Graphics.Rendering.Chart.Plot.AreaSpots:renderAreaSpots4D from Chart-1.5.3

Percentage Accurate: 84.2% → 96.9%

Time: 15.7s

Alternatives: 14

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 84.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 96.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x \cdot \frac{y - z}{t - z} \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 86.5%

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

   1. associate-*l/ 82.5%

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

3. Simplified 82.5%

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

4. Taylor expanded in x around 0 86.5%

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

   1. associate-*r/ 97.7%

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

6. Simplified 97.7%

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

7. Final simplification 97.7%

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

Alternative 2: 57.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{\frac{t}{y}}\\ t_2 := x \cdot \frac{-z}{t}\\ \mathbf{if}\;z \leq -2.65 \cdot 10^{+57}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -4.8 \cdot 10^{+23}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -7.5 \cdot 10^{-6}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -1.9 \cdot 10^{-61}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.16 \cdot 10^{-66}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -1.8 \cdot 10^{-150}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{+46}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 4 \cdot 10^{+84}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 3.25 \cdot 10^{+125}:\\ \;\;\;\;x \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ x (/ t y))) (t_2 (* x (/ (- z) t))))
   (if (<= z -2.65e+57)
     x
     (if (<= z -4.8e+23)
       t_2
       (if (<= z -7.5e-6)
         x
         (if (<= z -1.9e-61)
           t_1
           (if (<= z -1.16e-66)
             x
             (if (<= z -1.8e-150)
               t_2
               (if (<= z 3.2e+46)
                 t_1
                 (if (<= z 4e+84)
                   x
                   (if (<= z 3.25e+125) (* x (/ y t)) x)))))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x / (t / y);
	double t_2 = x * (-z / t);
	double tmp;
	if (z <= -2.65e+57) {
		tmp = x;
	} else if (z <= -4.8e+23) {
		tmp = t_2;
	} else if (z <= -7.5e-6) {
		tmp = x;
	} else if (z <= -1.9e-61) {
		tmp = t_1;
	} else if (z <= -1.16e-66) {
		tmp = x;
	} else if (z <= -1.8e-150) {
		tmp = t_2;
	} else if (z <= 3.2e+46) {
		tmp = t_1;
	} else if (z <= 4e+84) {
		tmp = x;
	} else if (z <= 3.25e+125) {
		tmp = x * (y / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x / (t / y)
    t_2 = x * (-z / t)
    if (z <= (-2.65d+57)) then
        tmp = x
    else if (z <= (-4.8d+23)) then
        tmp = t_2
    else if (z <= (-7.5d-6)) then
        tmp = x
    else if (z <= (-1.9d-61)) then
        tmp = t_1
    else if (z <= (-1.16d-66)) then
        tmp = x
    else if (z <= (-1.8d-150)) then
        tmp = t_2
    else if (z <= 3.2d+46) then
        tmp = t_1
    else if (z <= 4d+84) then
        tmp = x
    else if (z <= 3.25d+125) then
        tmp = x * (y / t)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x / (t / y);
	double t_2 = x * (-z / t);
	double tmp;
	if (z <= -2.65e+57) {
		tmp = x;
	} else if (z <= -4.8e+23) {
		tmp = t_2;
	} else if (z <= -7.5e-6) {
		tmp = x;
	} else if (z <= -1.9e-61) {
		tmp = t_1;
	} else if (z <= -1.16e-66) {
		tmp = x;
	} else if (z <= -1.8e-150) {
		tmp = t_2;
	} else if (z <= 3.2e+46) {
		tmp = t_1;
	} else if (z <= 4e+84) {
		tmp = x;
	} else if (z <= 3.25e+125) {
		tmp = x * (y / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x / (t / y)
	t_2 = x * (-z / t)
	tmp = 0
	if z <= -2.65e+57:
		tmp = x
	elif z <= -4.8e+23:
		tmp = t_2
	elif z <= -7.5e-6:
		tmp = x
	elif z <= -1.9e-61:
		tmp = t_1
	elif z <= -1.16e-66:
		tmp = x
	elif z <= -1.8e-150:
		tmp = t_2
	elif z <= 3.2e+46:
		tmp = t_1
	elif z <= 4e+84:
		tmp = x
	elif z <= 3.25e+125:
		tmp = x * (y / t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x / Float64(t / y))
	t_2 = Float64(x * Float64(Float64(-z) / t))
	tmp = 0.0
	if (z <= -2.65e+57)
		tmp = x;
	elseif (z <= -4.8e+23)
		tmp = t_2;
	elseif (z <= -7.5e-6)
		tmp = x;
	elseif (z <= -1.9e-61)
		tmp = t_1;
	elseif (z <= -1.16e-66)
		tmp = x;
	elseif (z <= -1.8e-150)
		tmp = t_2;
	elseif (z <= 3.2e+46)
		tmp = t_1;
	elseif (z <= 4e+84)
		tmp = x;
	elseif (z <= 3.25e+125)
		tmp = Float64(x * Float64(y / t));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x / (t / y);
	t_2 = x * (-z / t);
	tmp = 0.0;
	if (z <= -2.65e+57)
		tmp = x;
	elseif (z <= -4.8e+23)
		tmp = t_2;
	elseif (z <= -7.5e-6)
		tmp = x;
	elseif (z <= -1.9e-61)
		tmp = t_1;
	elseif (z <= -1.16e-66)
		tmp = x;
	elseif (z <= -1.8e-150)
		tmp = t_2;
	elseif (z <= 3.2e+46)
		tmp = t_1;
	elseif (z <= 4e+84)
		tmp = x;
	elseif (z <= 3.25e+125)
		tmp = x * (y / t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x / N[(t / y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[((-z) / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.65e+57], x, If[LessEqual[z, -4.8e+23], t$95$2, If[LessEqual[z, -7.5e-6], x, If[LessEqual[z, -1.9e-61], t$95$1, If[LessEqual[z, -1.16e-66], x, If[LessEqual[z, -1.8e-150], t$95$2, If[LessEqual[z, 3.2e+46], t$95$1, If[LessEqual[z, 4e+84], x, If[LessEqual[z, 3.25e+125], N[(x * N[(y / t), $MachinePrecision]), $MachinePrecision], x]]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2.64999999999999993e57 or -4.8e23 < z < -7.50000000000000019e-6 or -1.8999999999999999e-61 < z < -1.16000000000000002e-66 or 3.1999999999999998e46 < z < 4.00000000000000023e84 or 3.2499999999999999e125 < z

