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

Percentage Accurate: 68.2% → 91.7%

Time: 26.2s

Alternatives: 21

Speedup: 0.9×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 68.2% 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: 91.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ y \cdot \frac{z - t}{a - t} - x \cdot \left(\frac{z}{a - t} + \left(-1 - \frac{t}{a - t}\right)\right) \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (- (* y (/ (- z t) (- a t))) (* x (+ (/ z (- a t)) (- -1.0 (/ t (- a t)))))))

C

double code(double x, double y, double z, double t, double a) {
	return (y * ((z - t) / (a - t))) - (x * ((z / (a - t)) + (-1.0 - (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 = (y * ((z - t) / (a - t))) - (x * ((z / (a - t)) + ((-1.0d0) - (t / (a - t)))))
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	return (y * ((z - t) / (a - t))) - (x * ((z / (a - t)) + (-1.0 - (t / (a - t)))));
}

Python

def code(x, y, z, t, a):
	return (y * ((z - t) / (a - t))) - (x * ((z / (a - t)) + (-1.0 - (t / (a - t)))))

Julia

function code(x, y, z, t, a)
	return Float64(Float64(y * Float64(Float64(z - t) / Float64(a - t))) - Float64(x * Float64(Float64(z / Float64(a - t)) + Float64(-1.0 - Float64(t / Float64(a - t))))))
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = (y * ((z - t) / (a - t))) - (x * ((z / (a - t)) + (-1.0 - (t / (a - t)))));
end

Wolfram

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

Derivation

1. Initial program 67.0%

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

   1. associate-*l/ 79.1%

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

3. Simplified 79.1%

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

4. Taylor expanded in x around -inf 80.9%

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

   1. +-commutative 80.9%

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

   2. *-commutative 80.9%

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

   3. associate-*r/ 92.4%

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

   4. mul-1-neg 92.4%

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

   5. unsub-neg 92.4%

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

   6. *-commutative 92.4%

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

6. Simplified 92.4%

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

7. Final simplification 92.4%

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

Alternative 2: 37.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{z}{a - t}\\ \mathbf{if}\;t \leq -1.6 \cdot 10^{+119}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -46000000000000:\\ \;\;\;\;z \cdot \frac{x}{t}\\ \mathbf{elif}\;t \leq -7.2 \cdot 10^{-215}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.02 \cdot 10^{-169}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 2.8 \cdot 10^{+86}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ z (- a t)))))
   (if (<= t -1.6e+119)
     y
     (if (<= t -46000000000000.0)
       (* z (/ x t))
       (if (<= t -7.2e-215)
         t_1
         (if (<= t 1.02e-169) x (if (<= t 2.8e+86) t_1 y)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * (z / (a - t));
	double tmp;
	if (t <= -1.6e+119) {
		tmp = y;
	} else if (t <= -46000000000000.0) {
		tmp = z * (x / t);
	} else if (t <= -7.2e-215) {
		tmp = t_1;
	} else if (t <= 1.02e-169) {
		tmp = x;
	} else if (t <= 2.8e+86) {
		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 = y * (z / (a - t))
    if (t <= (-1.6d+119)) then
        tmp = y
    else if (t <= (-46000000000000.0d0)) then
        tmp = z * (x / t)
    else if (t <= (-7.2d-215)) then
        tmp = t_1
    else if (t <= 1.02d-169) then
        tmp = x
    else if (t <= 2.8d+86) 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 = y * (z / (a - t));
	double tmp;
	if (t <= -1.6e+119) {
		tmp = y;
	} else if (t <= -46000000000000.0) {
		tmp = z * (x / t);
	} else if (t <= -7.2e-215) {
		tmp = t_1;
	} else if (t <= 1.02e-169) {
		tmp = x;
	} else if (t <= 2.8e+86) {
		tmp = t_1;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * (z / (a - t))
	tmp = 0
	if t <= -1.6e+119:
		tmp = y
	elif t <= -46000000000000.0:
		tmp = z * (x / t)
	elif t <= -7.2e-215:
		tmp = t_1
	elif t <= 1.02e-169:
		tmp = x
	elif t <= 2.8e+86:
		tmp = t_1
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(z / Float64(a - t)))
	tmp = 0.0
	if (t <= -1.6e+119)
		tmp = y;
	elseif (t <= -46000000000000.0)
		tmp = Float64(z * Float64(x / t));
	elseif (t <= -7.2e-215)
		tmp = t_1;
	elseif (t <= 1.02e-169)
		tmp = x;
	elseif (t <= 2.8e+86)
		tmp = t_1;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * (z / (a - t));
	tmp = 0.0;
	if (t <= -1.6e+119)
		tmp = y;
	elseif (t <= -46000000000000.0)
		tmp = z * (x / t);
	elseif (t <= -7.2e-215)
		tmp = t_1;
	elseif (t <= 1.02e-169)
		tmp = x;
	elseif (t <= 2.8e+86)
		tmp = t_1;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.6e+119], y, If[LessEqual[t, -46000000000000.0], N[(z * N[(x / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -7.2e-215], t$95$1, If[LessEqual[t, 1.02e-169], x, If[LessEqual[t, 2.8e+86], t$95$1, y]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -1.59999999999999995e119 or 2.80000000000000004e86 < t

   1. Initial program 37.7%

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

      1. associate-*l/ 60.9%

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

   3. Simplified 60.9%

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

   4. Taylor expanded in t around inf 53.2%

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

   if -1.59999999999999995e119 < t < -4.6e13

   1. Initial program 60.9%

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

      1. associate-*l/ 75.7%

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

   3. Simplified 75.7%

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

   4. Taylor expanded in x around -inf 90.1%

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

      1. +-commutative 90.1%

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

      2. *-commutative 90.1%

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

      3. associate-*r/ 99.7%

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

      4. mul-1-neg 99.7%

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

      5. unsub-neg 99.7%

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

      6. *-commutative 99.7%

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

   6. Simplified 99.7%

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

   7. Taylor expanded in a around 0 71.1%

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

      1. mul-1-neg 71.1%

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

      2. associate-/l* 80.3%

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

      3. distribute-neg-frac 80.3%

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

   9. Simplified 80.3%

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

   10. Taylor expanded in y around 0 37.3%

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

       1. associate-*r/ 46.4%

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

   12. Simplified 46.4%

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

   if -4.6e13 < t < -7.1999999999999998e-215 or 1.01999999999999996e-169 < t < 2.80000000000000004e86

   1. Initial program 85.0%

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

      1. associate-*l/ 89.8%

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

   3. Simplified 89.8%

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

   4. Taylor expanded in x around 0 49.2%

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

      1. associate-*r/ 54.7%

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

      2. *-commutative 54.7%

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

   6. Applied egg-rr 54.7%

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

   7. Taylor expanded in z around inf 42.0%

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

   if -7.1999999999999998e-215 < t < 1.01999999999999996e-169

   1. Initial program 95.2%

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

      1. associate-*l/ 97.5%

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

   3. Simplified 97.5%

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

   4. Taylor expanded in a around inf 44.4%

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

4. Final simplification 46.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.6 \cdot 10^{+119}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -46000000000000:\\ \;\;\;\;z \cdot \frac{x}{t}\\ \mathbf{elif}\;t \leq -7.2 \cdot 10^{-215}:\\ \;\;\;\;y \cdot \frac{z}{a - t}\\ \mathbf{elif}\;t \leq 1.02 \cdot 10^{-169}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 2.8 \cdot 10^{+86}:\\ \;\;\;\;y \cdot \frac{z}{a - t}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 3: 36.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{z}{a - t}\\ \mathbf{if}\;t \leq -1.4 \cdot 10^{+217}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -25000000000000:\\ \;\;\;\;x \cdot \frac{z - a}{t}\\ \mathbf{elif}\;t \leq -1.16 \cdot 10^{-212}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 6.2 \cdot 10^{-170}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 2.3 \cdot 10^{+86}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ z (- a t)))))
   (if (<= t -1.4e+217)
     y
     (if (<= t -25000000000000.0)
       (* x (/ (- z a) t))
       (if (<= t -1.16e-212)
         t_1
         (if (<= t 6.2e-170) x (if (<= t 2.3e+86) t_1 y)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * (z / (a - t));
	double tmp;
	if (t <= -1.4e+217) {
		tmp = y;
	} else if (t <= -25000000000000.0) {
		tmp = x * ((z - a) / t);
	} else if (t <= -1.16e-212) {
		tmp = t_1;
	} else if (t <= 6.2e-170) {
		tmp = x;
	} else if (t <= 2.3e+86) {
		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 = y * (z / (a - t))
    if (t <= (-1.4d+217)) then
        tmp = y
    else if (t <= (-25000000000000.0d0)) then
        tmp = x * ((z - a) / t)
    else if (t <= (-1.16d-212)) then
        tmp = t_1
    else if (t <= 6.2d-170) then
        tmp = x
    else if (t <= 2.3d+86) 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 = y * (z / (a - t));
	double tmp;
	if (t <= -1.4e+217) {
		tmp = y;
	} else if (t <= -25000000000000.0) {
		tmp = x * ((z - a) / t);
	} else if (t <= -1.16e-212) {
		tmp = t_1;
	} else if (t <= 6.2e-170) {
		tmp = x;
	} else if (t <= 2.3e+86) {
		tmp = t_1;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * (z / (a - t))
	tmp = 0
	if t <= -1.4e+217:
		tmp = y
	elif t <= -25000000000000.0:
		tmp = x * ((z - a) / t)
	elif t <= -1.16e-212:
		tmp = t_1
	elif t <= 6.2e-170:
		tmp = x
	elif t <= 2.3e+86:
		tmp = t_1
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(z / Float64(a - t)))
	tmp = 0.0
	if (t <= -1.4e+217)
		tmp = y;
	elseif (t <= -25000000000000.0)
		tmp = Float64(x * Float64(Float64(z - a) / t));
	elseif (t <= -1.16e-212)
		tmp = t_1;
	elseif (t <= 6.2e-170)
		tmp = x;
	elseif (t <= 2.3e+86)
		tmp = t_1;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * (z / (a - t));
	tmp = 0.0;
	if (t <= -1.4e+217)
		tmp = y;
	elseif (t <= -25000000000000.0)
		tmp = x * ((z - a) / t);
	elseif (t <= -1.16e-212)
		tmp = t_1;
	elseif (t <= 6.2e-170)
		tmp = x;
	elseif (t <= 2.3e+86)
		tmp = t_1;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.4e+217], y, If[LessEqual[t, -25000000000000.0], N[(x * N[(N[(z - a), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -1.16e-212], t$95$1, If[LessEqual[t, 6.2e-170], x, If[LessEqual[t, 2.3e+86], t$95$1, y]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -1.39999999999999997e217 or 2.2999999999999999e86 < t

   1. Initial program 39.5%

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

      1. associate-*l/ 62.4%

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

   3. Simplified 62.4%

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

   4. Taylor expanded in t around inf 62.4%

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

   if -1.39999999999999997e217 < t < -2.5e13

   1. Initial program 44.9%

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

      1. associate-*l/ 64.9%

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

   3. Simplified 64.9%

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

   4. Taylor expanded in t around -inf 61.5%

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

      1. mul-1-neg 61.5%

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

      2. unsub-neg 61.5%

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

      3. div-sub 61.5%

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

      4. *-commutative 61.5%

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

      5. div-sub 61.5%

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

      6. distribute-rgt-out-- 63.6%

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

   6. Simplified 63.6%

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

   7. Taylor expanded in y around 0 36.0%

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

   8. Taylor expanded in z around 0 34.0%

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

      1. mul-1-neg 34.0%

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

      2. sub-neg 34.0%

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

      3. associate-/l* 39.8%

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

      4. associate-/l* 44.1%

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

      5. div-sub 44.1%

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

      6. associate-/r/ 44.0%

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

   10. Simplified 44.0%

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

   if -2.5e13 < t < -1.16e-212 or 6.19999999999999971e-170 < t < 2.2999999999999999e86

