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

Percentage Accurate: 67.5% → 86.4%

Time: 22.5s

Alternatives: 20

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 67.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 86.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -4.2 \cdot 10^{-164}:\\ \;\;\;\;x + \frac{y - x}{\frac{a - t}{z - t}}\\ \mathbf{elif}\;a \leq 3.6 \cdot 10^{-116}:\\ \;\;\;\;y - \frac{z}{\frac{t}{y - x}}\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z - t}{a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -4.2e-164)
   (+ x (/ (- y x) (/ (- a t) (- z t))))
   (if (<= a 3.6e-116)
     (- y (/ z (/ t (- y x))))
     (+ x (* (- y x) (/ (- z t) (- a t)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -4.2e-164) {
		tmp = x + ((y - x) / ((a - t) / (z - t)));
	} else if (a <= 3.6e-116) {
		tmp = y - (z / (t / (y - x)));
	} else {
		tmp = x + ((y - x) * ((z - t) / (a - t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-4.2d-164)) then
        tmp = x + ((y - x) / ((a - t) / (z - t)))
    else if (a <= 3.6d-116) then
        tmp = y - (z / (t / (y - x)))
    else
        tmp = x + ((y - x) * ((z - t) / (a - t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -4.2e-164) {
		tmp = x + ((y - x) / ((a - t) / (z - t)));
	} else if (a <= 3.6e-116) {
		tmp = y - (z / (t / (y - x)));
	} else {
		tmp = x + ((y - x) * ((z - t) / (a - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -4.2e-164:
		tmp = x + ((y - x) / ((a - t) / (z - t)))
	elif a <= 3.6e-116:
		tmp = y - (z / (t / (y - x)))
	else:
		tmp = x + ((y - x) * ((z - t) / (a - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -4.2e-164)
		tmp = Float64(x + Float64(Float64(y - x) / Float64(Float64(a - t) / Float64(z - t))));
	elseif (a <= 3.6e-116)
		tmp = Float64(y - Float64(z / Float64(t / Float64(y - x))));
	else
		tmp = Float64(x + Float64(Float64(y - x) * Float64(Float64(z - t) / Float64(a - t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -4.2e-164)
		tmp = x + ((y - x) / ((a - t) / (z - t)));
	elseif (a <= 3.6e-116)
		tmp = y - (z / (t / (y - x)));
	else
		tmp = x + ((y - x) * ((z - t) / (a - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -4.2e-164], N[(x + N[(N[(y - x), $MachinePrecision] / N[(N[(a - t), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3.6e-116], N[(y - N[(z / N[(t / N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y - x), $MachinePrecision] * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < -4.1999999999999998e-164

   1. Initial program 75.2%

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

      1. associate-/l* 87.2%

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

   3. Simplified 87.2%

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

   if -4.1999999999999998e-164 < a < 3.59999999999999975e-116

   1. Initial program 50.8%

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

      1. associate-/l* 58.9%

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

   3. Simplified 58.9%

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

   4. Taylor expanded in a around 0 56.2%

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

      1. neg-mul-1 56.2%

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

      2. distribute-neg-frac 56.2%

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

   6. Simplified 56.2%

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

   7. Taylor expanded in t around 0 89.3%

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

      1. mul-1-neg 89.3%

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

      2. unsub-neg 89.3%

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

      3. associate-/l* 92.0%

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

   9. Simplified 92.0%

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

   if 3.59999999999999975e-116 < a

   1. Initial program 68.5%

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

      1. associate-/l* 88.5%

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

      2. clear-num 88.4%

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

      3. associate-/r/ 88.4%

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

      4. clear-num 88.5%

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

   3. Applied egg-rr 88.5%

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

4. Final simplification 89.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4.2 \cdot 10^{-164}:\\ \;\;\;\;x + \frac{y - x}{\frac{a - t}{z - t}}\\ \mathbf{elif}\;a \leq 3.6 \cdot 10^{-116}:\\ \;\;\;\;y - \frac{z}{\frac{t}{y - x}}\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z - t}{a - t}\\ \end{array} \]

Alternative 2: 65.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(y - x\right) \cdot \frac{z}{a}\\ t_2 := y \cdot \frac{z - t}{a - t}\\ \mathbf{if}\;t \leq -2.7 \cdot 10^{+135}:\\ \;\;\;\;y \cdot \frac{t - z}{t}\\ \mathbf{elif}\;t \leq -6.5 \cdot 10^{+50}:\\ \;\;\;\;x - \frac{t}{\frac{a - t}{y}}\\ \mathbf{elif}\;t \leq -2 \cdot 10^{+21}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 1.4 \cdot 10^{-89}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 3.6 \cdot 10^{-24}:\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \mathbf{elif}\;t \leq 1.45 \cdot 10^{+80}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- y x) (/ z a)))) (t_2 (* y (/ (- z t) (- a t)))))
   (if (<= t -2.7e+135)
     (* y (/ (- t z) t))
     (if (<= t -6.5e+50)
       (- x (/ t (/ (- a t) y)))
       (if (<= t -2e+21)
         t_2
         (if (<= t 1.4e-89)
           t_1
           (if (<= t 3.6e-24)
             (* z (/ (- y x) (- a t)))
             (if (<= t 1.45e+80) t_1 t_2))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - x) * (z / a));
	double t_2 = y * ((z - t) / (a - t));
	double tmp;
	if (t <= -2.7e+135) {
		tmp = y * ((t - z) / t);
	} else if (t <= -6.5e+50) {
		tmp = x - (t / ((a - t) / y));
	} else if (t <= -2e+21) {
		tmp = t_2;
	} else if (t <= 1.4e-89) {
		tmp = t_1;
	} else if (t <= 3.6e-24) {
		tmp = z * ((y - x) / (a - t));
	} else if (t <= 1.45e+80) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x + ((y - x) * (z / a))
    t_2 = y * ((z - t) / (a - t))
    if (t <= (-2.7d+135)) then
        tmp = y * ((t - z) / t)
    else if (t <= (-6.5d+50)) then
        tmp = x - (t / ((a - t) / y))
    else if (t <= (-2d+21)) then
        tmp = t_2
    else if (t <= 1.4d-89) then
        tmp = t_1
    else if (t <= 3.6d-24) then
        tmp = z * ((y - x) / (a - t))
    else if (t <= 1.45d+80) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - x) * (z / a));
	double t_2 = y * ((z - t) / (a - t));
	double tmp;
	if (t <= -2.7e+135) {
		tmp = y * ((t - z) / t);
	} else if (t <= -6.5e+50) {
		tmp = x - (t / ((a - t) / y));
	} else if (t <= -2e+21) {
		tmp = t_2;
	} else if (t <= 1.4e-89) {
		tmp = t_1;
	} else if (t <= 3.6e-24) {
		tmp = z * ((y - x) / (a - t));
	} else if (t <= 1.45e+80) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((y - x) * (z / a))
	t_2 = y * ((z - t) / (a - t))
	tmp = 0
	if t <= -2.7e+135:
		tmp = y * ((t - z) / t)
	elif t <= -6.5e+50:
		tmp = x - (t / ((a - t) / y))
	elif t <= -2e+21:
		tmp = t_2
	elif t <= 1.4e-89:
		tmp = t_1
	elif t <= 3.6e-24:
		tmp = z * ((y - x) / (a - t))
	elif t <= 1.45e+80:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(y - x) * Float64(z / a)))
	t_2 = Float64(y * Float64(Float64(z - t) / Float64(a - t)))
	tmp = 0.0
	if (t <= -2.7e+135)
		tmp = Float64(y * Float64(Float64(t - z) / t));
	elseif (t <= -6.5e+50)
		tmp = Float64(x - Float64(t / Float64(Float64(a - t) / y)));
	elseif (t <= -2e+21)
		tmp = t_2;
	elseif (t <= 1.4e-89)
		tmp = t_1;
	elseif (t <= 3.6e-24)
		tmp = Float64(z * Float64(Float64(y - x) / Float64(a - t)));
	elseif (t <= 1.45e+80)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((y - x) * (z / a));
	t_2 = y * ((z - t) / (a - t));
	tmp = 0.0;
	if (t <= -2.7e+135)
		tmp = y * ((t - z) / t);
	elseif (t <= -6.5e+50)
		tmp = x - (t / ((a - t) / y));
	elseif (t <= -2e+21)
		tmp = t_2;
	elseif (t <= 1.4e-89)
		tmp = t_1;
	elseif (t <= 3.6e-24)
		tmp = z * ((y - x) / (a - t));
	elseif (t <= 1.45e+80)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(y - x), $MachinePrecision] * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.7e+135], N[(y * N[(N[(t - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -6.5e+50], N[(x - N[(t / N[(N[(a - t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -2e+21], t$95$2, If[LessEqual[t, 1.4e-89], t$95$1, If[LessEqual[t, 3.6e-24], N[(z * N[(N[(y - x), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.45e+80], t$95$1, t$95$2]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -2.69999999999999985e135

   1. Initial program 14.3%

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

      1. associate-/l* 43.3%

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

      2. clear-num 43.2%

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

      3. associate-/r/ 43.3%

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

      4. clear-num 43.4%

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

   3. Applied egg-rr 43.4%

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

   4. Taylor expanded in y around inf 63.3%

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

      1. div-sub 63.3%

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

   6. Simplified 63.3%

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

   7. Taylor expanded in a around 0 63.3%

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

      1. associate-*r/ 63.3%

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

      2. mul-1-neg 63.3%

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

   9. Simplified 63.3%

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

   if -2.69999999999999985e135 < t < -6.5000000000000003e50

   1. Initial program 64.2%

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

      1. associate-*l/ 82.3%

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

   3. Simplified 82.3%

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

   4. Taylor expanded in z around 0 47.6%

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

      1. mul-1-neg 47.6%

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

      2. unsub-neg 47.6%

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

      3. associate-/l* 62.3%

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

   6. Simplified 62.3%

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

   7. Taylor expanded in y around inf 61.0%

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

      1. associate-/l* 61.5%

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

   9. Simplified 61.5%

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

   if -6.5000000000000003e50 < t < -2e21 or 1.44999999999999993e80 < t

   1. Initial program 33.5%

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

      1. associate-/l* 60.2%

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

      2. clear-num 60.0%

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

      3. associate-/r/ 60.1%

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

      4. clear-num 60.1%

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

   3. Applied egg-rr 60.1%

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

   4. Taylor expanded in y around inf 73.8%

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

      1. div-sub 73.9%

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

   6. Simplified 73.9%

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

   if -2e21 < t < 1.3999999999999999e-89 or 3.6000000000000001e-24 < t < 1.44999999999999993e80