   1. Initial program 75.7%

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

      1. associate-*l/ 71.3%

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

   3. Simplified 71.3%

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

   4. Taylor expanded in z around inf 69.1%

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

   if -2.64999999999999993e57 < z < -4.8e23 or -1.16000000000000002e-66 < z < -1.8000000000000001e-150

   1. Initial program 96.0%

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

      1. associate-*l/ 92.6%

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

   3. Simplified 92.6%

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

   4. Taylor expanded in x around 0 96.0%

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

      1. associate-*r/ 99.2%

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

   6. Simplified 99.2%

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

   7. Taylor expanded in y around 0 55.2%

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

      1. associate-*r/ 55.2%

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

      2. neg-mul-1 55.2%

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

   9. Simplified 55.2%

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

   10. Taylor expanded in z around 0 50.9%

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

       1. mul-1-neg 50.9%

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

       2. distribute-neg-frac 50.9%

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

   12. Simplified 50.9%

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

   if -7.50000000000000019e-6 < z < -1.8999999999999999e-61 or -1.8000000000000001e-150 < z < 3.1999999999999998e46

   1. Initial program 95.4%

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

      1. associate-*l/ 93.7%

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

   3. Simplified 93.7%

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

   4. Taylor expanded in z around 0 68.8%

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

      1. associate-/l* 70.8%

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

   6. Simplified 70.8%

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

   if 4.00000000000000023e84 < z < 3.2499999999999999e125

   1. Initial program 80.8%

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

      1. associate-*l/ 53.2%

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

   3. Simplified 53.2%

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

   4. Taylor expanded in x around 0 80.8%

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

      1. associate-*r/ 99.7%

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

   6. Simplified 99.7%

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

   7. Taylor expanded in z around 0 51.9%

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

4. Final simplification 67.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.65 \cdot 10^{+57}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -4.8 \cdot 10^{+23}:\\ \;\;\;\;x \cdot \frac{-z}{t}\\ \mathbf{elif}\;z \leq -7.5 \cdot 10^{-6}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -1.9 \cdot 10^{-61}:\\ \;\;\;\;\frac{x}{\frac{t}{y}}\\ \mathbf{elif}\;z \leq -1.16 \cdot 10^{-66}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -1.8 \cdot 10^{-150}:\\ \;\;\;\;x \cdot \frac{-z}{t}\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{+46}:\\ \;\;\;\;\frac{x}{\frac{t}{y}}\\ \mathbf{elif}\;z \leq 4 \cdot 10^{+84}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 3.25 \cdot 10^{+125}:\\ \;\;\;\;x \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 3: 58.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{\frac{t}{y}}\\ \mathbf{if}\;z \leq -2.7 \cdot 10^{+57}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -1.2 \cdot 10^{+19}:\\ \;\;\;\;x \cdot \frac{-z}{t}\\ \mathbf{elif}\;z \leq -7.5 \cdot 10^{-6}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -1.9 \cdot 10^{-61}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -2.7 \cdot 10^{-68}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -1.8 \cdot 10^{-150}:\\ \;\;\;\;z \cdot \frac{-x}{t}\\ \mathbf{elif}\;z \leq 4.1 \cdot 10^{+47}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 9.2 \cdot 10^{+85}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 3.25 \cdot 10^{+125}:\\ \;\;\;\;x \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ x (/ t y))))