   1. Initial program 85.0%

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

      1. associate-*l/ 89.8%

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

   3. Simplified 89.8%

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

   4. Taylor expanded in x around 0 49.2%

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

      1. associate-*r/ 54.7%

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

      2. *-commutative 54.7%

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

   6. Applied egg-rr 54.7%

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

   7. Taylor expanded in z around inf 42.0%

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

   if -1.16e-212 < t < 6.19999999999999971e-170

   1. Initial program 95.2%

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

      1. associate-*l/ 97.5%

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

   3. Simplified 97.5%

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

   4. Taylor expanded in a around inf 44.4%

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

4. Final simplification 48.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.4 \cdot 10^{+217}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -25000000000000:\\ \;\;\;\;x \cdot \frac{z - a}{t}\\ \mathbf{elif}\;t \leq -1.16 \cdot 10^{-212}:\\ \;\;\;\;y \cdot \frac{z}{a - t}\\ \mathbf{elif}\;t \leq 6.2 \cdot 10^{-170}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 2.3 \cdot 10^{+86}:\\ \;\;\;\;y \cdot \frac{z}{a - t}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 4: 36.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + a \cdot \frac{y}{t}\\ t_2 := y \cdot \frac{z}{a - t}\\ \mathbf{if}\;t \leq -1.15 \cdot 10^{+216}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -18000000000000:\\ \;\;\;\;x \cdot \frac{z - a}{t}\\ \mathbf{elif}\;t \leq -1.5 \cdot 10^{-214}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 1.02 \cdot 10^{-170}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 1.8 \cdot 10^{+86}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ y (* a (/ y t)))) (t_2 (* y (/ z (- a t)))))
   (if (<= t -1.15e+216)
     t_1
     (if (<= t -18000000000000.0)
       (* x (/ (- z a) t))
       (if (<= t -1.5e-214)
         t_2
         (if (<= t 1.02e-170) x (if (<= t 1.8e+86) t_2 t_1)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y + (a * (y / t));
	double t_2 = y * (z / (a - t));
	double tmp;
	if (t <= -1.15e+216) {
		tmp = t_1;
	} else if (t <= -18000000000000.0) {
		tmp = x * ((z - a) / t);
	} else if (t <= -1.5e-214) {
		tmp = t_2;
	} else if (t <= 1.02e-170) {
		tmp = x;
	} else if (t <= 1.8e+86) {
		tmp = t_2;
	} 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) :: t_2
    real(8) :: tmp
    t_1 = y + (a * (y / t))
    t_2 = y * (z / (a - t))
    if (t <= (-1.15d+216)) then
        tmp = t_1
    else if (t <= (-18000000000000.0d0)) then
        tmp = x * ((z - a) / t)
    else if (t <= (-1.5d-214)) then
        tmp = t_2
    else if (t <= 1.02d-170) then
        tmp = x
    else if (t <= 1.8d+86) then
        tmp = t_2
    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 + (a * (y / t));
	double t_2 = y * (z / (a - t));
	double tmp;
	if (t <= -1.15e+216) {
		tmp = t_1;
	} else if (t <= -18000000000000.0) {
		tmp = x * ((z - a) / t);
	} else if (t <= -1.5e-214) {
		tmp = t_2;
	} else if (t <= 1.02e-170) {
		tmp = x;
	} else if (t <= 1.8e+86) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y + (a * (y / t))
	t_2 = y * (z / (a - t))
	tmp = 0
	if t <= -1.15e+216:
		tmp = t_1
	elif t <= -18000000000000.0:
		tmp = x * ((z - a) / t)
	elif t <= -1.5e-214:
		tmp = t_2
	elif t <= 1.02e-170:
		tmp = x
	elif t <= 1.8e+86:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y + Float64(a * Float64(y / t)))
	t_2 = Float64(y * Float64(z / Float64(a - t)))
	tmp = 0.0
	if (t <= -1.15e+216)
		tmp = t_1;
	elseif (t <= -18000000000000.0)
		tmp = Float64(x * Float64(Float64(z - a) / t));
	elseif (t <= -1.5e-214)
		tmp = t_2;
	elseif (t <= 1.02e-170)
		tmp = x;
	elseif (t <= 1.8e+86)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y + (a * (y / t));
	t_2 = y * (z / (a - t));
	tmp = 0.0;
	if (t <= -1.15e+216)
		tmp = t_1;
	elseif (t <= -18000000000000.0)
		tmp = x * ((z - a) / t);
	elseif (t <= -1.5e-214)
		tmp = t_2;
	elseif (t <= 1.02e-170)
		tmp = x;
	elseif (t <= 1.8e+86)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y + N[(a * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.15e+216], t$95$1, If[LessEqual[t, -18000000000000.0], N[(x * N[(N[(z - a), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -1.5e-214], t$95$2, If[LessEqual[t, 1.02e-170], x, If[LessEqual[t, 1.8e+86], t$95$2, t$95$1]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -1.14999999999999998e216 or 1.80000000000000003e86 < t

   1. Initial program 39.5%

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

      1. associate-*l/ 62.4%

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

   3. Simplified 62.4%

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

   4. Taylor expanded in x around 0 47.5%

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

      1. associate-*r/ 72.4%

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

      2. *-commutative 72.4%

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

   6. Applied egg-rr 72.4%

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

   7. Taylor expanded in z around 0 62.4%

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

      1. neg-mul-1 62.4%

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

      2. distribute-neg-frac 62.4%

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

   9. Simplified 62.4%

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

   10. Taylor expanded in t around inf 58.4%

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

       1. associate-*r/ 62.5%

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

       2. +-commutative 62.5%

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

   12. Simplified 62.5%

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

   if -1.14999999999999998e216 < t < -1.8e13

   1. Initial program 44.9%

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

      1. associate-*l/ 64.9%

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

   3. Simplified 64.9%

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

   4. Taylor expanded in t around -inf 61.5%

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

      1. mul-1-neg 61.5%

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

      2. unsub-neg 61.5%

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

      3. div-sub 61.5%

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

      4. *-commutative 61.5%

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

      5. div-sub 61.5%

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

      6. distribute-rgt-out-- 63.6%

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

   6. Simplified 63.6%

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

   7. Taylor expanded in y around 0 36.0%

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

   8. Taylor expanded in z around 0 34.0%

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

      1. mul-1-neg 34.0%

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

      2. sub-neg 34.0%

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

      3. associate-/l* 39.8%

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

      4. associate-/l* 44.1%

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

      5. div-sub 44.1%

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

      6. associate-/r/ 44.0%

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

   10. Simplified 44.0%

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

   if -1.8e13 < t < -1.49999999999999997e-214 or 1.02e-170 < t < 1.80000000000000003e86

   1. Initial program 85.0%

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

      1. associate-*l/ 89.8%

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

   3. Simplified 89.8%

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

   4. Taylor expanded in x around 0 49.2%

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

      1. associate-*r/ 54.7%

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

      2. *-commutative 54.7%

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

   6. Applied egg-rr 54.7%

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

   7. Taylor expanded in z around inf 42.0%

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

   if -1.49999999999999997e-214 < t < 1.02e-170

   1. Initial program 95.2%

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

      1. associate-*l/ 97.5%

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

   3. Simplified 97.5%

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

   4. Taylor expanded in a around inf 44.4%

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

4. Final simplification 48.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.15 \cdot 10^{+216}:\\ \;\;\;\;y + a \cdot \frac{y}{t}\\ \mathbf{elif}\;t \leq -18000000000000:\\ \;\;\;\;x \cdot \frac{z - a}{t}\\ \mathbf{elif}\;t \leq -1.5 \cdot 10^{-214}:\\ \;\;\;\;y \cdot \frac{z}{a - t}\\ \mathbf{elif}\;t \leq 1.02 \cdot 10^{-170}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 1.8 \cdot 10^{+86}:\\ \;\;\;\;y \cdot \frac{z}{a - t}\\ \mathbf{else}:\\ \;\;\;\;y + a \cdot \frac{y}{t}\\ \end{array} \]

Alternative 5: 36.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + a \cdot \frac{y}{t}\\ t_2 := y \cdot \frac{z}{a - t}\\ \mathbf{if}\;t \leq -2.6 \cdot 10^{+216}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -7500000000000:\\ \;\;\;\;\frac{z - a}{\frac{t}{x}}\\ \mathbf{elif}\;t \leq -1.05 \cdot 10^{-216}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 5.4 \cdot 10^{-170}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 1.75 \cdot 10^{+86}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ y (* a (/ y t)))) (t_2 (* y (/ z (- a t)))))
   (if (<= t -2.6e+216)
     t_1
     (if (<= t -7500000000000.0)
       (/ (- z a) (/ t x))
       (if (<= t -1.05e-216)
         t_2
         (if (<= t 5.4e-170) x (if (<= t 1.75e+86) t_2 t_1)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y + (a * (y / t));
	double t_2 = y * (z / (a - t));
	double tmp;
	if (t <= -2.6e+216) {
		tmp = t_1;
	} else if (t <= -7500000000000.0) {
		tmp = (z - a) / (t / x);
	} else if (t <= -1.05e-216) {
		tmp = t_2;
	} else if (t <= 5.4e-170) {
		tmp = x;
	} else if (t <= 1.75e+86) {
		tmp = t_2;
	} 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) :: t_2
    real(8) :: tmp
    t_1 = y + (a * (y / t))
    t_2 = y * (z / (a - t))
    if (t <= (-2.6d+216)) then
        tmp = t_1
    else if (t <= (-7500000000000.0d0)) then
        tmp = (z - a) / (t / x)
    else if (t <= (-1.05d-216)) then
        tmp = t_2
    else if (t <= 5.4d-170) then
        tmp = x
    else if (t <= 1.75d+86) then
        tmp = t_2
    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 + (a * (y / t));
	double t_2 = y * (z / (a - t));
	double tmp;
	if (t <= -2.6e+216) {
		tmp = t_1;
	} else if (t <= -7500000000000.0) {
		tmp = (z - a) / (t / x);
	} else if (t <= -1.05e-216) {
		tmp = t_2;
	} else if (t <= 5.4e-170) {
		tmp = x;
	} else if (t <= 1.75e+86) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y + (a * (y / t))
	t_2 = y * (z / (a - t))
	tmp = 0
	if t <= -2.6e+216:
		tmp = t_1
	elif t <= -7500000000000.0:
		tmp = (z - a) / (t / x)
	elif t <= -1.05e-216:
		tmp = t_2
	elif t <= 5.4e-170:
		tmp = x
	elif t <= 1.75e+86:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y + Float64(a * Float64(y / t)))
	t_2 = Float64(y * Float64(z / Float64(a - t)))
	tmp = 0.0
	if (t <= -2.6e+216)
		tmp = t_1;
	elseif (t <= -7500000000000.0)
		tmp = Float64(Float64(z - a) / Float64(t / x));
	elseif (t <= -1.05e-216)
		tmp = t_2;
	elseif (t <= 5.4e-170)
		tmp = x;
	elseif (t <= 1.75e+86)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y + (a * (y / t));
	t_2 = y * (z / (a - t));
	tmp = 0.0;
	if (t <= -2.6e+216)
		tmp = t_1;
	elseif (t <= -7500000000000.0)
		tmp = (z - a) / (t / x);
	elseif (t <= -1.05e-216)
		tmp = t_2;
	elseif (t <= 5.4e-170)
		tmp = x;
	elseif (t <= 1.75e+86)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y + N[(a * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.6e+216], t$95$1, If[LessEqual[t, -7500000000000.0], N[(N[(z - a), $MachinePrecision] / N[(t / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -1.05e-216], t$95$2, If[LessEqual[t, 5.4e-170], x, If[LessEqual[t, 1.75e+86], t$95$2, t$95$1]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -2.5999999999999999e216 or 1.75000000000000009e86 < t