   1. Initial program 87.3%

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

      1. associate-/l* 91.8%

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

      2. clear-num 91.9%

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

      3. associate-/r/ 91.3%

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

      4. clear-num 91.4%

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

   3. Applied egg-rr 91.4%

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

   4. Taylor expanded in t around 0 75.8%

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

   if 1.3999999999999999e-89 < t < 3.6000000000000001e-24

   1. Initial program 84.2%

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

      1. associate-*l/ 91.4%

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

   3. Simplified 91.4%

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

   4. Taylor expanded in z around inf 68.0%

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

      1. div-sub 68.0%

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

   6. Simplified 68.0%

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

4. Final simplification 72.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.7 \cdot 10^{+135}:\\ \;\;\;\;y \cdot \frac{t - z}{t}\\ \mathbf{elif}\;t \leq -6.5 \cdot 10^{+50}:\\ \;\;\;\;x - \frac{t}{\frac{a - t}{y}}\\ \mathbf{elif}\;t \leq -2 \cdot 10^{+21}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;t \leq 1.4 \cdot 10^{-89}:\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq 3.6 \cdot 10^{-24}:\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \mathbf{elif}\;t \leq 1.45 \cdot 10^{+80}:\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \end{array} \]

Alternative 3: 52.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{-t}{a - t}\\ t_2 := x + \frac{y \cdot z}{a}\\ \mathbf{if}\;t \leq -3.9 \cdot 10^{+127}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -3.45 \cdot 10^{+50}:\\ \;\;\;\;x - \frac{y}{\frac{a}{t}}\\ \mathbf{elif}\;t \leq -4.8 \cdot 10^{+19}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 5.5 \cdot 10^{-169}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 6.6 \cdot 10^{-114}:\\ \;\;\;\;\frac{z}{\frac{a}{y - x}}\\ \mathbf{elif}\;t \leq 1.7 \cdot 10^{+80}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ (- t) (- a t)))) (t_2 (+ x (/ (* y z) a))))
   (if (<= t -3.9e+127)
     t_1
     (if (<= t -3.45e+50)
       (- x (/ y (/ a t)))
       (if (<= t -4.8e+19)
         t_1
         (if (<= t 5.5e-169)
           t_2
           (if (<= t 6.6e-114)
             (/ z (/ a (- y x)))
             (if (<= t 1.7e+80) t_2 t_1))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * (-t / (a - t));
	double t_2 = x + ((y * z) / a);
	double tmp;
	if (t <= -3.9e+127) {
		tmp = t_1;
	} else if (t <= -3.45e+50) {
		tmp = x - (y / (a / t));
	} else if (t <= -4.8e+19) {
		tmp = t_1;
	} else if (t <= 5.5e-169) {
		tmp = t_2;
	} else if (t <= 6.6e-114) {
		tmp = z / (a / (y - x));
	} else if (t <= 1.7e+80) {
		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 * (-t / (a - t))
    t_2 = x + ((y * z) / a)
    if (t <= (-3.9d+127)) then
        tmp = t_1
    else if (t <= (-3.45d+50)) then
        tmp = x - (y / (a / t))
    else if (t <= (-4.8d+19)) then
        tmp = t_1
    else if (t <= 5.5d-169) then
        tmp = t_2
    else if (t <= 6.6d-114) then
        tmp = z / (a / (y - x))
    else if (t <= 1.7d+80) 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 * (-t / (a - t));
	double t_2 = x + ((y * z) / a);
	double tmp;
	if (t <= -3.9e+127) {
		tmp = t_1;
	} else if (t <= -3.45e+50) {
		tmp = x - (y / (a / t));
	} else if (t <= -4.8e+19) {
		tmp = t_1;
	} else if (t <= 5.5e-169) {
		tmp = t_2;
	} else if (t <= 6.6e-114) {
		tmp = z / (a / (y - x));
	} else if (t <= 1.7e+80) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * (-t / (a - t))
	t_2 = x + ((y * z) / a)
	tmp = 0
	if t <= -3.9e+127:
		tmp = t_1
	elif t <= -3.45e+50:
		tmp = x - (y / (a / t))
	elif t <= -4.8e+19:
		tmp = t_1
	elif t <= 5.5e-169:
		tmp = t_2
	elif t <= 6.6e-114:
		tmp = z / (a / (y - x))
	elif t <= 1.7e+80:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(Float64(-t) / Float64(a - t)))
	t_2 = Float64(x + Float64(Float64(y * z) / a))
	tmp = 0.0
	if (t <= -3.9e+127)
		tmp = t_1;
	elseif (t <= -3.45e+50)
		tmp = Float64(x - Float64(y / Float64(a / t)));
	elseif (t <= -4.8e+19)
		tmp = t_1;
	elseif (t <= 5.5e-169)
		tmp = t_2;
	elseif (t <= 6.6e-114)
		tmp = Float64(z / Float64(a / Float64(y - x)));
	elseif (t <= 1.7e+80)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * (-t / (a - t));
	t_2 = x + ((y * z) / a);
	tmp = 0.0;
	if (t <= -3.9e+127)
		tmp = t_1;
	elseif (t <= -3.45e+50)
		tmp = x - (y / (a / t));
	elseif (t <= -4.8e+19)
		tmp = t_1;
	elseif (t <= 5.5e-169)
		tmp = t_2;
	elseif (t <= 6.6e-114)
		tmp = z / (a / (y - x));
	elseif (t <= 1.7e+80)
		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[((-t) / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(y * z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -3.9e+127], t$95$1, If[LessEqual[t, -3.45e+50], N[(x - N[(y / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -4.8e+19], t$95$1, If[LessEqual[t, 5.5e-169], t$95$2, If[LessEqual[t, 6.6e-114], N[(z / N[(a / N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.7e+80], t$95$2, t$95$1]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -3.89999999999999981e127 or -3.45000000000000016e50 < t < -4.8e19 or 1.69999999999999996e80 < t

   1. Initial program 27.9%

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

      1. associate-/l* 55.6%

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

      2. clear-num 55.5%

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

      3. associate-/r/ 55.5%

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

      4. clear-num 55.6%

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

   3. Applied egg-rr 55.6%

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

   4. Taylor expanded in y around inf 69.8%

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

      1. div-sub 69.9%

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

   6. Simplified 69.9%

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

   7. Taylor expanded in z around 0 64.6%

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

      1. mul-1-neg 64.6%

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

      2. distribute-neg-frac 64.6%

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

   9. Simplified 64.6%

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

   if -3.89999999999999981e127 < t < -3.45000000000000016e50

   1. Initial program 61.3%

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

      1. associate-*l/ 80.9%

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

   3. Simplified 80.9%

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

   4. Taylor expanded in z around 0 43.4%

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

      1. mul-1-neg 43.4%

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

      2. unsub-neg 43.4%

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

      3. associate-/l* 59.3%

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

   6. Simplified 59.3%

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

   7. Taylor expanded in y around inf 57.9%

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

      1. associate-/l* 58.4%

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

   9. Simplified 58.4%

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

   10. Taylor expanded in t around 0 46.9%

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

       1. *-commutative 46.9%

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

       2. associate-/l* 50.6%

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

   12. Simplified 50.6%

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

   if -4.8e19 < t < 5.4999999999999994e-169 or 6.60000000000000069e-114 < t < 1.69999999999999996e80

   1. Initial program 87.4%

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

      1. associate-/l* 91.3%

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

      2. clear-num 91.3%

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

      3. associate-/r/ 90.7%

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

      4. clear-num 90.8%

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

   3. Applied egg-rr 90.8%

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

   4. Taylor expanded in t around 0 70.4%

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

   5. Taylor expanded in y around inf 57.9%

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

   if 5.4999999999999994e-169 < t < 6.60000000000000069e-114

   1. Initial program 89.5%

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

      1. associate-*l/ 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in z around inf 92.9%

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

      1. div-sub 92.9%

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

      2. associate-*r/ 82.6%

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

      3. associate-/l* 92.8%

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

   6. Simplified 92.8%

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

   7. Taylor expanded in a around inf 81.8%

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

4. Final simplification 60.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.9 \cdot 10^{+127}:\\ \;\;\;\;y \cdot \frac{-t}{a - t}\\ \mathbf{elif}\;t \leq -3.45 \cdot 10^{+50}:\\ \;\;\;\;x - \frac{y}{\frac{a}{t}}\\ \mathbf{elif}\;t \leq -4.8 \cdot 10^{+19}:\\ \;\;\;\;y \cdot \frac{-t}{a - t}\\ \mathbf{elif}\;t \leq 5.5 \cdot 10^{-169}:\\ \;\;\;\;x + \frac{y \cdot z}{a}\\ \mathbf{elif}\;t \leq 6.6 \cdot 10^{-114}:\\ \;\;\;\;\frac{z}{\frac{a}{y - x}}\\ \mathbf{elif}\;t \leq 1.7 \cdot 10^{+80}:\\ \;\;\;\;x + \frac{y \cdot z}{a}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{-t}{a - t}\\ \end{array} \]

Alternative 4: 51.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - x \cdot \frac{z}{a}\\ \mathbf{if}\;t \leq -1.15 \cdot 10^{+133}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -3.4 \cdot 10^{+22}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq -6 \cdot 10^{-20}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -2.2 \cdot 10^{-36}:\\ \;\;\;\;\frac{y}{\frac{t}{-z}}\\ \mathbf{elif}\;t \leq -1.75 \cdot 10^{-178}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.85 \cdot 10^{+80}:\\ \;\;\;\;x + \frac{y \cdot z}{a}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (* x (/ z a)))))
   (if (<= t -1.15e+133)
     y
     (if (<= t -3.4e+22)
       (+ x y)
       (if (<= t -6e-20)
         t_1
         (if (<= t -2.2e-36)
           (/ y (/ t (- z)))
           (if (<= t -1.75e-178)
             t_1
             (if (<= t 1.85e+80) (+ x (/ (* y z) a)) y))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (x * (z / a));
	double tmp;
	if (t <= -1.15e+133) {
		tmp = y;
	} else if (t <= -3.4e+22) {
		tmp = x + y;
	} else if (t <= -6e-20) {
		tmp = t_1;
	} else if (t <= -2.2e-36) {
		tmp = y / (t / -z);
	} else if (t <= -1.75e-178) {
		tmp = t_1;
	} else if (t <= 1.85e+80) {
		tmp = x + ((y * z) / a);
	} else {
		tmp = y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x - (x * (z / a))
    if (t <= (-1.15d+133)) then
        tmp = y
    else if (t <= (-3.4d+22)) then
        tmp = x + y
    else if (t <= (-6d-20)) then
        tmp = t_1
    else if (t <= (-2.2d-36)) then
        tmp = y / (t / -z)
    else if (t <= (-1.75d-178)) then
        tmp = t_1
    else if (t <= 1.85d+80) then
        tmp = x + ((y * z) / a)
    else
        tmp = y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (x * (z / a));
	double tmp;
	if (t <= -1.15e+133) {
		tmp = y;
	} else if (t <= -3.4e+22) {
		tmp = x + y;
	} else if (t <= -6e-20) {
		tmp = t_1;
	} else if (t <= -2.2e-36) {
		tmp = y / (t / -z);
	} else if (t <= -1.75e-178) {
		tmp = t_1;
	} else if (t <= 1.85e+80) {
		tmp = x + ((y * z) / a);
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - (x * (z / a))
	tmp = 0
	if t <= -1.15e+133:
		tmp = y
	elif t <= -3.4e+22:
		tmp = x + y
	elif t <= -6e-20:
		tmp = t_1
	elif t <= -2.2e-36:
		tmp = y / (t / -z)
	elif t <= -1.75e-178:
		tmp = t_1
	elif t <= 1.85e+80:
		tmp = x + ((y * z) / a)
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(x * Float64(z / a)))
	tmp = 0.0
	if (t <= -1.15e+133)
		tmp = y;
	elseif (t <= -3.4e+22)
		tmp = Float64(x + y);
	elseif (t <= -6e-20)
		tmp = t_1;
	elseif (t <= -2.2e-36)
		tmp = Float64(y / Float64(t / Float64(-z)));
	elseif (t <= -1.75e-178)
		tmp = t_1;
	elseif (t <= 1.85e+80)
		tmp = Float64(x + Float64(Float64(y * z) / a));
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - (x * (z / a));
	tmp = 0.0;
	if (t <= -1.15e+133)
		tmp = y;
	elseif (t <= -3.4e+22)
		tmp = x + y;
	elseif (t <= -6e-20)
		tmp = t_1;
	elseif (t <= -2.2e-36)
		tmp = y / (t / -z);
	elseif (t <= -1.75e-178)
		tmp = t_1;
	elseif (t <= 1.85e+80)
		tmp = x + ((y * z) / a);
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x - N[(x * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.15e+133], y, If[LessEqual[t, -3.4e+22], N[(x + y), $MachinePrecision], If[LessEqual[t, -6e-20], t$95$1, If[LessEqual[t, -2.2e-36], N[(y / N[(t / (-z)), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -1.75e-178], t$95$1, If[LessEqual[t, 1.85e+80], N[(x + N[(N[(y * z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], y]]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -1.14999999999999995e133 or 1.84999999999999998e80 < t

