <= -5.2e+47:
		tmp = t_1
	elif a <= -2.8e-38:
		tmp = x - (z / (a / x))
	elif a <= 4.8e-41:
		tmp = (t - z) / (t / y)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(y / Float64(a / z)))
	tmp = 0.0
	if (a <= -5.2e+47)
		tmp = t_1;
	elseif (a <= -2.8e-38)
		tmp = Float64(x - Float64(z / Float64(a / x)));
	elseif (a <= 4.8e-41)
		tmp = Float64(Float64(t - z) / Float64(t / y));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (y / (a / z));
	tmp = 0.0;
	if (a <= -5.2e+47)
		tmp = t_1;
	elseif (a <= -2.8e-38)
		tmp = x - (z / (a / x));
	elseif (a <= 4.8e-41)
		tmp = (t - z) / (t / y);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -5.2e+47], t$95$1, If[LessEqual[a, -2.8e-38], N[(x - N[(z / N[(a / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 4.8e-41], N[(N[(t - z), $MachinePrecision] / N[(t / y), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if a < -5.20000000000000007e47 or 4.80000000000000044e-41 < a

   1. Initial program 69.6%

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

      1. associate-*l/ 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 58.9%

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

   5. Taylor expanded in y around inf 57.6%

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

      1. associate-/l* 61.4%

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

   7. Simplified 61.4%

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

   if -5.20000000000000007e47 < a < -2.8e-38

   1. Initial program 79.5%

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

      1. associate-*l/ 74.3%

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

   3. Simplified 74.3%

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

   4. Taylor expanded in t around 0 64.6%

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

   5. Taylor expanded in y around 0 64.6%

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

      1. +-commutative 64.6%

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

      2. mul-1-neg 64.6%

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

      3. unsub-neg 64.6%

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

      4. associate-/l* 64.5%

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

   7. Simplified 64.5%

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

   if -2.8e-38 < a < 4.80000000000000044e-41

   1. Initial program 59.5%

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

      1. associate-*l/ 66.8%

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

   3. Simplified 66.8%

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

   4. Taylor expanded in x around 0 46.7%

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

   5. Taylor expanded in a around 0 43.1%

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

      1. mul-1-neg 43.1%

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

      2. associate-/l* 58.1%

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

   7. Simplified 58.1%

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

4. Final simplification 60.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -5.2 \cdot 10^{+47}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;a \leq -2.8 \cdot 10^{-38}:\\ \;\;\;\;x - \frac{z}{\frac{a}{x}}\\ \mathbf{elif}\;a \leq 4.8 \cdot 10^{-41}:\\ \;\;\;\;\frac{t - z}{\frac{t}{y}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \end{array} \]

Alternative 19: 60.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -5.2 \cdot 10^{-97} \lor \neg \left(t \leq 0.012\right):\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -5.2e-97) (not (<= t 0.012)))
   (* y (/ (- z t) (- a t)))
   (+ x (/ y (/ a z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -5.2e-97) || !(t <= 0.012)) {
		tmp = y * ((z - t) / (a - t));
	} else {
		tmp = x + (y / (a / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-5.2d-97)) .or. (.not. (t <= 0.012d0))) then
        tmp = y * ((z - t) / (a - t))
    else
        tmp = x + (y / (a / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -5.2e-97) || !(t <= 0.012)) {
		tmp = y * ((z - t) / (a - t));
	} else {
		tmp = x + (y / (a / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -5.2e-97) or not (t <= 0.012):
		tmp = y * ((z - t) / (a - t))
	else:
		tmp = x + (y / (a / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -5.2e-97) || !(t <= 0.012))
		tmp = Float64(y * Float64(Float64(z - t) / Float64(a - t)));
	else
		tmp = Float64(x + Float64(y / Float64(a / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -5.2e-97) || ~((t <= 0.012)))
		tmp = y * ((z - t) / (a - t));
	else
		tmp = x + (y / (a / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -5.2e-97], N[Not[LessEqual[t, 0.012]], $MachinePrecision]], N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -5.20000000000000014e-97 or 0.012 < t

   1. Initial program 49.2%

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

      1. associate-*l/ 67.0%

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

   3. Simplified 67.0%

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

   4. Taylor expanded in x around 0 42.7%

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

      1. associate-*r/ 59.2%

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

   6. Simplified 59.2%

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

   if -5.20000000000000014e-97 < t < 0.012

   1. Initial program 90.1%

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

      1. associate-*l/ 94.6%

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

   3. Simplified 94.6%

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

   4. Taylor expanded in t around 0 71.7%

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

   5. Taylor expanded in y around inf 62.2%

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

      1. associate-/l* 68.8%

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

   7. Simplified 68.8%

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

4. Final simplification 63.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.2 \cdot 10^{-97} \lor \neg \left(t \leq 0.012\right):\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \end{array} \]

Alternative 20: 39.2% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.4 \cdot 10^{+21}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 0.55:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -2.4e+21) x (if (<= a 0.55) y x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -2.4e+21) {
		tmp = x;
	} else if (a <= 0.55) {
		tmp = y;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-2.4d+21)) then
        tmp = x
    else if (a <= 0.55d0) then
        tmp = y
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -2.4e+21) {
		tmp = x;
	} else if (a <= 0.55) {
		tmp = y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -2.4e+21:
		tmp = x
	elif a <= 0.55:
		tmp = y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -2.4e+21)
		tmp = x;
	elseif (a <= 0.55)
		tmp = y;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -2.4e+21)
		tmp = x;
	elseif (a <= 0.55)
		tmp = y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -2.4e+21], x, If[LessEqual[a, 0.55], y, x]]

Derivation

1. Split input into 2 regimes

2. if a < -2.4e21 or 0.55000000000000004 < a

   1. Initial program 70.3%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   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 a around inf 47.3%

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

   if -2.4e21 < a < 0.55000000000000004

   1. Initial program 61.8%

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

      1. associate-*l/ 67.9%

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

   3. Simplified 67.9%

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

   4. Taylor expanded in t around inf 42.7%

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

4. Final simplification 45.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.4 \cdot 10^{+21}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 0.55:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 21: 25.4% 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 66.1%

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

   1. associate-*l/ 78.4%

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

3. Simplified 78.4%

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

4. Taylor expanded in a around inf 27.8%

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

5. Final simplification 27.8%

   \[\leadsto x \]

Developer target: 86.9% 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 2023279 
(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))))