   1. Initial program 39.5%

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

      1. associate-*l/ 62.4%

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

   3. Simplified 62.4%

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

   4. Taylor expanded in x around 0 47.5%

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

      1. associate-*r/ 72.4%

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

      2. *-commutative 72.4%

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

   6. Applied egg-rr 72.4%

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

   7. Taylor expanded in z around 0 62.4%

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

      1. neg-mul-1 62.4%

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

      2. distribute-neg-frac 62.4%

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

   9. Simplified 62.4%

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

   10. Taylor expanded in t around inf 58.4%

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

       1. associate-*r/ 62.5%

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

       2. +-commutative 62.5%

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

   12. Simplified 62.5%

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

   if -2.5999999999999999e216 < t < -7.5e12

   1. Initial program 44.9%

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

      1. associate-*l/ 64.9%

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

   3. Simplified 64.9%

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

   4. Taylor expanded in t around -inf 61.5%

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

      1. mul-1-neg 61.5%

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

      2. unsub-neg 61.5%

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

      3. div-sub 61.5%

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

      4. *-commutative 61.5%

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

      5. div-sub 61.5%

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

      6. distribute-rgt-out-- 63.6%

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

   6. Simplified 63.6%

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

   7. Taylor expanded in y around 0 36.0%

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

      1. associate-/l* 44.1%

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

   9. Simplified 44.1%

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

   if -7.5e12 < t < -1.0500000000000001e-216 or 5.3999999999999997e-170 < t < 1.75000000000000009e86

   1. Initial program 85.0%

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

      1. associate-*l/ 89.8%

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

   3. Simplified 89.8%

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

   4. Taylor expanded in x around 0 49.2%

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

      1. associate-*r/ 54.7%

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

      2. *-commutative 54.7%

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

   6. Applied egg-rr 54.7%

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

   7. Taylor expanded in z around inf 42.0%

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

   if -1.0500000000000001e-216 < t < 5.3999999999999997e-170

   1. Initial program 95.2%

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

      1. associate-*l/ 97.5%

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

   3. Simplified 97.5%

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

   4. Taylor expanded in a around inf 44.4%

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

4. Final simplification 48.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.6 \cdot 10^{+216}:\\ \;\;\;\;y + a \cdot \frac{y}{t}\\ \mathbf{elif}\;t \leq -7500000000000:\\ \;\;\;\;\frac{z - a}{\frac{t}{x}}\\ \mathbf{elif}\;t \leq -1.05 \cdot 10^{-216}:\\ \;\;\;\;y \cdot \frac{z}{a - t}\\ \mathbf{elif}\;t \leq 5.4 \cdot 10^{-170}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 1.75 \cdot 10^{+86}:\\ \;\;\;\;y \cdot \frac{z}{a - t}\\ \mathbf{else}:\\ \;\;\;\;y + a \cdot \frac{y}{t}\\ \end{array} \]

Alternative 6: 42.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x - y}{\frac{t}{z}}\\ \mathbf{if}\;a \leq -2.4 \cdot 10^{+105}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -7.2 \cdot 10^{-66}:\\ \;\;\;\;y + a \cdot \frac{y}{t}\\ \mathbf{elif}\;a \leq -1.55 \cdot 10^{-184}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -2.55 \cdot 10^{-294}:\\ \;\;\;\;y\\ \mathbf{elif}\;a \leq 6.6 \cdot 10^{-8}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- x y) (/ t z))))
   (if (<= a -2.4e+105)
     x
     (if (<= a -7.2e-66)
       (+ y (* a (/ y t)))
       (if (<= a -1.55e-184)
         t_1
         (if (<= a -2.55e-294) y (if (<= a 6.6e-8) t_1 x)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (x - y) / (t / z);
	double tmp;
	if (a <= -2.4e+105) {
		tmp = x;
	} else if (a <= -7.2e-66) {
		tmp = y + (a * (y / t));
	} else if (a <= -1.55e-184) {
		tmp = t_1;
	} else if (a <= -2.55e-294) {
		tmp = y;
	} else if (a <= 6.6e-8) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = (x - y) / (t / z)
    if (a <= (-2.4d+105)) then
        tmp = x
    else if (a <= (-7.2d-66)) then
        tmp = y + (a * (y / t))
    else if (a <= (-1.55d-184)) then
        tmp = t_1
    else if (a <= (-2.55d-294)) then
        tmp = y
    else if (a <= 6.6d-8) then
        tmp = t_1
    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 t_1 = (x - y) / (t / z);
	double tmp;
	if (a <= -2.4e+105) {
		tmp = x;
	} else if (a <= -7.2e-66) {
		tmp = y + (a * (y / t));
	} else if (a <= -1.55e-184) {
		tmp = t_1;
	} else if (a <= -2.55e-294) {
		tmp = y;
	} else if (a <= 6.6e-8) {
		tmp = t_1;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (x - y) / (t / z)
	tmp = 0
	if a <= -2.4e+105:
		tmp = x
	elif a <= -7.2e-66:
		tmp = y + (a * (y / t))
	elif a <= -1.55e-184:
		tmp = t_1
	elif a <= -2.55e-294:
		tmp = y
	elif a <= 6.6e-8:
		tmp = t_1
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(x - y) / Float64(t / z))
	tmp = 0.0
	if (a <= -2.4e+105)
		tmp = x;
	elseif (a <= -7.2e-66)
		tmp = Float64(y + Float64(a * Float64(y / t)));
	elseif (a <= -1.55e-184)
		tmp = t_1;
	elseif (a <= -2.55e-294)
		tmp = y;
	elseif (a <= 6.6e-8)
		tmp = t_1;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (x - y) / (t / z);
	tmp = 0.0;
	if (a <= -2.4e+105)
		tmp = x;
	elseif (a <= -7.2e-66)
		tmp = y + (a * (y / t));
	elseif (a <= -1.55e-184)
		tmp = t_1;
	elseif (a <= -2.55e-294)
		tmp = y;
	elseif (a <= 6.6e-8)
		tmp = t_1;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(x - y), $MachinePrecision] / N[(t / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -2.4e+105], x, If[LessEqual[a, -7.2e-66], N[(y + N[(a * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -1.55e-184], t$95$1, If[LessEqual[a, -2.55e-294], y, If[LessEqual[a, 6.6e-8], t$95$1, x]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -2.39999999999999975e105 or 6.59999999999999954e-8 < a

   1. Initial program 64.7%

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

      1. associate-*l/ 90.6%

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

   3. Simplified 90.6%

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

   4. Taylor expanded in a around inf 48.6%

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

   if -2.39999999999999975e105 < a < -7.20000000000000025e-66

   1. Initial program 65.3%

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

      1. associate-*l/ 71.8%

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

   3. Simplified 71.8%

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

   4. Taylor expanded in x around 0 58.7%

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

      1. associate-*r/ 72.4%

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

      2. *-commutative 72.4%

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

   6. Applied egg-rr 72.4%

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

   7. Taylor expanded in z around 0 48.9%

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

      1. neg-mul-1 48.9%

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

      2. distribute-neg-frac 48.9%

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

   9. Simplified 48.9%

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

   10. Taylor expanded in t around inf 43.4%

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

       1. associate-*r/ 46.1%

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

       2. +-commutative 46.1%

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

   12. Simplified 46.1%

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

   if -7.20000000000000025e-66 < a < -1.5500000000000001e-184 or -2.55000000000000003e-294 < a < 6.59999999999999954e-8

   1. Initial program 73.9%

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

      1. associate-*l/ 71.7%

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

   3. Simplified 71.7%

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

   4. Taylor expanded in t around -inf 80.3%

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

      1. mul-1-neg 80.3%

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

      2. unsub-neg 80.3%

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

      3. div-sub 75.9%

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

      4. *-commutative 75.9%

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

      5. div-sub 80.3%

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

      6. distribute-rgt-out-- 80.3%

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

   6. Simplified 80.3%

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

   7. Taylor expanded in z around -inf 56.5%

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

      1. mul-1-neg 56.5%

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

      2. associate-/l* 62.6%

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

   9. Simplified 62.6%

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

   if -1.5500000000000001e-184 < a < -2.55000000000000003e-294

   1. Initial program 49.6%

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

      1. associate-*l/ 60.2%

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

   3. Simplified 60.2%

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

   4. Taylor expanded in t around inf 65.3%

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

4. Final simplification 54.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.4 \cdot 10^{+105}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -7.2 \cdot 10^{-66}:\\ \;\;\;\;y + a \cdot \frac{y}{t}\\ \mathbf{elif}\;a \leq -1.55 \cdot 10^{-184}:\\ \;\;\;\;\frac{x - y}{\frac{t}{z}}\\ \mathbf{elif}\;a \leq -2.55 \cdot 10^{-294}:\\ \;\;\;\;y\\ \mathbf{elif}\;a \leq 6.6 \cdot 10^{-8}:\\ \;\;\;\;\frac{x - y}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 7: 42.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x - y}{\frac{t}{z}}\\ t_2 := y \cdot \frac{-t}{a - t}\\ \mathbf{if}\;a \leq -4.5 \cdot 10^{+98}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -1.12 \cdot 10^{-69}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -2.4 \cdot 10^{-184}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -1.52 \cdot 10^{-294}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 4.5 \cdot 10^{-8}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- x y) (/ t z))) (t_2 (* y (/ (- t) (- a t)))))
   (if (<= a -4.5e+98)
     x
     (if (<= a -1.12e-69)
       t_2
       (if (<= a -2.4e-184)
         t_1
         (if (<= a -1.52e-294) t_2 (if (<= a 4.5e-8) t_1 x)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (x - y) / (t / z);
	double t_2 = y * (-t / (a - t));
	double tmp;
	if (a <= -4.5e+98) {
		tmp = x;
	} else if (a <= -1.12e-69) {
		tmp = t_2;
	} else if (a <= -2.4e-184) {
		tmp = t_1;
	} else if (a <= -1.52e-294) {
		tmp = t_2;
	} else if (a <= 4.5e-8) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (x - y) / (t / z)
    t_2 = y * (-t / (a - t))
    if (a <= (-4.5d+98)) then
        tmp = x
    else if (a <= (-1.12d-69)) then
        tmp = t_2
    else if (a <= (-2.4d-184)) then
        tmp = t_1
    else if (a <= (-1.52d-294)) then
        tmp = t_2
    else if (a <= 4.5d-8) then
        tmp = t_1
    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 t_1 = (x - y) / (t / z);
	double t_2 = y * (-t / (a - t));
	double tmp;
	if (a <= -4.5e+98) {
		tmp = x;
	} else if (a <= -1.12e-69) {
		tmp = t_2;
	} else if (a <= -2.4e-184) {
		tmp = t_1;
	} else if (a <= -1.52e-294) {
		tmp = t_2;
	} else if (a <= 4.5e-8) {
		tmp = t_1;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (x - y) / (t / z)
	t_2 = y * (-t / (a - t))
	tmp = 0
	if a <= -4.5e+98:
		tmp = x
	elif a <= -1.12e-69:
		tmp = t_2
	elif a <= -2.4e-184:
		tmp = t_1
	elif a <= -1.52e-294:
		tmp = t_2
	elif a <= 4.5e-8:
		tmp = t_1
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(x - y) / Float64(t / z))
	t_2 = Float64(y * Float64(Float64(-t) / Float64(a - t)))
	tmp = 0.0
	if (a <= -4.5e+98)
		tmp = x;
	elseif (a <= -1.12e-69)
		tmp = t_2;
	elseif (a <= -2.4e-184)
		tmp = t_1;
	elseif (a <= -1.52e-294)
		tmp = t_2;
	elseif (a <= 4.5e-8)
		tmp = t_1;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (x - y) / (t / z);
	t_2 = y * (-t / (a - t));
	tmp = 0.0;
	if (a <= -4.5e+98)
		tmp = x;
	elseif (a <= -1.12e-69)
		tmp = t_2;
	elseif (a <= -2.4e-184)
		tmp = t_1;
	elseif (a <= -1.52e-294)
		tmp = t_2;
	elseif (a <= 4.5e-8)
		tmp = t_1;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(x - y), $MachinePrecision] / N[(t / z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[((-t) / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -4.5e+98], x, If[LessEqual[a, -1.12e-69], t$95$2, If[LessEqual[a, -2.4e-184], t$95$1, If[LessEqual[a, -1.52e-294], t$95$2, If[LessEqual[a, 4.5e-8], t$95$1, x]]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -4.5000000000000002e98 or 4.49999999999999993e-8 < a