   1. Initial program 21.5%

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

      1. associate-*l/ 48.6%

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

   3. Simplified 48.6%

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

   4. Taylor expanded in t around inf 59.7%

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

   if -1.14999999999999995e133 < t < -3.4e22

   1. Initial program 67.8%

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

      1. associate-*l/ 82.4%

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

   3. Simplified 82.4%

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

   4. Taylor expanded in z around 0 50.2%

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

      1. mul-1-neg 50.2%

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

      2. unsub-neg 50.2%

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

      3. associate-/l* 62.2%

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

   6. Simplified 62.2%

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

   7. Taylor expanded in y around inf 61.2%

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

      1. associate-/l* 61.6%

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

   9. Simplified 61.6%

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

   10. Taylor expanded in t around inf 43.5%

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

       1. neg-mul-1 43.5%

          \[\leadsto x - \color{blue}{\left(-y\right)} \]

   12. Simplified 43.5%

       \[\leadsto x - \color{blue}{\left(-y\right)} \]

   if -3.4e22 < t < -6.00000000000000057e-20 or -2.1999999999999999e-36 < t < -1.74999999999999992e-178

   1. Initial program 84.5%

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

      1. associate-/l* 91.1%

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

      2. clear-num 91.2%

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

      3. associate-/r/ 89.4%

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

      4. clear-num 89.3%

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

   3. Applied egg-rr 89.3%

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

   4. Taylor expanded in t around 0 71.2%

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

   5. Taylor expanded in x around inf 60.8%

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

      1. distribute-lft-in 60.8%

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

      2. *-rgt-identity 60.8%

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

      3. mul-1-neg 60.8%

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

      4. distribute-rgt-neg-in 60.8%

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

      5. unsub-neg 60.8%

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

   7. Simplified 60.8%

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

   if -6.00000000000000057e-20 < t < -2.1999999999999999e-36

   1. Initial program 100.0%

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

      1. associate-/l* 99.6%

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

      2. clear-num 100.0%

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

      3. associate-/r/ 100.0%

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

      4. clear-num 100.0%

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

   3. Applied egg-rr 100.0%

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

   4. Taylor expanded in y around inf 100.0%

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

      1. div-sub 100.0%

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

   6. Simplified 100.0%

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

   7. Taylor expanded in z around inf 76.2%

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

   8. Taylor expanded in a around 0 76.2%

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

      1. associate-*r/ 76.2%

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

      2. neg-mul-1 76.2%

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

      3. distribute-rgt-neg-in 76.2%

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

      4. associate-/l* 76.2%

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

   10. Simplified 76.2%

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

   if -1.74999999999999992e-178 < t < 1.84999999999999998e80

   1. Initial program 87.4%

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

      1. associate-/l* 91.8%

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

      2. clear-num 91.8%

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

      3. associate-/r/ 91.7%

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

      4. clear-num 91.9%

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

   3. Applied egg-rr 91.9%

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

   4. Taylor expanded in t around 0 72.6%

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

   5. Taylor expanded in y around inf 58.4%

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

4. Final simplification 57.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.15 \cdot 10^{+133}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -3.4 \cdot 10^{+22}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq -6 \cdot 10^{-20}:\\ \;\;\;\;x - x \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq -2.2 \cdot 10^{-36}:\\ \;\;\;\;\frac{y}{\frac{t}{-z}}\\ \mathbf{elif}\;t \leq -1.75 \cdot 10^{-178}:\\ \;\;\;\;x - x \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq 1.85 \cdot 10^{+80}:\\ \;\;\;\;x + \frac{y \cdot z}{a}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 5: 50.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y \cdot z}{a}\\ \mathbf{if}\;t \leq -9.2 \cdot 10^{+135}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -1.5 \cdot 10^{+29}:\\ \;\;\;\;x - \frac{y}{\frac{a}{t}}\\ \mathbf{elif}\;t \leq 5.5 \cdot 10^{-168}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 6.6 \cdot 10^{-114}:\\ \;\;\;\;\frac{z}{\frac{a}{y - x}}\\ \mathbf{elif}\;t \leq 1.8 \cdot 10^{+80}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ (* y z) a))))
   (if (<= t -9.2e+135)
     y
     (if (<= t -1.5e+29)
       (- x (/ y (/ a t)))
       (if (<= t 5.5e-168)
         t_1
         (if (<= t 6.6e-114)
           (/ z (/ a (- y x)))
           (if (<= t 1.8e+80) t_1 y)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y * z) / a);
	double tmp;
	if (t <= -9.2e+135) {
		tmp = y;
	} else if (t <= -1.5e+29) {
		tmp = x - (y / (a / t));
	} else if (t <= 5.5e-168) {
		tmp = t_1;
	} else if (t <= 6.6e-114) {
		tmp = z / (a / (y - x));
	} else if (t <= 1.8e+80) {
		tmp = t_1;
	} else {
		tmp = y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + ((y * z) / a)
    if (t <= (-9.2d+135)) then
        tmp = y
    else if (t <= (-1.5d+29)) then
        tmp = x - (y / (a / t))
    else if (t <= 5.5d-168) then
        tmp = t_1
    else if (t <= 6.6d-114) then
        tmp = z / (a / (y - x))
    else if (t <= 1.8d+80) then
        tmp = t_1
    else
        tmp = y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y * z) / a);
	double tmp;
	if (t <= -9.2e+135) {
		tmp = y;
	} else if (t <= -1.5e+29) {
		tmp = x - (y / (a / t));
	} else if (t <= 5.5e-168) {
		tmp = t_1;
	} else if (t <= 6.6e-114) {
		tmp = z / (a / (y - x));
	} else if (t <= 1.8e+80) {
		tmp = t_1;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((y * z) / a)
	tmp = 0
	if t <= -9.2e+135:
		tmp = y
	elif t <= -1.5e+29:
		tmp = x - (y / (a / t))
	elif t <= 5.5e-168:
		tmp = t_1
	elif t <= 6.6e-114:
		tmp = z / (a / (y - x))
	elif t <= 1.8e+80:
		tmp = t_1
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(y * z) / a))
	tmp = 0.0
	if (t <= -9.2e+135)
		tmp = y;
	elseif (t <= -1.5e+29)
		tmp = Float64(x - Float64(y / Float64(a / t)));
	elseif (t <= 5.5e-168)
		tmp = t_1;
	elseif (t <= 6.6e-114)
		tmp = Float64(z / Float64(a / Float64(y - x)));
	elseif (t <= 1.8e+80)
		tmp = t_1;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((y * z) / a);
	tmp = 0.0;
	if (t <= -9.2e+135)
		tmp = y;
	elseif (t <= -1.5e+29)
		tmp = x - (y / (a / t));
	elseif (t <= 5.5e-168)
		tmp = t_1;
	elseif (t <= 6.6e-114)
		tmp = z / (a / (y - x));
	elseif (t <= 1.8e+80)
		tmp = t_1;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(y * z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -9.2e+135], y, If[LessEqual[t, -1.5e+29], N[(x - N[(y / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 5.5e-168], t$95$1, If[LessEqual[t, 6.6e-114], N[(z / N[(a / N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.8e+80], t$95$1, y]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -9.2000000000000005e135 or 1.79999999999999997e80 < t

   1. Initial program 21.5%

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

      1. associate-*l/ 48.6%

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

   3. Simplified 48.6%

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

   4. Taylor expanded in t around inf 59.7%

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

   if -9.2000000000000005e135 < t < -1.5e29

   1. Initial program 66.8%

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

      1. associate-*l/ 81.9%

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

   3. Simplified 81.9%

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

   4. Taylor expanded in z around 0 48.6%

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

      1. mul-1-neg 48.6%

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

      2. unsub-neg 48.6%

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

      3. associate-/l* 61.1%

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

   6. Simplified 61.1%

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

   7. Taylor expanded in y around inf 60.0%

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

      1. associate-/l* 60.4%

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

   9. Simplified 60.4%

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

   10. Taylor expanded in t around 0 45.5%

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

       1. *-commutative 45.5%

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

       2. associate-/l* 48.4%

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

   12. Simplified 48.4%

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

   if -1.5e29 < t < 5.4999999999999999e-168 or 6.60000000000000069e-114 < t < 1.79999999999999997e80

   1. Initial program 86.9%

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

      1. associate-/l* 91.4%

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

      2. clear-num 91.4%

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

      3. associate-/r/ 90.9%

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

      4. clear-num 90.9%

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

   3. Applied egg-rr 90.9%

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

   4. Taylor expanded in t around 0 70.1%

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

   5. Taylor expanded in y around inf 57.1%

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

   if 5.4999999999999999e-168 < t < 6.60000000000000069e-114

   1. Initial program 89.5%

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

      1. associate-*l/ 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in z around inf 92.9%