   1. Initial program 64.7%

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

      1. associate-*l/ 90.6%

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

   3. Simplified 90.6%

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

   4. Taylor expanded in a around inf 48.6%

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

   if -4.5000000000000002e98 < a < -1.12e-69 or -2.40000000000000024e-184 < a < -1.52000000000000007e-294

   1. Initial program 59.7%

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

      1. associate-*l/ 67.6%

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

   3. Simplified 67.6%

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

   4. Taylor expanded in x around 0 60.9%

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

      1. associate-*r/ 76.8%

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

      2. *-commutative 76.8%

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

   6. Applied egg-rr 76.8%

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

   7. Taylor expanded in z around 0 56.1%

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

      1. neg-mul-1 56.1%

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

      2. distribute-neg-frac 56.1%

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

   9. Simplified 56.1%

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

   if -1.12e-69 < a < -2.40000000000000024e-184 or -1.52000000000000007e-294 < a < 4.49999999999999993e-8

   1. Initial program 73.9%

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

      1. associate-*l/ 71.7%

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

   3. Simplified 71.7%

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

   4. Taylor expanded in t around -inf 80.3%

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

      1. mul-1-neg 80.3%

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

      2. unsub-neg 80.3%

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

      3. div-sub 75.9%

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

      4. *-commutative 75.9%

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

      5. div-sub 80.3%

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

      6. distribute-rgt-out-- 80.3%

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

   6. Simplified 80.3%

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

   7. Taylor expanded in z around -inf 56.5%

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

      1. mul-1-neg 56.5%

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

      2. associate-/l* 62.6%

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

   9. Simplified 62.6%

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

4. Final simplification 55.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4.5 \cdot 10^{+98}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -1.12 \cdot 10^{-69}:\\ \;\;\;\;y \cdot \frac{-t}{a - t}\\ \mathbf{elif}\;a \leq -2.4 \cdot 10^{-184}:\\ \;\;\;\;\frac{x - y}{\frac{t}{z}}\\ \mathbf{elif}\;a \leq -1.52 \cdot 10^{-294}:\\ \;\;\;\;y \cdot \frac{-t}{a - t}\\ \mathbf{elif}\;a \leq 4.5 \cdot 10^{-8}:\\ \;\;\;\;\frac{x - y}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 8: 73.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{z - t}{\frac{a}{y - x}}\\ \mathbf{if}\;a \leq -1.15 \cdot 10^{+94}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -0.205:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;a \leq 1.4 \cdot 10^{+31}:\\ \;\;\;\;y - \frac{y - x}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ (- z t) (/ a (- y x))))))
   (if (<= a -1.15e+94)
     t_1
     (if (<= a -0.205)
       (* y (/ (- z t) (- a t)))
       (if (<= a 1.4e+31) (- y (/ (- y x) (/ t z))) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((z - t) / (a / (y - x)));
	double tmp;
	if (a <= -1.15e+94) {
		tmp = t_1;
	} else if (a <= -0.205) {
		tmp = y * ((z - t) / (a - t));
	} else if (a <= 1.4e+31) {
		tmp = y - ((y - x) / (t / z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + ((z - t) / (a / (y - x)))
    if (a <= (-1.15d+94)) then
        tmp = t_1
    else if (a <= (-0.205d0)) then
        tmp = y * ((z - t) / (a - t))
    else if (a <= 1.4d+31) then
        tmp = y - ((y - x) / (t / z))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((z - t) / (a / (y - x)));
	double tmp;
	if (a <= -1.15e+94) {
		tmp = t_1;
	} else if (a <= -0.205) {
		tmp = y * ((z - t) / (a - t));
	} else if (a <= 1.4e+31) {
		tmp = y - ((y - x) / (t / z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((z - t) / (a / (y - x)))
	tmp = 0
	if a <= -1.15e+94:
		tmp = t_1
	elif a <= -0.205:
		tmp = y * ((z - t) / (a - t))
	elif a <= 1.4e+31:
		tmp = y - ((y - x) / (t / z))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(z - t) / Float64(a / Float64(y - x))))
	tmp = 0.0
	if (a <= -1.15e+94)
		tmp = t_1;
	elseif (a <= -0.205)
		tmp = Float64(y * Float64(Float64(z - t) / Float64(a - t)));
	elseif (a <= 1.4e+31)
		tmp = Float64(y - Float64(Float64(y - x) / Float64(t / z)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((z - t) / (a / (y - x)));
	tmp = 0.0;
	if (a <= -1.15e+94)
		tmp = t_1;
	elseif (a <= -0.205)
		tmp = y * ((z - t) / (a - t));
	elseif (a <= 1.4e+31)
		tmp = y - ((y - x) / (t / z));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(z - t), $MachinePrecision] / N[(a / N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.15e+94], t$95$1, If[LessEqual[a, -0.205], N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.4e+31], N[(y - N[(N[(y - x), $MachinePrecision] / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.15e94 or 1.40000000000000008e31 < a

   1. Initial program 65.8%

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

      1. associate-*l/ 91.0%

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

   3. Simplified 91.0%

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

   4. Taylor expanded in a around inf 56.9%

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

      1. +-commutative 56.9%

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

      2. associate-/l* 78.5%

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

   6. Simplified 78.5%

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

   if -1.15e94 < a < -0.204999999999999988

   1. Initial program 66.0%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   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 x around 0 58.3%

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

      1. associate-*r/ 74.5%

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

   6. Simplified 74.5%

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

   if -0.204999999999999988 < a < 1.40000000000000008e31

   1. Initial program 68.3%

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

      1. associate-*l/ 69.3%

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

   3. Simplified 69.3%

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

   4. Taylor expanded in t around -inf 80.1%

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

      1. mul-1-neg 80.1%

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

      2. unsub-neg 80.1%

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

      3. div-sub 76.8%

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

      4. *-commutative 76.8%

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

      5. div-sub 80.1%

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

      6. distribute-rgt-out-- 80.1%

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

   6. Simplified 80.1%

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

   7. Taylor expanded in z around inf 75.7%

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

      1. *-commutative 75.7%

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

      2. associate-/l* 81.2%

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

   9. Simplified 81.2%

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

4. Final simplification 79.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.15 \cdot 10^{+94}:\\ \;\;\;\;x + \frac{z - t}{\frac{a}{y - x}}\\ \mathbf{elif}\;a \leq -0.205:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;a \leq 1.4 \cdot 10^{+31}:\\ \;\;\;\;y - \frac{y - x}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z - t}{\frac{a}{y - x}}\\ \end{array} \]

Alternative 9: 86.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.8 \cdot 10^{+116} \lor \neg \left(t \leq 4.8 \cdot 10^{+95}\right):\\ \;\;\;\;y + \frac{y - x}{t} \cdot \left(a - z\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y - x}{a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -2.8e+116) (not (<= t 4.8e+95)))
   (+ y (* (/ (- y x) t) (- a z)))
   (+ x (* (- z t) (/ (- y x) (- a t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -2.8e+116) || !(t <= 4.8e+95)) {
		tmp = y + (((y - x) / t) * (a - z));
	} 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 <= (-2.8d+116)) .or. (.not. (t <= 4.8d+95))) then
        tmp = y + (((y - x) / t) * (a - z))
    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 <= -2.8e+116) || !(t <= 4.8e+95)) {
		tmp = y + (((y - x) / t) * (a - z));
	} else {
		tmp = x + ((z - t) * ((y - x) / (a - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -2.8e+116) or not (t <= 4.8e+95):
		tmp = y + (((y - x) / t) * (a - z))
	else:
		tmp = x + ((z - t) * ((y - x) / (a - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -2.8e+116) || !(t <= 4.8e+95))
		tmp = Float64(y + Float64(Float64(Float64(y - x) / t) * Float64(a - z)));
	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 <= -2.8e+116) || ~((t <= 4.8e+95)))
		tmp = y + (((y - x) / t) * (a - z));
	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, -2.8e+116], N[Not[LessEqual[t, 4.8e+95]], $MachinePrecision]], N[(y + N[(N[(N[(y - x), $MachinePrecision] / t), $MachinePrecision] * N[(a - z), $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 < -2.80000000000000004e116 or 4.8000000000000001e95 < t

   1. Initial program 36.0%

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

      1. associate-*l/ 58.4%

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

   3. Simplified 58.4%

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

   4. Taylor expanded in t around -inf 67.2%

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

      1. mul-1-neg 67.2%

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

      2. unsub-neg 67.2%

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

      3. div-sub 67.2%

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

      4. *-commutative 67.2%

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

      5. div-sub 67.2%

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

      6. distribute-rgt-out-- 68.3%

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

   6. Simplified 68.3%

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

   7. Taylor expanded in z around inf 67.2%

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

      1. *-commutative 67.2%

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

      2. *-lft-identity 67.2%

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

      3. metadata-eval 67.2%

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

      4. cancel-sign-sub-inv 67.2%

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

      5. neg-mul-1 67.2%

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

      6. associate-*r/ 67.2%

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

      7. distribute-neg-frac 67.2%

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

      8. div-sub 67.2%

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

      9. sub-neg 67.2%

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

      10. remove-double-neg 67.2%

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

      11. +-commutative 67.2%

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

      12. associate-*r* 67.2%

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

      13. distribute-rgt-in 68.3%

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

      14. neg-mul-1 68.3%

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

      15. sub-neg 68.3%

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

      16. associate-/l* 84.5%

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

   9. Simplified 85.7%

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

   if -2.80000000000000004e116 < t < 4.8000000000000001e95

   1. Initial program 85.2%

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

      1. associate-*l/ 91.2%

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

   3. Simplified 91.2%

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

4. Final simplification 89.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.8 \cdot 10^{+116} \lor \neg \left(t \leq 4.8 \cdot 10^{+95}\right):\\ \;\;\;\;y + \frac{y - x}{t} \cdot \left(a - z\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y - x}{a - t}\\ \end{array} \]

Alternative 10: 88.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1 \cdot 10^{+116} \lor \neg \left(t \leq 5 \cdot 10^{+95}\right):\\ \;\;\;\;y + \frac{y - x}{t} \cdot \left(a - z\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{\frac{a - t}{z - t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -1e+116) (not (<= t 5e+95)))
   (+ y (* (/ (- y x) t) (- a z)))
   (+ x (/ (- y x) (/ (- a t) (- z t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -1e+116) || !(t <= 5e+95)) {
		tmp = y + (((y - x) / t) * (a - z));
	} 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 <= (-1d+116)) .or. (.not. (t <= 5d+95))) then
        tmp = y + (((y - x) / t) * (a - z))
    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 <= -1e+116) || !(t <= 5e+95)) {
		tmp = y + (((y - x) / t) * (a - z));
	} else {
		tmp = x + ((y - x) / ((a - t) / (z - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -1e+116) or not (t <= 5e+95):
		tmp = y + (((y - x) / t) * (a - z))
	else:
		tmp = x + ((y - x) / ((a - t) / (z - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -1e+116) || !(t <= 5e+95))
		tmp = Float64(y + Float64(Float64(Float64(y - x) / t) * Float64(a - z)));
	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 <= -1e+116) || ~((t <= 5e+95)))
		tmp = y + (((y - x) / t) * (a - z));
	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, -1e+116], N[Not[LessEqual[t, 5e+95]], $MachinePrecision]], N[(y + N[(N[(N[(y - x), $MachinePrecision] / t), $MachinePrecision] * N[(a - z), $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 < -1.00000000000000002e116 or 5.00000000000000025e95 < t

   1. Initial program 36.0%

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

      1. associate-*l/ 58.4%

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

   3. Simplified 58.4%

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

   4. Taylor expanded in t around -inf 67.2%

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

      1. mul-1-neg 67.2%

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

      2. unsub-neg 67.2%

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

      3. div-sub 67.2%

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

      4. *-commutative 67.2%

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

      5. div-sub 67.2%

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

      6. distribute-rgt-out-- 68.3%

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

   6. Simplified 68.3%

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

   7. Taylor expanded in z around inf 67.2%

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

      1. *-commutative 67.2%

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

      2. *-lft-identity 67.2%

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

      3. metadata-eval 67.2%

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

      4. cancel-sign-sub-inv 67.2%

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

      5. neg-mul-1 67.2%

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

      6. associate-*r/ 67.2%

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

      7. distribute-neg-frac 67.2%

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

      8. div-sub 67.2%

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

      9. sub-neg 67.2%

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

      10. remove-double-neg 67.2%

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

      11. +-commutative 67.2%

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

      12. associate-*r* 67.2%

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

      13. distribute-rgt-in 68.3%

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

      14. neg-mul-1 68.3%

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

      15. sub-neg 68.3%

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

      16. associate-/l* 84.5%

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

   9. Simplified 85.7%

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

   if -1.00000000000000002e116 < t < 5.00000000000000025e95

   1. Initial program 85.2%

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

      1. associate-/l* 95.1%

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

   3. Simplified 95.1%

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

4. Final simplification 91.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1 \cdot 10^{+116} \lor \neg \left(t \leq 5 \cdot 10^{+95}\right):\\ \;\;\;\;y + \frac{y - x}{t} \cdot \left(a - z\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{\frac{a - t}{z - t}}\\ \end{array} \]

Alternative 11: 36.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \frac{x}{t}\\ \mathbf{if}\;a \leq -2.75 \cdot 10^{+97}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -8.5 \cdot 10^{-78}:\\ \;\;\;\;y\\ \mathbf{elif}\;a \leq -7.2 \cdot 10^{-155}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -8.5 \cdot 10^{-303}:\\ \;\;\;\;y\\ \mathbf{elif}\;a \leq 8 \cdot 10^{-8}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* z (/ x t))))
   (if (<= a -2.75e+97)
     x
     (if (<= a -8.5e-78)
       y
       (if (<= a -7.2e-155)
         t_1
         (if (<= a -8.5e-303) y (if (<= a 8e-8) t_1 x)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = z * (x / t);
	double tmp;
	if (a <= -2.75e+97) {
		tmp = x;
	} else if (a <= -8.5e-78) {
		tmp = y;
	} else if (a <= -7.2e-155) {
		tmp = t_1;
	} else if (a <= -8.5e-303) {
		tmp = y;
	} else if (a <= 8e-8) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = z * (x / t)
    if (a <= (-2.75d+97)) then
        tmp = x
    else if (a <= (-8.5d-78)) then
        tmp = y
    else if (a <= (-7.2d-155)) then
        tmp = t_1
    else if (a <= (-8.5d-303)) then
        tmp = y
    else if (a <= 8d-8) then
        tmp = t_1
    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 t_1 = z * (x / t);
	double tmp;
	if (a <= -2.75e+97) {
		tmp = x;
	} else if (a <= -8.5e-78) {
		tmp = y;
	} else if (a <= -7.2e-155) {
		tmp = t_1;
	} else if (a <= -8.5e-303) {
		tmp = y;
	} else if (a <= 8e-8) {
		tmp = t_1;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = z * (x / t)
	tmp = 0
	if a <= -2.75e+97:
		tmp = x
	elif a <= -8.5e-78:
		tmp = y
	elif a <= -7.2e-155:
		tmp = t_1
	elif a <= -8.5e-303:
		tmp = y
	elif a <= 8e-8:
		tmp = t_1
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(z * Float64(x / t))
	tmp = 0.0
	if (a <= -2.75e+97)
		tmp = x;
	elseif (a <= -8.5e-78)
		tmp = y;
	elseif (a <= -7.2e-155)
		tmp = t_1;
	elseif (a <= -8.5e-303)
		tmp = y;
	elseif (a <= 8e-8)
		tmp = t_1;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = z * (x / t);
	tmp = 0.0;
	if (a <= -2.75e+97)
		tmp = x;
	elseif (a <= -8.5e-78)
		tmp = y;
	elseif (a <= -7.2e-155)
		tmp = t_1;
	elseif (a <= -8.5e-303)
		tmp = y;
	elseif (a <= 8e-8)
		tmp = t_1;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(z * N[(x / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -2.75e+97], x, If[LessEqual[a, -8.5e-78], y, If[LessEqual[a, -7.2e-155], t$95$1, If[LessEqual[a, -8.5e-303], y, If[LessEqual[a, 8e-8], t$95$1, x]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -2.75000000000000011e97 or 8.0000000000000002e-8 < a

   1. Initial program 64.7%

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

      1. associate-*l/ 90.6%

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

   3. Simplified 90.6%

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

   4. Taylor expanded in a around inf 48.6%

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

   if -2.75000000000000011e97 < a < -8.49999999999999957e-78 or -7.19999999999999977e-155 < a < -8.5e-303

   1. Initial program 59.1%

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

      1. associate-*l/ 66.6%

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

   3. Simplified 66.6%

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

   4. Taylor expanded in t around inf 50.0%

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

   if -8.49999999999999957e-78 < a < -7.19999999999999977e-155 or -8.5e-303 < a < 8.0000000000000002e-8

   1. Initial program 74.9%

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

      1. associate-*l/ 72.5%

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

   3. Simplified 72.5%

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

   4. Taylor expanded in x around -inf 89.3%

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

      1. +-commutative 89.3%

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

      2. *-commutative 89.3%

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

      3. associate-*r/ 92.4%

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

      4. mul-1-neg 92.4%

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

      5. unsub-neg 92.4%

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

      6. *-commutative 92.4%

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

   6. Simplified 92.4%

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

   7. Taylor expanded in a around 0 81.4%

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

      1. mul-1-neg 81.4%

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

      2. associate-/l* 84.7%

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

      3. distribute-neg-frac 84.7%

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

   9. Simplified 84.7%

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

   10. Taylor expanded in y around 0 34.6%

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

       1. associate-*r/ 36.9%

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

   12. Simplified 36.9%

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

4. Final simplification 44.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.75 \cdot 10^{+97}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -8.5 \cdot 10^{-78}:\\ \;\;\;\;y\\ \mathbf{elif}\;a \leq -7.2 \cdot 10^{-155}:\\ \;\;\;\;z \cdot \frac{x}{t}\\ \mathbf{elif}\;a \leq -8.5 \cdot 10^{-303}:\\ \;\;\;\;y\\ \mathbf{elif}\;a \leq 8 \cdot 10^{-8}:\\ \;\;\;\;z \cdot \frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 12: 37.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -8 \cdot 10^{+96}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -8.5 \cdot 10^{-71}:\\ \;\;\;\;y\\ \mathbf{elif}\;a \leq -5.2 \cdot 10^{-153}:\\ \;\;\;\;z \cdot \frac{x}{t}\\ \mathbf{elif}\;a \leq -5.4 \cdot 10^{-303}:\\ \;\;\;\;y\\ \mathbf{elif}\;a \leq 6 \cdot 10^{-9}:\\ \;\;\;\;\frac{z}{\frac{t}{x}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -8e+96)
   x
   (if (<= a -8.5e-71)
     y
     (if (<= a -5.2e-153)
       (* z (/ x t))
       (if (<= a -5.4e-303) y (if (<= a 6e-9) (/ z (/ t x)) x))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -8e+96) {
		tmp = x;
	} else if (a <= -8.5e-71) {
		tmp = y;
	} else if (a <= -5.2e-153) {
		tmp = z * (x / t);
	} else if (a <= -5.4e-303) {
		tmp = y;
	} else if (a <= 6e-9) {
		tmp = z / (t / x);
	} 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 <= (-8d+96)) then
        tmp = x
    else if (a <= (-8.5d-71)) then
        tmp = y
    else if (a <= (-5.2d-153)) then
        tmp = z * (x / t)
    else if (a <= (-5.4d-303)) then
        tmp = y
    else if (a <= 6d-9) then
        tmp = z / (t / x)
    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 <= -8e+96) {
		tmp = x;
	} else if (a <= -8.5e-71) {
		tmp = y;
	} else if (a <= -5.2e-153) {
		tmp = z * (x / t);
	} else if (a <= -5.4e-303) {
		tmp = y;
	} else if (a <= 6e-9) {
		tmp = z / (t / x);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -8e+96:
		tmp = x
	elif a <= -8.5e-71:
		tmp = y
	elif a <= -5.2e-153:
		tmp = z * (x / t)
	elif a <= -5.4e-303:
		tmp = y
	elif a <= 6e-9:
		tmp = z / (t / x)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -8e+96)
		tmp = x;
	elseif (a <= -8.5e-71)
		tmp = y;
	elseif (a <= -5.2e-153)
		tmp = Float64(z * Float64(x / t));
	elseif (a <= -5.4e-303)
		tmp = y;
	elseif (a <= 6e-9)
		tmp = Float64(z / Float64(t / x));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -8e+96)
		tmp = x;
	elseif (a <= -8.5e-71)
		tmp = y;
	elseif (a <= -5.2e-153)
		tmp = z * (x / t);
	elseif (a <= -5.4e-303)
		tmp = y;
	elseif (a <= 6e-9)
		tmp = z / (t / x);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -8e+96], x, If[LessEqual[a, -8.5e-71], y, If[LessEqual[a, -5.2e-153], N[(z * N[(x / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -5.4e-303], y, If[LessEqual[a, 6e-9], N[(z / N[(t / x), $MachinePrecision]), $MachinePrecision], x]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -8.0000000000000004e96 or 5.99999999999999996e-9 < a

   1. Initial program 64.7%

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

      1. associate-*l/ 90.6%

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

   3. Simplified 90.6%

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

   4. Taylor expanded in a around inf 48.6%

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

   if -8.0000000000000004e96 < a < -8.49999999999999988e-71 or -5.2000000000000003e-153 < a < -5.39999999999999972e-303