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

      1. div-sub 92.9%

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

      2. associate-*r/ 82.6%

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

      3. associate-/l* 92.8%

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

   6. Simplified 92.8%

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

   7. Taylor expanded in a around inf 81.8%

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

4. Final simplification 57.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -9.2 \cdot 10^{+135}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -1.5 \cdot 10^{+29}:\\ \;\;\;\;x - \frac{y}{\frac{a}{t}}\\ \mathbf{elif}\;t \leq 5.5 \cdot 10^{-168}:\\ \;\;\;\;x + \frac{y \cdot z}{a}\\ \mathbf{elif}\;t \leq 6.6 \cdot 10^{-114}:\\ \;\;\;\;\frac{z}{\frac{a}{y - x}}\\ \mathbf{elif}\;t \leq 1.8 \cdot 10^{+80}:\\ \;\;\;\;x + \frac{y \cdot z}{a}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 6: 66.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(y - x\right) \cdot \frac{z}{a}\\ t_2 := y \cdot \frac{z - t}{a - t}\\ \mathbf{if}\;t \leq -1 \cdot 10^{+23}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 1.4 \cdot 10^{-89}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.55 \cdot 10^{-24}:\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \mathbf{elif}\;t \leq 1.3 \cdot 10^{+80}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- y x) (/ z a)))) (t_2 (* y (/ (- z t) (- a t)))))
   (if (<= t -1e+23)
     t_2
     (if (<= t 1.4e-89)
       t_1
       (if (<= t 1.55e-24)
         (* z (/ (- y x) (- a t)))
         (if (<= t 1.3e+80) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - x) * (z / a));
	double t_2 = y * ((z - t) / (a - t));
	double tmp;
	if (t <= -1e+23) {
		tmp = t_2;
	} else if (t <= 1.4e-89) {
		tmp = t_1;
	} else if (t <= 1.55e-24) {
		tmp = z * ((y - x) / (a - t));
	} else if (t <= 1.3e+80) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x + ((y - x) * (z / a))
    t_2 = y * ((z - t) / (a - t))
    if (t <= (-1d+23)) then
        tmp = t_2
    else if (t <= 1.4d-89) then
        tmp = t_1
    else if (t <= 1.55d-24) then
        tmp = z * ((y - x) / (a - t))
    else if (t <= 1.3d+80) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - x) * (z / a));
	double t_2 = y * ((z - t) / (a - t));
	double tmp;
	if (t <= -1e+23) {
		tmp = t_2;
	} else if (t <= 1.4e-89) {
		tmp = t_1;
	} else if (t <= 1.55e-24) {
		tmp = z * ((y - x) / (a - t));
	} else if (t <= 1.3e+80) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((y - x) * (z / a))
	t_2 = y * ((z - t) / (a - t))
	tmp = 0
	if t <= -1e+23:
		tmp = t_2
	elif t <= 1.4e-89:
		tmp = t_1
	elif t <= 1.55e-24:
		tmp = z * ((y - x) / (a - t))
	elif t <= 1.3e+80:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(y - x) * Float64(z / a)))
	t_2 = Float64(y * Float64(Float64(z - t) / Float64(a - t)))
	tmp = 0.0
	if (t <= -1e+23)
		tmp = t_2;
	elseif (t <= 1.4e-89)
		tmp = t_1;
	elseif (t <= 1.55e-24)
		tmp = Float64(z * Float64(Float64(y - x) / Float64(a - t)));
	elseif (t <= 1.3e+80)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((y - x) * (z / a));
	t_2 = y * ((z - t) / (a - t));
	tmp = 0.0;
	if (t <= -1e+23)
		tmp = t_2;
	elseif (t <= 1.4e-89)
		tmp = t_1;
	elseif (t <= 1.55e-24)
		tmp = z * ((y - x) / (a - t));
	elseif (t <= 1.3e+80)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(y - x), $MachinePrecision] * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1e+23], t$95$2, If[LessEqual[t, 1.4e-89], t$95$1, If[LessEqual[t, 1.55e-24], N[(z * N[(N[(y - x), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.3e+80], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -9.9999999999999992e22 or 1.29999999999999991e80 < t

   1. Initial program 36.1%

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

      1. associate-/l* 62.2%

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

      2. clear-num 62.0%

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

      3. associate-/r/ 62.1%

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

      4. clear-num 62.1%

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

   3. Applied egg-rr 62.1%

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

   4. Taylor expanded in y around inf 63.9%

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

      1. div-sub 63.9%

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

   6. Simplified 63.9%

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

   if -9.9999999999999992e22 < t < 1.3999999999999999e-89 or 1.55e-24 < t < 1.29999999999999991e80

   1. Initial program 87.3%

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

      1. associate-/l* 91.8%

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

      2. clear-num 91.9%

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

      3. associate-/r/ 91.3%

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

      4. clear-num 91.4%

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

   3. Applied egg-rr 91.4%

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

   4. Taylor expanded in t around 0 75.8%

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

   if 1.3999999999999999e-89 < t < 1.55e-24

   1. Initial program 84.2%

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

      1. associate-*l/ 91.4%

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

   3. Simplified 91.4%

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

   4. Taylor expanded in z around inf 68.0%

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

      1. div-sub 68.0%

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

   6. Simplified 68.0%

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

4. Final simplification 70.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1 \cdot 10^{+23}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;t \leq 1.4 \cdot 10^{-89}:\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq 1.55 \cdot 10^{-24}:\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \mathbf{elif}\;t \leq 1.3 \cdot 10^{+80}:\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \end{array} \]

Alternative 7: 84.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.02 \cdot 10^{-165} \lor \neg \left(a \leq 2.25 \cdot 10^{-116}\right):\\ \;\;\;\;x + \left(t - z\right) \cdot \frac{x - y}{a - t}\\ \mathbf{else}:\\ \;\;\;\;y - \frac{z}{\frac{t}{y - x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -1.02e-165) (not (<= a 2.25e-116)))
   (+ x (* (- t z) (/ (- x y) (- a t))))
   (- y (/ z (/ t (- y x))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -1.02e-165) || !(a <= 2.25e-116)) {
		tmp = x + ((t - z) * ((x - y) / (a - t)));
	} else {
		tmp = y - (z / (t / (y - x)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a <= (-1.02d-165)) .or. (.not. (a <= 2.25d-116))) then
        tmp = x + ((t - z) * ((x - y) / (a - t)))
    else
        tmp = y - (z / (t / (y - x)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -1.02e-165) || !(a <= 2.25e-116)) {
		tmp = x + ((t - z) * ((x - y) / (a - t)));
	} else {
		tmp = y - (z / (t / (y - x)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -1.02e-165) or not (a <= 2.25e-116):
		tmp = x + ((t - z) * ((x - y) / (a - t)))
	else:
		tmp = y - (z / (t / (y - x)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -1.02e-165) || !(a <= 2.25e-116))
		tmp = Float64(x + Float64(Float64(t - z) * Float64(Float64(x - y) / Float64(a - t))));
	else
		tmp = Float64(y - Float64(z / Float64(t / Float64(y - x))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -1.02e-165) || ~((a <= 2.25e-116)))
		tmp = x + ((t - z) * ((x - y) / (a - t)));
	else
		tmp = y - (z / (t / (y - x)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -1.02e-165], N[Not[LessEqual[a, 2.25e-116]], $MachinePrecision]], N[(x + N[(N[(t - z), $MachinePrecision] * N[(N[(x - y), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y - N[(z / N[(t / N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -1.02e-165 or 2.25000000000000006e-116 < a

   1. Initial program 72.1%

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

      1. associate-*l/ 86.6%

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

   3. Simplified 86.6%

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

   if -1.02e-165 < a < 2.25000000000000006e-116

   1. Initial program 50.8%

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

      1. associate-/l* 58.9%

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

   3. Simplified 58.9%

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

   4. Taylor expanded in a around 0 56.2%

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

      1. neg-mul-1 56.2%

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

      2. distribute-neg-frac 56.2%

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

   6. Simplified 56.2%

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

   7. Taylor expanded in t around 0 89.3%

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

      1. mul-1-neg 89.3%

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

      2. unsub-neg 89.3%

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

      3. associate-/l* 92.0%

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

   9. Simplified 92.0%

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

4. Final simplification 88.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.02 \cdot 10^{-165} \lor \neg \left(a \leq 2.25 \cdot 10^{-116}\right):\\ \;\;\;\;x + \left(t - z\right) \cdot \frac{x - y}{a - t}\\ \mathbf{else}:\\ \;\;\;\;y - \frac{z}{\frac{t}{y - x}}\\ \end{array} \]

Alternative 8: 86.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -8.5 \cdot 10^{-166} \lor \neg \left(a \leq 1.75 \cdot 10^{-117}\right):\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;y - \frac{z}{\frac{t}{y - x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -8.5e-166) (not (<= a 1.75e-117)))
   (+ x (* (- y x) (/ (- z t) (- a t))))
   (- y (/ z (/ t (- y x))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -8.5e-166) || !(a <= 1.75e-117)) {
		tmp = x + ((y - x) * ((z - t) / (a - t)));
	} else {
		tmp = y - (z / (t / (y - x)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a <= (-8.5d-166)) .or. (.not. (a <= 1.75d-117))) then
        tmp = x + ((y - x) * ((z - t) / (a - t)))
    else
        tmp = y - (z / (t / (y - x)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -8.5e-166) || !(a <= 1.75e-117)) {
		tmp = x + ((y - x) * ((z - t) / (a - t)));
	} else {
		tmp = y - (z / (t / (y - x)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -8.5e-166) or not (a <= 1.75e-117):
		tmp = x + ((y - x) * ((z - t) / (a - t)))
	else:
		tmp = y - (z / (t / (y - x)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -8.5e-166) || !(a <= 1.75e-117))
		tmp = Float64(x + Float64(Float64(y - x) * Float64(Float64(z - t) / Float64(a - t))));
	else
		tmp = Float64(y - Float64(z / Float64(t / Float64(y - x))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -8.5e-166) || ~((a <= 1.75e-117)))
		tmp = x + ((y - x) * ((z - t) / (a - t)));
	else
		tmp = y - (z / (t / (y - x)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -8.5e-166], N[Not[LessEqual[a, 1.75e-117]], $MachinePrecision]], N[(x + N[(N[(y - x), $MachinePrecision] * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y - N[(z / N[(t / N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -8.5e-166 or 1.7499999999999999e-117 < a

   1. Initial program 72.1%

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

      1. associate-/l* 87.8%

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

      2. clear-num 87.7%

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

      3. associate-/r/ 87.3%

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

      4. clear-num 87.4%

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

   3. Applied egg-rr 87.4%

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

   if -8.5e-166 < a < 1.7499999999999999e-117

   1. Initial program 50.8%

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

      1. associate-/l* 58.9%

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

   3. Simplified 58.9%

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

   4. Taylor expanded in a around 0 56.2%

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

      1. neg-mul-1 56.2%

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

      2. distribute-neg-frac 56.2%

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

   6. Simplified 56.2%

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

   7. Taylor expanded in t around 0 89.3%

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

      1. mul-1-neg 89.3%

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

      2. unsub-neg 89.3%

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

      3. associate-/l* 92.0%

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

   9. Simplified 92.0%

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

4. Final simplification 88.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -8.5 \cdot 10^{-166} \lor \neg \left(a \leq 1.75 \cdot 10^{-117}\right):\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;y - \frac{z}{\frac{t}{y - x}}\\ \end{array} \]

Alternative 9: 75.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -9.5 \cdot 10^{+21} \lor \neg \left(a \leq 2 \cdot 10^{-50}\right):\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y}{a - t}\\ \mathbf{else}:\\ \;\;\;\;y - \frac{z}{\frac{t}{y - x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -9.5e+21) (not (<= a 2e-50)))
   (+ x (* (- z t) (/ y (- a t))))
   (- y (/ z (/ t (- y x))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -9.5e+21) || !(a <= 2e-50)) {
		tmp = x + ((z - t) * (y / (a - t)));
	} else {
		tmp = y - (z / (t / (y - x)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a <= (-9.5d+21)) .or. (.not. (a <= 2d-50))) then
        tmp = x + ((z - t) * (y / (a - t)))
    else
        tmp = y - (z / (t / (y - x)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -9.5e+21) || !(a <= 2e-50)) {
		tmp = x + ((z - t) * (y / (a - t)));
	} else {
		tmp = y - (z / (t / (y - x)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -9.5e+21) or not (a <= 2e-50):
		tmp = x + ((z - t) * (y / (a - t)))
	else:
		tmp = y - (z / (t / (y - x)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -9.5e+21) || !(a <= 2e-50))
		tmp = Float64(x + Float64(Float64(z - t) * Float64(y / Float64(a - t))));
	else
		tmp = Float64(y - Float64(z / Float64(t / Float64(y - x))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -9.5e+21) || ~((a <= 2e-50)))
		tmp = x + ((z - t) * (y / (a - t)));
	else
		tmp = y - (z / (t / (y - x)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -9.5e+21], N[Not[LessEqual[a, 2e-50]], $MachinePrecision]], N[(x + N[(N[(z - t), $MachinePrecision] * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y - N[(z / N[(t / N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -9.500000000000001e21 or 2.00000000000000002e-50 < a

   1. Initial program 70.6%

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

      1. associate-*l/ 88.6%

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

   3. Simplified 88.6%

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

   4. Taylor expanded in y around inf 78.0%

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

   if -9.500000000000001e21 < a < 2.00000000000000002e-50

   1. Initial program 60.8%

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

      1. associate-/l* 67.9%

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

   3. Simplified 67.9%

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

   4. Taylor expanded in a around 0 54.5%

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

      1. neg-mul-1 54.5%

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

      2. distribute-neg-frac 54.5%

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

   6. Simplified 54.5%

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

   7. Taylor expanded in t around 0 77.5%

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

      1. mul-1-neg 77.5%

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

      2. unsub-neg 77.5%

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

      3. associate-/l* 81.6%

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

   9. Simplified 81.6%

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

4. Final simplification 79.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -9.5 \cdot 10^{+21} \lor \neg \left(a \leq 2 \cdot 10^{-50}\right):\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y}{a - t}\\ \mathbf{else}:\\ \;\;\;\;y - \frac{z}{\frac{t}{y - x}}\\ \end{array} \]

Alternative 10: 53.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y \cdot z}{a}\\ \mathbf{if}\;a \leq -3.3 \cdot 10^{+22}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 1.75 \cdot 10^{-40}:\\ \;\;\;\;y \cdot \frac{t - z}{t}\\ \mathbf{elif}\;a \leq 2.3 \cdot 10^{+89}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{-z}{a} - -1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ (* y z) a))))
   (if (<= a -3.3e+22)
     t_1
     (if (<= a 1.75e-40)
       (* y (/ (- t z) t))
       (if (<= a 2.3e+89) t_1 (* x (- (/ (- z) a) -1.0)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y * z) / a);
	double tmp;
	if (a <= -3.3e+22) {
		tmp = t_1;
	} else if (a <= 1.75e-40) {
		tmp = y * ((t - z) / t);
	} else if (a <= 2.3e+89) {
		tmp = t_1;
	} else {
		tmp = x * ((-z / a) - -1.0);
	}
	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 * z) / a)
    if (a <= (-3.3d+22)) then
        tmp = t_1
    else if (a <= 1.75d-40) then
        tmp = y * ((t - z) / t)
    else if (a <= 2.3d+89) then
        tmp = t_1
    else
        tmp = x * ((-z / a) - (-1.0d0))
    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 * z) / a);
	double tmp;
	if (a <= -3.3e+22) {
		tmp = t_1;
	} else if (a <= 1.75e-40) {
		tmp = y * ((t - z) / t);
	} else if (a <= 2.3e+89) {
		tmp = t_1;
	} else {
		tmp = x * ((-z / a) - -1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((y * z) / a)
	tmp = 0
	if a <= -3.3e+22:
		tmp = t_1
	elif a <= 1.75e-40:
		tmp = y * ((t - z) / t)
	elif a <= 2.3e+89:
		tmp = t_1
	else:
		tmp = x * ((-z / a) - -1.0)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(y * z) / a))
	tmp = 0.0
	if (a <= -3.3e+22)
		tmp = t_1;
	elseif (a <= 1.75e-40)
		tmp = Float64(y * Float64(Float64(t - z) / t));
	elseif (a <= 2.3e+89)
		tmp = t_1;
	else
		tmp = Float64(x * Float64(Float64(Float64(-z) / a) - -1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((y * z) / a);
	tmp = 0.0;
	if (a <= -3.3e+22)
		tmp = t_1;
	elseif (a <= 1.75e-40)
		tmp = y * ((t - z) / t);
	elseif (a <= 2.3e+89)
		tmp = t_1;
	else
		tmp = x * ((-z / a) - -1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(y * z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -3.3e+22], t$95$1, If[LessEqual[a, 1.75e-40], N[(y * N[(N[(t - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.3e+89], t$95$1, N[(x * N[(N[((-z) / a), $MachinePrecision] - -1.0), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -3.2999999999999998e22 or 1.7500000000000001e-40 < a < 2.2999999999999999e89

   1. Initial program 73.2%

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

      1. associate-/l* 87.9%

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

      2. clear-num 87.8%

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

      3. associate-/r/ 87.8%

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

      4. clear-num 87.9%

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

   3. Applied egg-rr 87.9%

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

   4. Taylor expanded in t around 0 68.1%

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

   5. Taylor expanded in y around inf 60.8%

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

   if -3.2999999999999998e22 < a < 1.7500000000000001e-40

   1. Initial program 61.1%

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

      1. associate-/l* 68.2%

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

      2. clear-num 68.1%

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

      3. associate-/r/ 67.5%

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

      4. clear-num 67.7%

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

   3. Applied egg-rr 67.7%

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

   4. Taylor expanded in y around inf 60.7%

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

      1. div-sub 60.7%

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

   6. Simplified 60.7%

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

   7. Taylor expanded in a around 0 58.3%

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

      1. associate-*r/ 58.3%

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

      2. mul-1-neg 58.3%

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

   9. Simplified 58.3%

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

   if 2.2999999999999999e89 < a

   1. Initial program 64.3%

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

      1. associate-/l* 93.7%

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

      2. clear-num 93.6%

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

      3. associate-/r/ 93.5%

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

      4. clear-num 93.5%

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

   3. Applied egg-rr 93.5%

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

   4. Taylor expanded in t around 0 67.9%

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

   5. Taylor expanded in x around -inf 61.0%

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

      1. mul-1-neg 61.0%

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

      2. *-commutative 61.0%

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

      3. distribute-rgt-neg-in 61.0%

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

      4. sub-neg 61.0%

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

      5. metadata-eval 61.0%

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

   7. Simplified 61.0%

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

4. Final simplification 59.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.3 \cdot 10^{+22}:\\ \;\;\;\;x + \frac{y \cdot z}{a}\\ \mathbf{elif}\;a \leq 1.75 \cdot 10^{-40}:\\ \;\;\;\;y \cdot \frac{t - z}{t}\\ \mathbf{elif}\;a \leq 2.3 \cdot 10^{+89}:\\ \;\;\;\;x + \frac{y \cdot z}{a}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{-z}{a} - -1\right)\\ \end{array} \]

Alternative 11: 53.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y \cdot z}{a}\\ \mathbf{if}\;a \leq -2.05 \cdot 10^{+21}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 1.75 \cdot 10^{-40}:\\ \;\;\;\;-\frac{y}{\frac{t}{z - t}}\\ \mathbf{elif}\;a \leq 5.4 \cdot 10^{+88}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{-z}{a} - -1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ (* y z) a))))
   (if (<= a -2.05e+21)
     t_1
     (if (<= a 1.75e-40)
       (- (/ y (/ t (- z t))))
       (if (<= a 5.4e+88) t_1 (* x (- (/ (- z) a) -1.0)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y * z) / a);
	double tmp;
	if (a <= -2.05e+21) {
		tmp = t_1;
	} else if (a <= 1.75e-40) {
		tmp = -(y / (t / (z - t)));
	} else if (a <= 5.4e+88) {
		tmp = t_1;
	} else {
		tmp = x * ((-z / a) - -1.0);
	}
	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 * z) / a)
    if (a <= (-2.05d+21)) then
        tmp = t_1
    else if (a <= 1.75d-40) then
        tmp = -(y / (t / (z - t)))
    else if (a <= 5.4d+88) then
        tmp = t_1
    else
        tmp = x * ((-z / a) - (-1.0d0))
    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 * z) / a);
	double tmp;
	if (a <= -2.05e+21) {
		tmp = t_1;
	} else if (a <= 1.75e-40) {
		tmp = -(y / (t / (z - t)));
	} else if (a <= 5.4e+88) {
		tmp = t_1;
	} else {
		tmp = x * ((-z / a) - -1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((y * z) / a)
	tmp = 0
	if a <= -2.05e+21:
		tmp = t_1
	elif a <= 1.75e-40:
		tmp = -(y / (t / (z - t)))
	elif a <= 5.4e+88:
		tmp = t_1
	else:
		tmp = x * ((-z / a) - -1.0)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(y * z) / a))
	tmp = 0.0
	if (a <= -2.05e+21)
		tmp = t_1;
	elseif (a <= 1.75e-40)
		tmp = Float64(-Float64(y / Float64(t / Float64(z - t))));
	elseif (a <= 5.4e+88)
		tmp = t_1;
	else
		tmp = Float64(x * Float64(Float64(Float64(-z) / a) - -1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((y * z) / a);
	tmp = 0.0;
	if (a <= -2.05e+21)
		tmp = t_1;
	elseif (a <= 1.75e-40)
		tmp = -(y / (t / (z - t)));
	elseif (a <= 5.4e+88)
		tmp = t_1;
	else
		tmp = x * ((-z / a) - -1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(y * z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -2.05e+21], t$95$1, If[LessEqual[a, 1.75e-40], (-N[(y / N[(t / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), If[LessEqual[a, 5.4e+88], t$95$1, N[(x * N[(N[((-z) / a), $MachinePrecision] - -1.0), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -2.05e21 or 1.7500000000000001e-40 < a < 5.40000000000000031e88