   1. Initial program 59.1%

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

      1. associate-*l/ 66.6%

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

   3. Simplified 66.6%

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

   4. Taylor expanded in t around inf 50.0%

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

   if -8.49999999999999988e-71 < a < -5.2000000000000003e-153

   1. Initial program 72.4%

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

      1. associate-*l/ 71.4%

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

   3. Simplified 71.4%

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

   4. Taylor expanded in x around -inf 88.4%

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

      1. +-commutative 88.4%

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

      2. *-commutative 88.4%

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

      3. associate-*r/ 93.9%

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

      4. mul-1-neg 93.9%

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

      5. unsub-neg 93.9%

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

      6. *-commutative 93.9%

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

   6. Simplified 93.9%

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

   7. Taylor expanded in a around 0 66.4%

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

      1. mul-1-neg 66.4%

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

      2. associate-/l* 72.1%

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

      3. distribute-neg-frac 72.1%

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

   9. Simplified 72.1%

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

   10. Taylor expanded in y around 0 43.8%

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

       1. associate-*r/ 49.4%

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

   12. Simplified 49.4%

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

   if -5.39999999999999972e-303 < a < 5.99999999999999996e-9

   1. Initial program 75.5%

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

      1. associate-*l/ 72.8%

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

   3. Simplified 72.8%

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

   4. Taylor expanded in t around -inf 82.6%

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

      1. mul-1-neg 82.6%

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

      2. unsub-neg 82.6%

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

      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 82.6%

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

      6. distribute-rgt-out-- 82.6%

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

   6. Simplified 82.6%

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

   7. Taylor expanded in y around 0 35.8%

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

   8. Taylor expanded in z around inf 32.5%

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

      1. associate-/l* 33.9%

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

   10. Simplified 33.9%

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

4. Final simplification 44.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -8 \cdot 10^{+96}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -8.5 \cdot 10^{-71}:\\ \;\;\;\;y\\ \mathbf{elif}\;a \leq -5.2 \cdot 10^{-153}:\\ \;\;\;\;z \cdot \frac{x}{t}\\ \mathbf{elif}\;a \leq -5.4 \cdot 10^{-303}:\\ \;\;\;\;y\\ \mathbf{elif}\;a \leq 6 \cdot 10^{-9}:\\ \;\;\;\;\frac{z}{\frac{t}{x}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 13: 48.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{t - z}{t}\\ \mathbf{if}\;a \leq -1.75 \cdot 10^{+103}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -1.75 \cdot 10^{-299}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 5.5 \cdot 10^{-169}:\\ \;\;\;\;\frac{x - y}{\frac{t}{z}}\\ \mathbf{elif}\;a \leq 4.1 \cdot 10^{+80}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ (- t z) t))))
   (if (<= a -1.75e+103)
     x
     (if (<= a -1.75e-299)
       t_1
       (if (<= a 5.5e-169) (/ (- x y) (/ t z)) (if (<= a 4.1e+80) t_1 x))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((t - z) / t);
	double tmp;
	if (a <= -1.75e+103) {
		tmp = x;
	} else if (a <= -1.75e-299) {
		tmp = t_1;
	} else if (a <= 5.5e-169) {
		tmp = (x - y) / (t / z);
	} else if (a <= 4.1e+80) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = y * ((t - z) / t)
    if (a <= (-1.75d+103)) then
        tmp = x
    else if (a <= (-1.75d-299)) then
        tmp = t_1
    else if (a <= 5.5d-169) then
        tmp = (x - y) / (t / z)
    else if (a <= 4.1d+80) then
        tmp = t_1
    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 t_1 = y * ((t - z) / t);
	double tmp;
	if (a <= -1.75e+103) {
		tmp = x;
	} else if (a <= -1.75e-299) {
		tmp = t_1;
	} else if (a <= 5.5e-169) {
		tmp = (x - y) / (t / z);
	} else if (a <= 4.1e+80) {
		tmp = t_1;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * ((t - z) / t)
	tmp = 0
	if a <= -1.75e+103:
		tmp = x
	elif a <= -1.75e-299:
		tmp = t_1
	elif a <= 5.5e-169:
		tmp = (x - y) / (t / z)
	elif a <= 4.1e+80:
		tmp = t_1
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(Float64(t - z) / t))
	tmp = 0.0
	if (a <= -1.75e+103)
		tmp = x;
	elseif (a <= -1.75e-299)
		tmp = t_1;
	elseif (a <= 5.5e-169)
		tmp = Float64(Float64(x - y) / Float64(t / z));
	elseif (a <= 4.1e+80)
		tmp = t_1;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * ((t - z) / t);
	tmp = 0.0;
	if (a <= -1.75e+103)
		tmp = x;
	elseif (a <= -1.75e-299)
		tmp = t_1;
	elseif (a <= 5.5e-169)
		tmp = (x - y) / (t / z);
	elseif (a <= 4.1e+80)
		tmp = t_1;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(N[(t - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.75e+103], x, If[LessEqual[a, -1.75e-299], t$95$1, If[LessEqual[a, 5.5e-169], N[(N[(x - y), $MachinePrecision] / N[(t / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 4.1e+80], t$95$1, x]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.75e103 or 4.10000000000000001e80 < a

   1. Initial program 65.2%

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

      1. associate-*l/ 92.2%

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

   3. Simplified 92.2%

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

   4. Taylor expanded in a around inf 52.7%

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

   if -1.75e103 < a < -1.74999999999999995e-299 or 5.4999999999999994e-169 < a < 4.10000000000000001e80

   1. Initial program 63.7%

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

      1. associate-*l/ 70.1%

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

   3. Simplified 70.1%

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

   4. Taylor expanded in x around 0 50.4%

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

      1. associate-*r/ 63.4%

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

      2. *-commutative 63.4%

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

   6. Applied egg-rr 63.4%

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

   7. Taylor expanded in a around 0 51.9%

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

      1. associate-*r/ 51.9%

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

      2. mul-1-neg 51.9%

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

   9. Simplified 51.9%

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

   if -1.74999999999999995e-299 < a < 5.4999999999999994e-169

   1. Initial program 81.9%

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

      1. associate-*l/ 74.6%

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

   3. Simplified 74.6%

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

   4. Taylor expanded in t around -inf 85.7%

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

      1. mul-1-neg 85.7%

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

      2. unsub-neg 85.7%

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

      3. div-sub 85.7%

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

      4. *-commutative 85.7%

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

      5. div-sub 85.7%

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

      6. distribute-rgt-out-- 85.7%

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

   6. Simplified 85.7%

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

   7. Taylor expanded in z around -inf 72.7%

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

      1. mul-1-neg 72.7%

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

      2. associate-/l* 77.6%

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

   9. Simplified 77.6%

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

4. Final simplification 56.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.75 \cdot 10^{+103}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -1.75 \cdot 10^{-299}:\\ \;\;\;\;y \cdot \frac{t - z}{t}\\ \mathbf{elif}\;a \leq 5.5 \cdot 10^{-169}:\\ \;\;\;\;\frac{x - y}{\frac{t}{z}}\\ \mathbf{elif}\;a \leq 4.1 \cdot 10^{+80}:\\ \;\;\;\;y \cdot \frac{t - z}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 14: 49.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + \frac{z}{\frac{t}{x}}\\ \mathbf{if}\;a \leq -2.45 \cdot 10^{+156}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -2.6 \cdot 10^{-294}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 2 \cdot 10^{-163}:\\ \;\;\;\;\frac{x - y}{\frac{t}{z}}\\ \mathbf{elif}\;a \leq 9 \cdot 10^{+34}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ y (/ z (/ t x)))))
   (if (<= a -2.45e+156)
     x
     (if (<= a -2.6e-294)
       t_1
       (if (<= a 2e-163) (/ (- x y) (/ t z)) (if (<= a 9e+34) t_1 x))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y + (z / (t / x));
	double tmp;
	if (a <= -2.45e+156) {
		tmp = x;
	} else if (a <= -2.6e-294) {
		tmp = t_1;
	} else if (a <= 2e-163) {
		tmp = (x - y) / (t / z);
	} else if (a <= 9e+34) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = y + (z / (t / x))
    if (a <= (-2.45d+156)) then
        tmp = x
    else if (a <= (-2.6d-294)) then
        tmp = t_1
    else if (a <= 2d-163) then
        tmp = (x - y) / (t / z)
    else if (a <= 9d+34) then
        tmp = t_1
    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 t_1 = y + (z / (t / x));
	double tmp;
	if (a <= -2.45e+156) {
		tmp = x;
	} else if (a <= -2.6e-294) {
		tmp = t_1;
	} else if (a <= 2e-163) {
		tmp = (x - y) / (t / z);
	} else if (a <= 9e+34) {
		tmp = t_1;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y + (z / (t / x))
	tmp = 0
	if a <= -2.45e+156:
		tmp = x
	elif a <= -2.6e-294:
		tmp = t_1
	elif a <= 2e-163:
		tmp = (x - y) / (t / z)
	elif a <= 9e+34:
		tmp = t_1
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y + Float64(z / Float64(t / x)))
	tmp = 0.0
	if (a <= -2.45e+156)
		tmp = x;
	elseif (a <= -2.6e-294)
		tmp = t_1;
	elseif (a <= 2e-163)
		tmp = Float64(Float64(x - y) / Float64(t / z));
	elseif (a <= 9e+34)
		tmp = t_1;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y + (z / (t / x));
	tmp = 0.0;
	if (a <= -2.45e+156)
		tmp = x;
	elseif (a <= -2.6e-294)
		tmp = t_1;
	elseif (a <= 2e-163)
		tmp = (x - y) / (t / z);
	elseif (a <= 9e+34)
		tmp = t_1;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y + N[(z / N[(t / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -2.45e+156], x, If[LessEqual[a, -2.6e-294], t$95$1, If[LessEqual[a, 2e-163], N[(N[(x - y), $MachinePrecision] / N[(t / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 9e+34], t$95$1, x]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -2.44999999999999984e156 or 9.0000000000000001e34 < a

   1. Initial program 63.5%

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

      1. associate-*l/ 91.5%

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

   3. Simplified 91.5%

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

   4. Taylor expanded in a around inf 50.7%

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

   if -2.44999999999999984e156 < a < -2.5999999999999999e-294 or 1.99999999999999985e-163 < a < 9.0000000000000001e34

   1. Initial program 64.4%

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

      1. associate-*l/ 72.0%

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

   3. Simplified 72.0%

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

   4. Taylor expanded in x around -inf 79.2%

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

      1. +-commutative 79.2%

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

      2. *-commutative 79.2%

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

      3. associate-*r/ 91.7%

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

      4. mul-1-neg 91.7%

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

      5. unsub-neg 91.7%

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

      6. *-commutative 91.7%

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

   6. Simplified 91.7%

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

   7. Taylor expanded in a around 0 71.5%

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

      1. mul-1-neg 71.5%

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

      2. associate-/l* 72.9%

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

      3. distribute-neg-frac 72.9%

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

   9. Simplified 72.9%

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

   10. Taylor expanded in t around inf 59.4%

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

   if -2.5999999999999999e-294 < a < 1.99999999999999985e-163

   1. Initial program 82.8%

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

      1. associate-*l/ 73.6%

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

   3. Simplified 73.6%

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

   4. Taylor expanded in t around -inf 86.4%

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

      1. mul-1-neg 86.4%

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

      2. unsub-neg 86.4%

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

      3. div-sub 86.4%

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

      4. *-commutative 86.4%

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

      5. div-sub 86.4%

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

      6. distribute-rgt-out-- 86.4%

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

   6. Simplified 86.4%

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

   7. Taylor expanded in z around -inf 71.6%

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

      1. mul-1-neg 71.6%

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

      2. associate-/l* 76.2%

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

   9. Simplified 76.2%

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

4. Final simplification 59.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.45 \cdot 10^{+156}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -2.6 \cdot 10^{-294}:\\ \;\;\;\;y + \frac{z}{\frac{t}{x}}\\ \mathbf{elif}\;a \leq 2 \cdot 10^{-163}:\\ \;\;\;\;\frac{x - y}{\frac{t}{z}}\\ \mathbf{elif}\;a \leq 9 \cdot 10^{+34}:\\ \;\;\;\;y + \frac{z}{\frac{t}{x}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 15: 56.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.7 \cdot 10^{+142}:\\ \;\;\;\;x \cdot \frac{z - a}{t}\\ \mathbf{elif}\;x \leq -3.4 \cdot 10^{+15} \lor \neg \left(x \leq 1.8 \cdot 10^{+146}\right):\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= x -2.7e+142)
   (* x (/ (- z a) t))
   (if (or (<= x -3.4e+15) (not (<= x 1.8e+146)))
     (* z (/ (- y x) (- a t)))
     (* y (/ (- z t) (- a t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -2.7e+142) {
		tmp = x * ((z - a) / t);
	} else if ((x <= -3.4e+15) || !(x <= 1.8e+146)) {
		tmp = z * ((y - x) / (a - t));
	} else {
		tmp = y * ((z - t) / (a - t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (x <= (-2.7d+142)) then
        tmp = x * ((z - a) / t)
    else if ((x <= (-3.4d+15)) .or. (.not. (x <= 1.8d+146))) then
        tmp = z * ((y - x) / (a - t))
    else
        tmp = y * ((z - t) / (a - t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -2.7e+142) {
		tmp = x * ((z - a) / t);
	} else if ((x <= -3.4e+15) || !(x <= 1.8e+146)) {
		tmp = z * ((y - x) / (a - t));
	} else {
		tmp = y * ((z - t) / (a - t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if x <= -2.7e+142:
		tmp = x * ((z - a) / t)
	elif (x <= -3.4e+15) or not (x <= 1.8e+146):
		tmp = z * ((y - x) / (a - t))
	else:
		tmp = y * ((z - t) / (a - t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (x <= -2.7e+142)
		tmp = Float64(x * Float64(Float64(z - a) / t));
	elseif ((x <= -3.4e+15) || !(x <= 1.8e+146))
		tmp = Float64(z * Float64(Float64(y - x) / Float64(a - t)));
	else
		tmp = Float64(y * Float64(Float64(z - t) / Float64(a - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (x <= -2.7e+142)
		tmp = x * ((z - a) / t);
	elseif ((x <= -3.4e+15) || ~((x <= 1.8e+146)))
		tmp = z * ((y - x) / (a - t));
	else
		tmp = y * ((z - t) / (a - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[x, -2.7e+142], N[(x * N[(N[(z - a), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[x, -3.4e+15], N[Not[LessEqual[x, 1.8e+146]], $MachinePrecision]], N[(z * N[(N[(y - x), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.69999999999999983e142