   1. Initial program 73.2%

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

      1. associate-/l* 87.9%

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

      2. clear-num 87.8%

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

      3. associate-/r/ 87.8%

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

      4. clear-num 87.9%

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

   3. Applied egg-rr 87.9%

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

   4. Taylor expanded in t around 0 68.1%

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

   5. Taylor expanded in y around inf 60.8%

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

   if -2.05e21 < a < 1.7500000000000001e-40

   1. Initial program 61.1%

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

      1. associate-*l/ 66.9%

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

   3. Simplified 66.9%

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

   4. Taylor expanded in x around 0 44.8%

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

   5. Taylor expanded in a around 0 41.7%

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

      1. mul-1-neg 41.7%

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

      2. associate-/l* 58.3%

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

      3. distribute-neg-frac 58.3%

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

   7. Simplified 58.3%

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

   if 5.40000000000000031e88 < a

   1. Initial program 64.3%

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

      1. associate-/l* 93.7%

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

      2. clear-num 93.6%

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

      3. associate-/r/ 93.5%

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

      4. clear-num 93.5%

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

   3. Applied egg-rr 93.5%

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

   4. Taylor expanded in t around 0 67.9%

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

   5. Taylor expanded in x around -inf 61.0%

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

      1. mul-1-neg 61.0%

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

      2. *-commutative 61.0%

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

      3. distribute-rgt-neg-in 61.0%

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

      4. sub-neg 61.0%

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

      5. metadata-eval 61.0%

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

   7. Simplified 61.0%

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

4. Final simplification 59.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.05 \cdot 10^{+21}:\\ \;\;\;\;x + \frac{y \cdot z}{a}\\ \mathbf{elif}\;a \leq 1.75 \cdot 10^{-40}:\\ \;\;\;\;-\frac{y}{\frac{t}{z - t}}\\ \mathbf{elif}\;a \leq 5.4 \cdot 10^{+88}:\\ \;\;\;\;x + \frac{y \cdot z}{a}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{-z}{a} - -1\right)\\ \end{array} \]

Alternative 12: 51.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.8 \cdot 10^{+135}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -2.1 \cdot 10^{+22}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq 1.3 \cdot 10^{+80}:\\ \;\;\;\;x + \frac{y \cdot z}{a}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -1.8e+135)
   y
   (if (<= t -2.1e+22) (+ x y) (if (<= t 1.3e+80) (+ x (/ (* y z) a)) y))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.8e+135) {
		tmp = y;
	} else if (t <= -2.1e+22) {
		tmp = x + y;
	} else if (t <= 1.3e+80) {
		tmp = x + ((y * z) / a);
	} else {
		tmp = y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-1.8d+135)) then
        tmp = y
    else if (t <= (-2.1d+22)) then
        tmp = x + y
    else if (t <= 1.3d+80) then
        tmp = x + ((y * z) / a)
    else
        tmp = y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.8e+135) {
		tmp = y;
	} else if (t <= -2.1e+22) {
		tmp = x + y;
	} else if (t <= 1.3e+80) {
		tmp = x + ((y * z) / a);
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -1.8e+135:
		tmp = y
	elif t <= -2.1e+22:
		tmp = x + y
	elif t <= 1.3e+80:
		tmp = x + ((y * z) / a)
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -1.8e+135)
		tmp = y;
	elseif (t <= -2.1e+22)
		tmp = Float64(x + y);
	elseif (t <= 1.3e+80)
		tmp = Float64(x + Float64(Float64(y * z) / a));
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -1.8e+135)
		tmp = y;
	elseif (t <= -2.1e+22)
		tmp = x + y;
	elseif (t <= 1.3e+80)
		tmp = x + ((y * z) / a);
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -1.8e+135], y, If[LessEqual[t, -2.1e+22], N[(x + y), $MachinePrecision], If[LessEqual[t, 1.3e+80], N[(x + N[(N[(y * z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], y]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.7999999999999999e135 or 1.29999999999999991e80 < t

   1. Initial program 21.5%

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

      1. associate-*l/ 48.6%

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

   3. Simplified 48.6%

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

   4. Taylor expanded in t around inf 59.7%

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

   if -1.7999999999999999e135 < t < -2.0999999999999998e22

   1. Initial program 67.8%

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

      1. associate-*l/ 82.4%

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

   3. Simplified 82.4%

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

   4. Taylor expanded in z around 0 50.2%

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

      1. mul-1-neg 50.2%

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

      2. unsub-neg 50.2%

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

      3. associate-/l* 62.2%

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

   6. Simplified 62.2%

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

   7. Taylor expanded in y around inf 61.2%

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

      1. associate-/l* 61.6%

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

   9. Simplified 61.6%

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

   10. Taylor expanded in t around inf 43.5%

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

       1. neg-mul-1 43.5%

          \[\leadsto x - \color{blue}{\left(-y\right)} \]

   12. Simplified 43.5%

       \[\leadsto x - \color{blue}{\left(-y\right)} \]

   if -2.0999999999999998e22 < t < 1.29999999999999991e80

   1. Initial program 87.0%

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

      1. associate-/l* 91.8%

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

      2. clear-num 91.8%

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

      3. associate-/r/ 91.3%

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

      4. clear-num 91.4%

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

   3. Applied egg-rr 91.4%

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

   4. Taylor expanded in t around 0 71.7%

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

   5. Taylor expanded in y around inf 56.2%

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

4. Final simplification 55.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.8 \cdot 10^{+135}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -2.1 \cdot 10^{+22}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq 1.3 \cdot 10^{+80}:\\ \;\;\;\;x + \frac{y \cdot z}{a}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 13: 51.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -6.8 \cdot 10^{+134}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -7.8 \cdot 10^{+28}:\\ \;\;\;\;x - \frac{y}{\frac{a}{t}}\\ \mathbf{elif}\;t \leq 1.16 \cdot 10^{+80}:\\ \;\;\;\;x + \frac{y \cdot z}{a}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -6.8e+134)
   y
   (if (<= t -7.8e+28)
     (- x (/ y (/ a t)))
     (if (<= t 1.16e+80) (+ x (/ (* y z) a)) y))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -6.8e+134) {
		tmp = y;
	} else if (t <= -7.8e+28) {
		tmp = x - (y / (a / t));
	} else if (t <= 1.16e+80) {
		tmp = x + ((y * z) / a);
	} else {
		tmp = y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-6.8d+134)) then
        tmp = y
    else if (t <= (-7.8d+28)) then
        tmp = x - (y / (a / t))
    else if (t <= 1.16d+80) then
        tmp = x + ((y * z) / a)
    else
        tmp = y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -6.8e+134) {
		tmp = y;
	} else if (t <= -7.8e+28) {
		tmp = x - (y / (a / t));
	} else if (t <= 1.16e+80) {
		tmp = x + ((y * z) / a);
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -6.8e+134:
		tmp = y
	elif t <= -7.8e+28:
		tmp = x - (y / (a / t))
	elif t <= 1.16e+80:
		tmp = x + ((y * z) / a)
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -6.8e+134)
		tmp = y;
	elseif (t <= -7.8e+28)
		tmp = Float64(x - Float64(y / Float64(a / t)));
	elseif (t <= 1.16e+80)
		tmp = Float64(x + Float64(Float64(y * z) / a));
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -6.8e+134)
		tmp = y;
	elseif (t <= -7.8e+28)
		tmp = x - (y / (a / t));
	elseif (t <= 1.16e+80)
		tmp = x + ((y * z) / a);
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -6.8e+134], y, If[LessEqual[t, -7.8e+28], N[(x - N[(y / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.16e+80], N[(x + N[(N[(y * z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], y]]]

Derivation

1. Split input into 3 regimes

2. if t < -6.80000000000000035e134 or 1.15999999999999997e80 < t

   1. Initial program 21.5%

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

      1. associate-*l/ 48.6%

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

   3. Simplified 48.6%

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

   4. Taylor expanded in t around inf 59.7%

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

   if -6.80000000000000035e134 < t < -7.7999999999999997e28

   1. Initial program 66.8%

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

      1. associate-*l/ 81.9%

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

   3. Simplified 81.9%

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

   4. Taylor expanded in z around 0 48.6%

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

      1. mul-1-neg 48.6%

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

      2. unsub-neg 48.6%

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

      3. associate-/l* 61.1%

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

   6. Simplified 61.1%

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

   7. Taylor expanded in y around inf 60.0%

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

      1. associate-/l* 60.4%

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

   9. Simplified 60.4%

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

   10. Taylor expanded in t around 0 45.5%

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

       1. *-commutative 45.5%

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

       2. associate-/l* 48.4%

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

   12. Simplified 48.4%

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

   if -7.7999999999999997e28 < t < 1.15999999999999997e80

   1. Initial program 87.1%

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

      1. associate-/l* 91.9%

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

      2. clear-num 91.9%

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

      3. associate-/r/ 91.4%

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

      4. clear-num 91.5%

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

   3. Applied egg-rr 91.5%

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

   4. Taylor expanded in t around 0 71.2%

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

   5. Taylor expanded in y around inf 55.8%

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

4. Final simplification 56.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.8 \cdot 10^{+134}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -7.8 \cdot 10^{+28}:\\ \;\;\;\;x - \frac{y}{\frac{a}{t}}\\ \mathbf{elif}\;t \leq 1.16 \cdot 10^{+80}:\\ \;\;\;\;x + \frac{y \cdot z}{a}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 14: 53.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y \cdot z}{a}\\ \mathbf{if}\;a \leq -2.85 \cdot 10^{+23}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 1.02 \cdot 10^{-41}:\\ \;\;\;\;y \cdot \frac{t - z}{t}\\ \mathbf{elif}\;a \leq 2.9 \cdot 10^{+88}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x - x \cdot \frac{z}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ (* y z) a))))
   (if (<= a -2.85e+23)
     t_1
     (if (<= a 1.02e-41)
       (* y (/ (- t z) t))
       (if (<= a 2.9e+88) t_1 (- x (* x (/ z a))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y * z) / a);
	double tmp;
	if (a <= -2.85e+23) {
		tmp = t_1;
	} else if (a <= 1.02e-41) {
		tmp = y * ((t - z) / t);
	} else if (a <= 2.9e+88) {
		tmp = t_1;
	} else {
		tmp = x - (x * (z / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + ((y * z) / a)
    if (a <= (-2.85d+23)) then
        tmp = t_1
    else if (a <= 1.02d-41) then
        tmp = y * ((t - z) / t)
    else if (a <= 2.9d+88) then
        tmp = t_1
    else
        tmp = x - (x * (z / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y * z) / a);
	double tmp;
	if (a <= -2.85e+23) {
		tmp = t_1;
	} else if (a <= 1.02e-41) {
		tmp = y * ((t - z) / t);
	} else if (a <= 2.9e+88) {
		tmp = t_1;
	} else {
		tmp = x - (x * (z / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((y * z) / a)
	tmp = 0
	if a <= -2.85e+23:
		tmp = t_1
	elif a <= 1.02e-41:
		tmp = y * ((t - z) / t)
	elif a <= 2.9e+88:
		tmp = t_1
	else:
		tmp = x - (x * (z / a))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(y * z) / a))
	tmp = 0.0
	if (a <= -2.85e+23)
		tmp = t_1;
	elseif (a <= 1.02e-41)
		tmp = Float64(y * Float64(Float64(t - z) / t));
	elseif (a <= 2.9e+88)
		tmp = t_1;
	else
		tmp = Float64(x - Float64(x * Float64(z / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((y * z) / a);
	tmp = 0.0;
	if (a <= -2.85e+23)
		tmp = t_1;
	elseif (a <= 1.02e-41)
		tmp = y * ((t - z) / t);
	elseif (a <= 2.9e+88)
		tmp = t_1;
	else
		tmp = x - (x * (z / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(y * z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -2.85e+23], t$95$1, If[LessEqual[a, 1.02e-41], N[(y * N[(N[(t - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.9e+88], t$95$1, N[(x - N[(x * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -2.85e23 or 1.02e-41 < a < 2.9e88

   1. Initial program 73.2%

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

      1. associate-/l* 87.9%

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

      2. clear-num 87.8%

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

      3. associate-/r/ 87.8%

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

      4. clear-num 87.9%

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

   3. Applied egg-rr 87.9%

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

   4. Taylor expanded in t around 0 68.1%

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

   5. Taylor expanded in y around inf 60.8%

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

   if -2.85e23 < a < 1.02e-41

   1. Initial program 61.1%

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

      1. associate-/l* 68.2%

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

      2. clear-num 68.1%

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

      3. associate-/r/ 67.5%

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

      4. clear-num 67.7%

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

   3. Applied egg-rr 67.7%

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

   4. Taylor expanded in y around inf 60.7%

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

      1. div-sub 60.7%

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

   6. Simplified 60.7%

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

   7. Taylor expanded in a around 0 58.3%

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

      1. associate-*r/ 58.3%

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

      2. mul-1-neg 58.3%

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

   9. Simplified 58.3%

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

   if 2.9e88 < a

   1. Initial program 64.3%

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

      1. associate-/l* 93.7%

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

      2. clear-num 93.6%

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

      3. associate-/r/ 93.5%

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

      4. clear-num 93.5%

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

   3. Applied egg-rr 93.5%

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

   4. Taylor expanded in t around 0 67.9%

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

   5. Taylor expanded in x around inf 61.0%

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

      1. distribute-lft-in 61.0%

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

      2. *-rgt-identity 61.0%

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

      3. mul-1-neg 61.0%

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

      4. distribute-rgt-neg-in 61.0%

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

      5. unsub-neg 61.0%

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

   7. Simplified 61.0%

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

4. Final simplification 59.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.85 \cdot 10^{+23}:\\ \;\;\;\;x + \frac{y \cdot z}{a}\\ \mathbf{elif}\;a \leq 1.02 \cdot 10^{-41}:\\ \;\;\;\;y \cdot \frac{t - z}{t}\\ \mathbf{elif}\;a \leq 2.9 \cdot 10^{+88}:\\ \;\;\;\;x + \frac{y \cdot z}{a}\\ \mathbf{else}:\\ \;\;\;\;x - x \cdot \frac{z}{a}\\ \end{array} \]

Alternative 15: 70.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.8 \cdot 10^{+18} \lor \neg \left(a \leq 1150\right):\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;y - \frac{z}{\frac{t}{y - x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -2.8e+18) (not (<= a 1150.0)))
   (+ x (* (- y x) (/ z a)))
   (- y (/ z (/ t (- y x))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -2.8e+18) || !(a <= 1150.0)) {
		tmp = x + ((y - x) * (z / a));
	} else {
		tmp = y - (z / (t / (y - x)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a <= (-2.8d+18)) .or. (.not. (a <= 1150.0d0))) then
        tmp = x + ((y - x) * (z / a))
    else
        tmp = y - (z / (t / (y - x)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -2.8e+18) || !(a <= 1150.0)) {
		tmp = x + ((y - x) * (z / a));
	} else {
		tmp = y - (z / (t / (y - x)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -2.8e+18) or not (a <= 1150.0):
		tmp = x + ((y - x) * (z / a))
	else:
		tmp = y - (z / (t / (y - x)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -2.8e+18) || !(a <= 1150.0))
		tmp = Float64(x + Float64(Float64(y - x) * Float64(z / a)));
	else
		tmp = Float64(y - Float64(z / Float64(t / Float64(y - x))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -2.8e+18) || ~((a <= 1150.0)))
		tmp = x + ((y - x) * (z / a));
	else
		tmp = y - (z / (t / (y - x)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -2.8e+18], N[Not[LessEqual[a, 1150.0]], $MachinePrecision]], N[(x + N[(N[(y - x), $MachinePrecision] * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y - N[(z / N[(t / N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -2.8e18 or 1150 < a

   1. Initial program 70.3%

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

      1. associate-/l* 89.8%

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

      2. clear-num 89.8%

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

      3. associate-/r/ 89.8%

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

      4. clear-num 89.8%

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

   3. Applied egg-rr 89.8%

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

   4. Taylor expanded in t around 0 68.8%

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

   if -2.8e18 < a < 1150

   1. Initial program 61.8%

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

      1. associate-/l* 69.1%

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

   3. Simplified 69.1%

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

   4. Taylor expanded in a around 0 54.3%

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

      1. neg-mul-1 54.3%

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

      2. distribute-neg-frac 54.3%

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

   6. Simplified 54.3%

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

   7. Taylor expanded in t around 0 76.6%

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

      1. mul-1-neg 76.6%

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

      2. unsub-neg 76.6%

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

      3. associate-/l* 80.4%

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

   9. Simplified 80.4%

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

4. Final simplification 74.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.8 \cdot 10^{+18} \lor \neg \left(a \leq 1150\right):\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;y - \frac{z}{\frac{t}{y - x}}\\ \end{array} \]

Alternative 16: 58.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.8 \cdot 10^{+25}:\\ \;\;\;\;x + \frac{y \cdot z}{a}\\ \mathbf{elif}\;a \leq 7.4 \cdot 10^{+150}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x - x \cdot \frac{z}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -2.8e+25)
   (+ x (/ (* y z) a))
   (if (<= a 7.4e+150) (* y (/ (- z t) (- a t))) (- x (* x (/ z a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -2.8e+25) {
		tmp = x + ((y * z) / a);
	} else if (a <= 7.4e+150) {
		tmp = y * ((z - t) / (a - t));
	} else {
		tmp = x - (x * (z / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-2.8d+25)) then
        tmp = x + ((y * z) / a)
    else if (a <= 7.4d+150) then
        tmp = y * ((z - t) / (a - t))
    else
        tmp = x - (x * (z / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -2.8e+25) {
		tmp = x + ((y * z) / a);
	} else if (a <= 7.4e+150) {
		tmp = y * ((z - t) / (a - t));
	} else {
		tmp = x - (x * (z / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -2.8e+25:
		tmp = x + ((y * z) / a)
	elif a <= 7.4e+150:
		tmp = y * ((z - t) / (a - t))
	else:
		tmp = x - (x * (z / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -2.8e+25)
		tmp = Float64(x + Float64(Float64(y * z) / a));
	elseif (a <= 7.4e+150)
		tmp = Float64(y * Float64(Float64(z - t) / Float64(a - t)));
	else
		tmp = Float64(x - Float64(x * Float64(z / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -2.8e+25)
		tmp = x + ((y * z) / a);
	elseif (a <= 7.4e+150)
		tmp = y * ((z - t) / (a - t));
	else
		tmp = x - (x * (z / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -2.8e+25], N[(x + N[(N[(y * z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 7.4e+150], N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(x * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < -2.8000000000000002e25

   1. Initial program 73.0%

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

      1. associate-/l* 89.9%

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

      2. clear-num 89.9%

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

      3. associate-/r/ 89.9%

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

      4. clear-num 90.0%

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

   3. Applied egg-rr 90.0%

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

   4. Taylor expanded in t around 0 73.9%

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

   5. Taylor expanded in y around inf 63.4%

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

   if -2.8000000000000002e25 < a < 7.39999999999999975e150

   1. Initial program 64.5%

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

      1. associate-/l* 72.0%

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

      2. clear-num 71.9%

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

      3. associate-/r/ 71.5%

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

      4. clear-num 71.6%

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

   3. Applied egg-rr 71.6%

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

   4. Taylor expanded in y around inf 59.6%

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

      1. div-sub 59.6%

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

   6. Simplified 59.6%

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

   if 7.39999999999999975e150 < a

   1. Initial program 59.6%

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

      1. associate-/l* 99.0%

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

      2. clear-num 98.9%

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

      3. associate-/r/ 98.9%

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

      4. clear-num 98.9%

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

   3. Applied egg-rr 98.9%

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

   4. Taylor expanded in t around 0 79.6%

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

   5. Taylor expanded in x around inf 73.1%

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

      1. distribute-lft-in 73.1%

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

      2. *-rgt-identity 73.1%

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

      3. mul-1-neg 73.1%

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

      4. distribute-rgt-neg-in 73.1%

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

      5. unsub-neg 73.1%

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

   7. Simplified 73.1%

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

4. Final simplification 62.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.8 \cdot 10^{+25}:\\ \;\;\;\;x + \frac{y \cdot z}{a}\\ \mathbf{elif}\;a \leq 7.4 \cdot 10^{+150}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x - x \cdot \frac{z}{a}\\ \end{array} \]