   1. Initial program 38.6%

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

      1. associate-*l/ 61.2%

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

   3. Simplified 61.2%

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

   4. Taylor expanded in t around -inf 40.6%

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

      1. mul-1-neg 40.6%

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

      2. unsub-neg 40.6%

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

      3. div-sub 36.1%

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

      4. *-commutative 36.1%

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

      5. div-sub 40.6%

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

      6. distribute-rgt-out-- 43.3%

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

   6. Simplified 43.3%

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

   7. Taylor expanded in y around 0 36.9%

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

   8. Taylor expanded in z around 0 29.7%

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

      1. mul-1-neg 29.7%

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

      2. sub-neg 29.7%

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

      3. associate-/l* 24.9%

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

      4. associate-/l* 31.5%

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

      5. div-sub 37.4%

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

      6. associate-/r/ 43.6%

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

   10. Simplified 43.6%

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

   if -2.69999999999999983e142 < x < -3.4e15 or 1.7999999999999999e146 < x

   1. Initial program 60.4%

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

      1. associate-*l/ 77.7%

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

   3. Simplified 77.7%

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

   4. Taylor expanded in z around inf 58.7%

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

      1. div-sub 58.7%

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

   6. Simplified 58.7%

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

   if -3.4e15 < x < 1.7999999999999999e146

   1. Initial program 77.8%

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

      1. associate-*l/ 84.8%

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

   3. Simplified 84.8%

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

   4. Taylor expanded in x around 0 59.5%

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

      1. associate-*r/ 72.5%

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

   6. Simplified 72.5%

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

4. Final simplification 64.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.7 \cdot 10^{+142}:\\ \;\;\;\;x \cdot \frac{z - a}{t}\\ \mathbf{elif}\;x \leq -3.4 \cdot 10^{+15} \lor \neg \left(x \leq 1.8 \cdot 10^{+146}\right):\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \end{array} \]

Alternative 16: 66.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.85 \cdot 10^{+118}:\\ \;\;\;\;y + \frac{z}{\frac{t}{x}}\\ \mathbf{elif}\;t \leq -1.8 \cdot 10^{-85}:\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \mathbf{elif}\;t \leq 4.6 \cdot 10^{-30}:\\ \;\;\;\;x + \frac{y - x}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -1.85e+118)
   (+ y (/ z (/ t x)))
   (if (<= t -1.8e-85)
     (* z (/ (- y x) (- a t)))
     (if (<= t 4.6e-30) (+ x (/ (- y x) (/ a z))) (* y (/ (- z t) (- a t)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.85e+118) {
		tmp = y + (z / (t / x));
	} else if (t <= -1.8e-85) {
		tmp = z * ((y - x) / (a - t));
	} else if (t <= 4.6e-30) {
		tmp = x + ((y - x) / (a / z));
	} else {
		tmp = y * ((z - t) / (a - t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-1.85d+118)) then
        tmp = y + (z / (t / x))
    else if (t <= (-1.8d-85)) then
        tmp = z * ((y - x) / (a - t))
    else if (t <= 4.6d-30) then
        tmp = x + ((y - x) / (a / z))
    else
        tmp = y * ((z - t) / (a - t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.85e+118) {
		tmp = y + (z / (t / x));
	} else if (t <= -1.8e-85) {
		tmp = z * ((y - x) / (a - t));
	} else if (t <= 4.6e-30) {
		tmp = x + ((y - x) / (a / z));
	} else {
		tmp = y * ((z - t) / (a - t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -1.85e+118:
		tmp = y + (z / (t / x))
	elif t <= -1.8e-85:
		tmp = z * ((y - x) / (a - t))
	elif t <= 4.6e-30:
		tmp = x + ((y - x) / (a / z))
	else:
		tmp = y * ((z - t) / (a - t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -1.85e+118)
		tmp = Float64(y + Float64(z / Float64(t / x)));
	elseif (t <= -1.8e-85)
		tmp = Float64(z * Float64(Float64(y - x) / Float64(a - t)));
	elseif (t <= 4.6e-30)
		tmp = Float64(x + Float64(Float64(y - x) / Float64(a / z)));
	else
		tmp = Float64(y * Float64(Float64(z - t) / Float64(a - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -1.85e+118)
		tmp = y + (z / (t / x));
	elseif (t <= -1.8e-85)
		tmp = z * ((y - x) / (a - t));
	elseif (t <= 4.6e-30)
		tmp = x + ((y - x) / (a / z));
	else
		tmp = y * ((z - t) / (a - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -1.85e+118], N[(y + N[(z / N[(t / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -1.8e-85], N[(z * N[(N[(y - x), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4.6e-30], N[(x + N[(N[(y - x), $MachinePrecision] / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if t < -1.84999999999999993e118

   1. Initial program 32.4%

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

      1. associate-*l/ 57.7%

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

   3. Simplified 57.7%

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

   4. Taylor expanded in x around -inf 61.1%

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

      1. +-commutative 61.1%

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

      2. *-commutative 61.1%

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

      3. associate-*r/ 81.7%

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

      4. mul-1-neg 81.7%

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

      5. unsub-neg 81.7%

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

      6. *-commutative 81.7%

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

   6. Simplified 81.7%

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

   7. Taylor expanded in a around 0 63.5%

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

      1. mul-1-neg 63.5%

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

      2. associate-/l* 64.4%

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

      3. distribute-neg-frac 64.4%

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

   9. Simplified 64.4%

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

   10. Taylor expanded in t around inf 57.6%

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

   if -1.84999999999999993e118 < t < -1.7999999999999999e-85

   1. Initial program 68.7%

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

      1. associate-*l/ 84.3%

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

   3. Simplified 84.3%

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

   4. Taylor expanded in z around inf 71.7%

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

      1. div-sub 71.7%

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

   6. Simplified 71.7%

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

   if -1.7999999999999999e-85 < t < 4.59999999999999968e-30

   1. Initial program 89.3%

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

      1. associate-*l/ 91.2%

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

   3. Simplified 91.2%

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

   4. Taylor expanded in t around 0 68.0%

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

      1. +-commutative 68.0%

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

      2. associate-/l* 75.8%

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

   6. Simplified 75.8%

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

   if 4.59999999999999968e-30 < t

   1. Initial program 55.1%

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

      1. associate-*l/ 72.4%

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

   3. Simplified 72.4%

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

   4. Taylor expanded in x around 0 51.4%

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

      1. associate-*r/ 68.4%

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

   6. Simplified 68.4%

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

4. Final simplification 70.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.85 \cdot 10^{+118}:\\ \;\;\;\;y + \frac{z}{\frac{t}{x}}\\ \mathbf{elif}\;t \leq -1.8 \cdot 10^{-85}:\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \mathbf{elif}\;t \leq 4.6 \cdot 10^{-30}:\\ \;\;\;\;x + \frac{y - x}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \end{array} \]

Alternative 17: 70.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y - x}{\frac{a}{z}}\\ \mathbf{if}\;a \leq -1.95 \cdot 10^{+101}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -220000:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;a \leq 1.75 \cdot 10^{+28}:\\ \;\;\;\;y - \frac{y - x}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ (- y x) (/ a z)))))
   (if (<= a -1.95e+101)
     t_1
     (if (<= a -220000.0)
       (* y (/ (- z t) (- a t)))
       (if (<= a 1.75e+28) (- y (/ (- y x) (/ t z))) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - x) / (a / z));
	double tmp;
	if (a <= -1.95e+101) {
		tmp = t_1;
	} else if (a <= -220000.0) {
		tmp = y * ((z - t) / (a - t));
	} else if (a <= 1.75e+28) {
		tmp = y - ((y - x) / (t / z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + ((y - x) / (a / z))
    if (a <= (-1.95d+101)) then
        tmp = t_1
    else if (a <= (-220000.0d0)) then
        tmp = y * ((z - t) / (a - t))
    else if (a <= 1.75d+28) then
        tmp = y - ((y - x) / (t / z))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - x) / (a / z));
	double tmp;
	if (a <= -1.95e+101) {
		tmp = t_1;
	} else if (a <= -220000.0) {
		tmp = y * ((z - t) / (a - t));
	} else if (a <= 1.75e+28) {
		tmp = y - ((y - x) / (t / z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((y - x) / (a / z))
	tmp = 0
	if a <= -1.95e+101:
		tmp = t_1
	elif a <= -220000.0:
		tmp = y * ((z - t) / (a - t))
	elif a <= 1.75e+28:
		tmp = y - ((y - x) / (t / z))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(y - x) / Float64(a / z)))
	tmp = 0.0
	if (a <= -1.95e+101)
		tmp = t_1;
	elseif (a <= -220000.0)
		tmp = Float64(y * Float64(Float64(z - t) / Float64(a - t)));
	elseif (a <= 1.75e+28)
		tmp = Float64(y - Float64(Float64(y - x) / Float64(t / z)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((y - x) / (a / z));
	tmp = 0.0;
	if (a <= -1.95e+101)
		tmp = t_1;
	elseif (a <= -220000.0)
		tmp = y * ((z - t) / (a - t));
	elseif (a <= 1.75e+28)
		tmp = y - ((y - x) / (t / z));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(y - x), $MachinePrecision] / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.95e+101], t$95$1, If[LessEqual[a, -220000.0], N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.75e+28], N[(y - N[(N[(y - x), $MachinePrecision] / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.95e101 or 1.75e28 < a

   1. Initial program 65.8%

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

      1. associate-*l/ 91.0%

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

   3. Simplified 91.0%

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

   4. Taylor expanded in t around 0 58.2%

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

      1. +-commutative 58.2%

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

      2. associate-/l* 73.3%

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

   6. Simplified 73.3%

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

   if -1.95e101 < a < -2.2e5

   1. Initial program 66.0%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   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 x around 0 58.3%

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

      1. associate-*r/ 74.5%

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

   6. Simplified 74.5%

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

   if -2.2e5 < a < 1.75e28

   1. Initial program 68.3%

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

      1. associate-*l/ 69.3%

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

   3. Simplified 69.3%

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

   4. Taylor expanded in t around -inf 80.1%

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

      1. mul-1-neg 80.1%

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

      2. unsub-neg 80.1%

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

      3. div-sub 76.8%

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

      4. *-commutative 76.8%

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

      5. div-sub 80.1%

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

      6. distribute-rgt-out-- 80.1%

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

   6. Simplified 80.1%

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

   7. Taylor expanded in z around inf 75.7%

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

      1. *-commutative 75.7%

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

      2. associate-/l* 81.2%

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

   9. Simplified 81.2%

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

4. Final simplification 77.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.95 \cdot 10^{+101}:\\ \;\;\;\;x + \frac{y - x}{\frac{a}{z}}\\ \mathbf{elif}\;a \leq -220000:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;a \leq 1.75 \cdot 10^{+28}:\\ \;\;\;\;y - \frac{y - x}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{\frac{a}{z}}\\ \end{array} \]