Alternative 17: 38.8% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.2 \cdot 10^{+19}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.02 \cdot 10^{-268}:\\ \;\;\;\;y\\ \mathbf{elif}\;a \leq 1.55 \cdot 10^{-139}:\\ \;\;\;\;x \cdot \frac{z}{t}\\ \mathbf{elif}\;a \leq 9500:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -1.2e+19)
   x
   (if (<= a 1.02e-268)
     y
     (if (<= a 1.55e-139) (* x (/ z t)) (if (<= a 9500.0) y x)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.2e+19) {
		tmp = x;
	} else if (a <= 1.02e-268) {
		tmp = y;
	} else if (a <= 1.55e-139) {
		tmp = x * (z / t);
	} else if (a <= 9500.0) {
		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 <= (-1.2d+19)) then
        tmp = x
    else if (a <= 1.02d-268) then
        tmp = y
    else if (a <= 1.55d-139) then
        tmp = x * (z / t)
    else if (a <= 9500.0d0) 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 <= -1.2e+19) {
		tmp = x;
	} else if (a <= 1.02e-268) {
		tmp = y;
	} else if (a <= 1.55e-139) {
		tmp = x * (z / t);
	} else if (a <= 9500.0) {
		tmp = y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -1.2e+19:
		tmp = x
	elif a <= 1.02e-268:
		tmp = y
	elif a <= 1.55e-139:
		tmp = x * (z / t)
	elif a <= 9500.0:
		tmp = y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -1.2e+19)
		tmp = x;
	elseif (a <= 1.02e-268)
		tmp = y;
	elseif (a <= 1.55e-139)
		tmp = Float64(x * Float64(z / t));
	elseif (a <= 9500.0)
		tmp = y;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -1.2e+19)
		tmp = x;
	elseif (a <= 1.02e-268)
		tmp = y;
	elseif (a <= 1.55e-139)
		tmp = x * (z / t);
	elseif (a <= 9500.0)
		tmp = y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -1.2e+19], x, If[LessEqual[a, 1.02e-268], y, If[LessEqual[a, 1.55e-139], N[(x * N[(z / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 9500.0], y, x]]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.2e19 or 9500 < a

   1. Initial program 70.3%

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

      1. associate-*l/ 88.6%

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

   3. Simplified 88.6%

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

   4. Taylor expanded in a around inf 47.3%

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

   if -1.2e19 < a < 1.0200000000000001e-268 or 1.55e-139 < a < 9500

   1. Initial program 66.1%

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

      1. associate-*l/ 73.0%

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

   3. Simplified 73.0%

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

   4. Taylor expanded in t around inf 45.6%

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

   if 1.0200000000000001e-268 < a < 1.55e-139

   1. Initial program 48.6%

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

      1. associate-/l* 57.7%

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

   3. Simplified 57.7%

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

   4. Taylor expanded in a around 0 54.5%

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

      1. neg-mul-1 54.5%

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

      2. distribute-neg-frac 54.5%

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

   6. Simplified 54.5%

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

   7. Taylor expanded in x around inf 46.8%

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

      1. associate-/l* 51.3%

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

   9. Simplified 51.3%

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

       1. div-inv 51.3%

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

       2. clear-num 51.3%

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

   11. Applied egg-rr 51.3%

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

4. Final simplification 47.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.2 \cdot 10^{+19}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.02 \cdot 10^{-268}:\\ \;\;\;\;y\\ \mathbf{elif}\;a \leq 1.55 \cdot 10^{-139}:\\ \;\;\;\;x \cdot \frac{z}{t}\\ \mathbf{elif}\;a \leq 9500:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 18: 38.8% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.55 \cdot 10^{+23}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 6.6 \cdot 10^{-273}:\\ \;\;\;\;y\\ \mathbf{elif}\;a \leq 5.2 \cdot 10^{-139}:\\ \;\;\;\;\frac{x}{\frac{t}{z}}\\ \mathbf{elif}\;a \leq 2600:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -2.55e+23)
   x
   (if (<= a 6.6e-273)
     y
     (if (<= a 5.2e-139) (/ x (/ t z)) (if (<= a 2600.0) y x)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -2.55e+23) {
		tmp = x;
	} else if (a <= 6.6e-273) {
		tmp = y;
	} else if (a <= 5.2e-139) {
		tmp = x / (t / z);
	} else if (a <= 2600.0) {
		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 <= (-2.55d+23)) then
        tmp = x
    else if (a <= 6.6d-273) then
        tmp = y
    else if (a <= 5.2d-139) then
        tmp = x / (t / z)
    else if (a <= 2600.0d0) 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 <= -2.55e+23) {
		tmp = x;
	} else if (a <= 6.6e-273) {
		tmp = y;
	} else if (a <= 5.2e-139) {
		tmp = x / (t / z);
	} else if (a <= 2600.0) {
		tmp = y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -2.55e+23:
		tmp = x
	elif a <= 6.6e-273:
		tmp = y
	elif a <= 5.2e-139:
		tmp = x / (t / z)
	elif a <= 2600.0:
		tmp = y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -2.55e+23)
		tmp = x;
	elseif (a <= 6.6e-273)
		tmp = y;
	elseif (a <= 5.2e-139)
		tmp = Float64(x / Float64(t / z));
	elseif (a <= 2600.0)
		tmp = y;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -2.55e+23)
		tmp = x;
	elseif (a <= 6.6e-273)
		tmp = y;
	elseif (a <= 5.2e-139)
		tmp = x / (t / z);
	elseif (a <= 2600.0)
		tmp = y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -2.55e+23], x, If[LessEqual[a, 6.6e-273], y, If[LessEqual[a, 5.2e-139], N[(x / N[(t / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2600.0], y, x]]]]

Derivation

1. Split input into 3 regimes

2. if a < -2.5500000000000001e23 or 2600 < a

   1. Initial program 70.3%

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

      1. associate-*l/ 88.6%

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

   3. Simplified 88.6%

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

   4. Taylor expanded in a around inf 47.3%

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

   if -2.5500000000000001e23 < a < 6.5999999999999998e-273 or 5.1999999999999996e-139 < a < 2600

   1. Initial program 66.1%

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

      1. associate-*l/ 73.0%

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

   3. Simplified 73.0%

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

   4. Taylor expanded in t around inf 45.6%

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

   if 6.5999999999999998e-273 < a < 5.1999999999999996e-139

   1. Initial program 48.6%

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

      1. associate-/l* 57.7%

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

   3. Simplified 57.7%

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

   4. Taylor expanded in a around 0 54.5%

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

      1. neg-mul-1 54.5%

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

      2. distribute-neg-frac 54.5%

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

   6. Simplified 54.5%

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

   7. Taylor expanded in x around inf 46.8%

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

      1. associate-/l* 51.3%

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

   9. Simplified 51.3%

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

4. Final simplification 47.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.55 \cdot 10^{+23}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 6.6 \cdot 10^{-273}:\\ \;\;\;\;y\\ \mathbf{elif}\;a \leq 5.2 \cdot 10^{-139}:\\ \;\;\;\;\frac{x}{\frac{t}{z}}\\ \mathbf{elif}\;a \leq 2600:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 19: 39.2% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.05 \cdot 10^{+23}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 820:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -1.05e+23) x (if (<= a 820.0) y x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.05e+23) {
		tmp = x;
	} else if (a <= 820.0) {
		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 <= (-1.05d+23)) then
        tmp = x
    else if (a <= 820.0d0) 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 <= -1.05e+23) {
		tmp = x;
	} else if (a <= 820.0) {
		tmp = y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -1.05e+23:
		tmp = x
	elif a <= 820.0:
		tmp = y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -1.05e+23)
		tmp = x;
	elseif (a <= 820.0)
		tmp = y;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -1.05e+23)
		tmp = x;
	elseif (a <= 820.0)
		tmp = y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -1.05e+23], x, If[LessEqual[a, 820.0], y, x]]

Derivation

1. Split input into 2 regimes

2. if a < -1.0500000000000001e23 or 820 < a

   1. Initial program 70.3%

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

      1. associate-*l/ 88.6%

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

   3. Simplified 88.6%

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

   4. Taylor expanded in a around inf 47.3%

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

   if -1.0500000000000001e23 < a < 820

   1. Initial program 61.8%

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

      1. associate-*l/ 67.9%

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

   3. Simplified 67.9%

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

   4. Taylor expanded in t around inf 42.7%

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

4. Final simplification 45.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.05 \cdot 10^{+23}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 820:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 20: 25.4% accurate, 13.0× speedup

Math

\[\begin{array}{l} \\ x \end{array} \]

FPCore

(FPCore (x y z t a) :precision binary64 x)

C

double code(double x, double y, double z, double t, double a) {
	return x;
}

Fortran

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

Java

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

Python

def code(x, y, z, t, a):
	return x

Julia

function code(x, y, z, t, a)
	return x
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = x;
end

Wolfram

code[x_, y_, z_, t_, a_] := x

Derivation

1. Initial program 66.1%

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

   1. associate-*l/ 78.4%

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

3. Simplified 78.4%

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

4. Taylor expanded in a around inf 27.8%

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

5. Final simplification 27.8%

   \[\leadsto x \]

Developer target: 86.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y - x}{1} \cdot \frac{z - t}{a - t}\\ \mathbf{if}\;a < -1.6153062845442575 \cdot 10^{-142}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a < 3.774403170083174 \cdot 10^{-182}:\\ \;\;\;\;y - \frac{z}{t} \cdot \left(y - x\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (/ (- y x) 1.0) (/ (- z t) (- a t))))))
   (if (< a -1.6153062845442575e-142)
     t_1
     (if (< a 3.774403170083174e-182) (- y (* (/ z t) (- y x))) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (((y - x) / 1.0) * ((z - t) / (a - t)));
	double tmp;
	if (a < -1.6153062845442575e-142) {
		tmp = t_1;
	} else if (a < 3.774403170083174e-182) {
		tmp = y - ((z / t) * (y - x));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (((y - x) / 1.0d0) * ((z - t) / (a - t)))
    if (a < (-1.6153062845442575d-142)) then
        tmp = t_1
    else if (a < 3.774403170083174d-182) then
        tmp = y - ((z / t) * (y - x))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (((y - x) / 1.0) * ((z - t) / (a - t)));
	double tmp;
	if (a < -1.6153062845442575e-142) {
		tmp = t_1;
	} else if (a < 3.774403170083174e-182) {
		tmp = y - ((z / t) * (y - x));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (((y - x) / 1.0) * ((z - t) / (a - t)))
	tmp = 0
	if a < -1.6153062845442575e-142:
		tmp = t_1
	elif a < 3.774403170083174e-182:
		tmp = y - ((z / t) * (y - x))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(Float64(y - x) / 1.0) * Float64(Float64(z - t) / Float64(a - t))))
	tmp = 0.0
	if (a < -1.6153062845442575e-142)
		tmp = t_1;
	elseif (a < 3.774403170083174e-182)
		tmp = Float64(y - Float64(Float64(z / t) * Float64(y - x)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (((y - x) / 1.0) * ((z - t) / (a - t)));
	tmp = 0.0;
	if (a < -1.6153062845442575e-142)
		tmp = t_1;
	elseif (a < 3.774403170083174e-182)
		tmp = y - ((z / t) * (y - x));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(N[(y - x), $MachinePrecision] / 1.0), $MachinePrecision] * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Less[a, -1.6153062845442575e-142], t$95$1, If[Less[a, 3.774403170083174e-182], N[(y - N[(N[(z / t), $MachinePrecision] * N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Reproduce

herbie shell --seed 2023279 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Chart.Axis.Types:linMap from Chart-1.5.3"
  :precision binary64

  :herbie-target
  (if (< a -1.6153062845442575e-142) (+ x (* (/ (- y x) 1.0) (/ (- z t) (- a t)))) (if (< a 3.774403170083174e-182) (- y (* (/ z t) (- y x))) (+ x (* (/ (- y x) 1.0) (/ (- z t) (- a t))))))

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