Alternative 18: 74.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -440000000000 \lor \neg \left(t \leq 2.6 \cdot 10^{-24}\right):\\ \;\;\;\;y + \frac{y - x}{t} \cdot \left(a - z\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z - t}{\frac{a}{y - x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -440000000000.0) (not (<= t 2.6e-24)))
   (+ y (* (/ (- y x) t) (- a z)))
   (+ x (/ (- z t) (/ a (- y x))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -440000000000.0) || !(t <= 2.6e-24)) {
		tmp = y + (((y - x) / t) * (a - z));
	} else {
		tmp = x + ((z - t) / (a / (y - x)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-440000000000.0d0)) .or. (.not. (t <= 2.6d-24))) then
        tmp = y + (((y - x) / t) * (a - z))
    else
        tmp = x + ((z - t) / (a / (y - x)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -440000000000.0) || !(t <= 2.6e-24)) {
		tmp = y + (((y - x) / t) * (a - z));
	} else {
		tmp = x + ((z - t) / (a / (y - x)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -440000000000.0) or not (t <= 2.6e-24):
		tmp = y + (((y - x) / t) * (a - z))
	else:
		tmp = x + ((z - t) / (a / (y - x)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -440000000000.0) || !(t <= 2.6e-24))
		tmp = Float64(y + Float64(Float64(Float64(y - x) / t) * Float64(a - z)));
	else
		tmp = Float64(x + Float64(Float64(z - t) / Float64(a / Float64(y - x))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -440000000000.0) || ~((t <= 2.6e-24)))
		tmp = y + (((y - x) / t) * (a - z));
	else
		tmp = x + ((z - t) / (a / (y - x)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -440000000000.0], N[Not[LessEqual[t, 2.6e-24]], $MachinePrecision]], N[(y + N[(N[(N[(y - x), $MachinePrecision] / t), $MachinePrecision] * N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(z - t), $MachinePrecision] / N[(a / N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -4.4e11 or 2.6e-24 < t

   1. Initial program 49.1%

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

      1. associate-*l/ 68.0%

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

   3. Simplified 68.0%

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

   4. Taylor expanded in t around -inf 66.1%

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

      1. mul-1-neg 66.1%

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

      2. unsub-neg 66.1%

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

      3. div-sub 66.1%

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

      4. *-commutative 66.1%

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

      5. div-sub 66.1%

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

      6. distribute-rgt-out-- 66.8%

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

   6. Simplified 66.8%

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

   7. Taylor expanded in z around inf 66.1%

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

      1. *-commutative 66.1%

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

      2. *-lft-identity 66.1%

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

      3. metadata-eval 66.1%

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

      4. cancel-sign-sub-inv 66.1%

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

      5. neg-mul-1 66.1%

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

      6. associate-*r/ 66.1%

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

      7. distribute-neg-frac 66.1%

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

      8. div-sub 66.1%

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

      9. sub-neg 66.1%

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

      10. remove-double-neg 66.1%

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

      11. +-commutative 66.1%

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

      12. associate-*r* 66.1%

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

      13. distribute-rgt-in 66.8%

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

      14. neg-mul-1 66.8%

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

      15. sub-neg 66.8%

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

      16. associate-/l* 78.1%

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

   9. Simplified 78.9%

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

   if -4.4e11 < t < 2.6e-24

   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/ 92.0%

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

   3. Simplified 92.0%

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

   4. Taylor expanded in a around inf 69.0%

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

      1. +-commutative 69.0%

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

      2. associate-/l* 78.2%

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

   6. Simplified 78.2%

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

4. Final simplification 78.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -440000000000 \lor \neg \left(t \leq 2.6 \cdot 10^{-24}\right):\\ \;\;\;\;y + \frac{y - x}{t} \cdot \left(a - z\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z - t}{\frac{a}{y - x}}\\ \end{array} \]

Alternative 19: 55.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.4 \cdot 10^{+80}:\\ \;\;\;\;x \cdot \frac{z - a}{t}\\ \mathbf{elif}\;x \leq 3.7 \cdot 10^{+158}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;\frac{z - a}{\frac{t}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= x -3.4e+80)
   (* x (/ (- z a) t))
   (if (<= x 3.7e+158) (* y (/ (- z t) (- a t))) (/ (- z a) (/ t x)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -3.4e+80) {
		tmp = x * ((z - a) / t);
	} else if (x <= 3.7e+158) {
		tmp = y * ((z - t) / (a - t));
	} else {
		tmp = (z - a) / (t / 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 (x <= (-3.4d+80)) then
        tmp = x * ((z - a) / t)
    else if (x <= 3.7d+158) then
        tmp = y * ((z - t) / (a - t))
    else
        tmp = (z - a) / (t / 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 (x <= -3.4e+80) {
		tmp = x * ((z - a) / t);
	} else if (x <= 3.7e+158) {
		tmp = y * ((z - t) / (a - t));
	} else {
		tmp = (z - a) / (t / x);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if x <= -3.4e+80:
		tmp = x * ((z - a) / t)
	elif x <= 3.7e+158:
		tmp = y * ((z - t) / (a - t))
	else:
		tmp = (z - a) / (t / x)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (x <= -3.4e+80)
		tmp = Float64(x * Float64(Float64(z - a) / t));
	elseif (x <= 3.7e+158)
		tmp = Float64(y * Float64(Float64(z - t) / Float64(a - t)));
	else
		tmp = Float64(Float64(z - a) / Float64(t / x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (x <= -3.4e+80)
		tmp = x * ((z - a) / t);
	elseif (x <= 3.7e+158)
		tmp = y * ((z - t) / (a - t));
	else
		tmp = (z - a) / (t / x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[x, -3.4e+80], N[(x * N[(N[(z - a), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3.7e+158], N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(z - a), $MachinePrecision] / N[(t / x), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -3.39999999999999992e80

   1. Initial program 48.4%

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

      1. associate-*l/ 67.8%

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

   3. Simplified 67.8%

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

   4. Taylor expanded in t around -inf 41.0%

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

      1. mul-1-neg 41.0%

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

      2. unsub-neg 41.0%

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

      3. div-sub 37.2%

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

      4. *-commutative 37.2%

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

      5. div-sub 41.0%

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

      6. distribute-rgt-out-- 43.1%

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

   6. Simplified 43.1%

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

   7. Taylor expanded in y around 0 38.3%

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

   8. Taylor expanded in z around 0 32.4%

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

      1. mul-1-neg 32.4%

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

      2. sub-neg 32.4%

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

      3. associate-/l* 28.7%

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

      4. associate-/l* 33.9%

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

      5. div-sub 38.7%

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

      6. associate-/r/ 43.6%

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

   10. Simplified 43.6%

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

   if -3.39999999999999992e80 < x < 3.70000000000000011e158

   1. Initial program 75.1%

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

      1. associate-*l/ 84.1%

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

   3. Simplified 84.1%

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

   4. Taylor expanded in x around 0 55.4%

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

      1. associate-*r/ 69.2%

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

   6. Simplified 69.2%

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

   if 3.70000000000000011e158 < x

   1. Initial program 55.5%

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

      1. associate-*l/ 71.6%

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

   3. Simplified 71.6%

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

   4. Taylor expanded in t around -inf 42.0%

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

      1. mul-1-neg 42.0%

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

      2. unsub-neg 42.0%

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

      3. div-sub 35.0%

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

      4. *-commutative 35.0%

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

      5. div-sub 42.0%

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

      6. distribute-rgt-out-- 45.6%

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

   6. Simplified 45.6%

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

   7. Taylor expanded in y around 0 40.2%

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

      1. associate-/l* 52.3%

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

   9. Simplified 52.3%

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

4. Final simplification 61.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.4 \cdot 10^{+80}:\\ \;\;\;\;x \cdot \frac{z - a}{t}\\ \mathbf{elif}\;x \leq 3.7 \cdot 10^{+158}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;\frac{z - a}{\frac{t}{x}}\\ \end{array} \]

Alternative 20: 38.3% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.6 \cdot 10^{+105}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.75 \cdot 10^{+29}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -2.6e+105) x (if (<= a 1.75e+29) y x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -2.6e+105) {
		tmp = x;
	} else if (a <= 1.75e+29) {
		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 <= (-2.6d+105)) then
        tmp = x
    else if (a <= 1.75d+29) 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 <= -2.6e+105) {
		tmp = x;
	} else if (a <= 1.75e+29) {
		tmp = y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -2.6e+105:
		tmp = x
	elif a <= 1.75e+29:
		tmp = y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -2.6e+105)
		tmp = x;
	elseif (a <= 1.75e+29)
		tmp = y;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -2.6e+105)
		tmp = x;
	elseif (a <= 1.75e+29)
		tmp = y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -2.6e+105], x, If[LessEqual[a, 1.75e+29], y, x]]

Derivation

1. Split input into 2 regimes

2. if a < -2.6000000000000002e105 or 1.74999999999999989e29 < a

   1. Initial program 65.8%

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

      1. associate-*l/ 91.0%

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

   3. Simplified 91.0%

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

   4. Taylor expanded in a around inf 49.9%

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

   if -2.6000000000000002e105 < a < 1.74999999999999989e29

   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/ 70.6%

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

   3. Simplified 70.6%

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

   4. Taylor expanded in t around inf 33.7%

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

4. Final simplification 40.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.6 \cdot 10^{+105}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.75 \cdot 10^{+29}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 21: 25.2% accurate, 13.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 67.0%

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

   1. associate-*l/ 79.1%

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

3. Simplified 79.1%

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

4. Taylor expanded in a around inf 24.0%

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

5. Final simplification 24.0%

   \[\leadsto x \]

Developer target: 86.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y - x}{1} \cdot \frac{z - t}{a - t}\\ \mathbf{if}\;a < -1.6153062845442575 \cdot 10^{-142}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a < 3.774403170083174 \cdot 10^{-182}:\\ \;\;\;\;y - \frac{z}{t} \cdot \left(y - x\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (/ (- y x) 1.0) (/ (- z t) (- a t))))))
   (if (< a -1.6153062845442575e-142)
     t_1
     (if (< a 3.774403170083174e-182) (- y (* (/ z t) (- y x))) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (((y - x) / 1.0) * ((z - t) / (a - t)));
	double tmp;
	if (a < -1.6153062845442575e-142) {
		tmp = t_1;
	} else if (a < 3.774403170083174e-182) {
		tmp = y - ((z / t) * (y - x));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (((y - x) / 1.0d0) * ((z - t) / (a - t)))
    if (a < (-1.6153062845442575d-142)) then
        tmp = t_1
    else if (a < 3.774403170083174d-182) then
        tmp = y - ((z / t) * (y - x))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (((y - x) / 1.0) * ((z - t) / (a - t)));
	double tmp;
	if (a < -1.6153062845442575e-142) {
		tmp = t_1;
	} else if (a < 3.774403170083174e-182) {
		tmp = y - ((z / t) * (y - x));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (((y - x) / 1.0) * ((z - t) / (a - t)))
	tmp = 0
	if a < -1.6153062845442575e-142:
		tmp = t_1
	elif a < 3.774403170083174e-182:
		tmp = y - ((z / t) * (y - x))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(Float64(y - x) / 1.0) * Float64(Float64(z - t) / Float64(a - t))))
	tmp = 0.0
	if (a < -1.6153062845442575e-142)
		tmp = t_1;
	elseif (a < 3.774403170083174e-182)
		tmp = Float64(y - Float64(Float64(z / t) * Float64(y - x)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (((y - x) / 1.0) * ((z - t) / (a - t)));
	tmp = 0.0;
	if (a < -1.6153062845442575e-142)
		tmp = t_1;
	elseif (a < 3.774403170083174e-182)
		tmp = y - ((z / t) * (y - x));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(N[(y - x), $MachinePrecision] / 1.0), $MachinePrecision] * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Less[a, -1.6153062845442575e-142], t$95$1, If[Less[a, 3.774403170083174e-182], N[(y - N[(N[(z / t), $MachinePrecision] * N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Reproduce

herbie shell --seed 2023274 
(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))))