   (if (<= z -2.7e+57)
     x
     (if (<= z -1.2e+19)
       (* x (/ (- z) t))
       (if (<= z -7.5e-6)
         x
         (if (<= z -1.9e-61)
           t_1
           (if (<= z -2.7e-68)
             x
             (if (<= z -1.8e-150)
               (* z (/ (- x) t))
               (if (<= z 4.1e+47)
                 t_1
                 (if (<= z 9.2e+85)
                   x
                   (if (<= z 3.25e+125) (* x (/ y t)) x)))))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x / (t / y);
	double tmp;
	if (z <= -2.7e+57) {
		tmp = x;
	} else if (z <= -1.2e+19) {
		tmp = x * (-z / t);
	} else if (z <= -7.5e-6) {
		tmp = x;
	} else if (z <= -1.9e-61) {
		tmp = t_1;
	} else if (z <= -2.7e-68) {
		tmp = x;
	} else if (z <= -1.8e-150) {
		tmp = z * (-x / t);
	} else if (z <= 4.1e+47) {
		tmp = t_1;
	} else if (z <= 9.2e+85) {
		tmp = x;
	} else if (z <= 3.25e+125) {
		tmp = x * (y / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x / (t / y)
    if (z <= (-2.7d+57)) then
        tmp = x
    else if (z <= (-1.2d+19)) then
        tmp = x * (-z / t)
    else if (z <= (-7.5d-6)) then
        tmp = x
    else if (z <= (-1.9d-61)) then
        tmp = t_1
    else if (z <= (-2.7d-68)) then
        tmp = x
    else if (z <= (-1.8d-150)) then
        tmp = z * (-x / t)
    else if (z <= 4.1d+47) then
        tmp = t_1
    else if (z <= 9.2d+85) then
        tmp = x
    else if (z <= 3.25d+125) then
        tmp = x * (y / t)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x / (t / y);
	double tmp;
	if (z <= -2.7e+57) {
		tmp = x;
	} else if (z <= -1.2e+19) {
		tmp = x * (-z / t);
	} else if (z <= -7.5e-6) {
		tmp = x;
	} else if (z <= -1.9e-61) {
		tmp = t_1;
	} else if (z <= -2.7e-68) {
		tmp = x;
	} else if (z <= -1.8e-150) {
		tmp = z * (-x / t);
	} else if (z <= 4.1e+47) {
		tmp = t_1;
	} else if (z <= 9.2e+85) {
		tmp = x;
	} else if (z <= 3.25e+125) {
		tmp = x * (y / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x / (t / y)
	tmp = 0
	if z <= -2.7e+57:
		tmp = x
	elif z <= -1.2e+19:
		tmp = x * (-z / t)
	elif z <= -7.5e-6:
		tmp = x
	elif z <= -1.9e-61:
		tmp = t_1
	elif z <= -2.7e-68:
		tmp = x
	elif z <= -1.8e-150:
		tmp = z * (-x / t)
	elif z <= 4.1e+47:
		tmp = t_1
	elif z <= 9.2e+85:
		tmp = x
	elif z <= 3.25e+125:
		tmp = x * (y / t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x / Float64(t / y))
	tmp = 0.0
	if (z <= -2.7e+57)
		tmp = x;
	elseif (z <= -1.2e+19)
		tmp = Float64(x * Float64(Float64(-z) / t));
	elseif (z <= -7.5e-6)
		tmp = x;
	elseif (z <= -1.9e-61)
		tmp = t_1;
	elseif (z <= -2.7e-68)
		tmp = x;
	elseif (z <= -1.8e-150)
		tmp = Float64(z * Float64(Float64(-x) / t));
	elseif (z <= 4.1e+47)
		tmp = t_1;
	elseif (z <= 9.2e+85)
		tmp = x;
	elseif (z <= 3.25e+125)
		tmp = Float64(x * Float64(y / t));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x / (t / y);
	tmp = 0.0;
	if (z <= -2.7e+57)
		tmp = x;
	elseif (z <= -1.2e+19)
		tmp = x * (-z / t);
	elseif (z <= -7.5e-6)
		tmp = x;
	elseif (z <= -1.9e-61)
		tmp = t_1;
	elseif (z <= -2.7e-68)
		tmp = x;
	elseif (z <= -1.8e-150)
		tmp = z * (-x / t);
	elseif (z <= 4.1e+47)
		tmp = t_1;
	elseif (z <= 9.2e+85)
		tmp = x;
	elseif (z <= 3.25e+125)
		tmp = x * (y / t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x / N[(t / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.7e+57], x, If[LessEqual[z, -1.2e+19], N[(x * N[((-z) / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -7.5e-6], x, If[LessEqual[z, -1.9e-61], t$95$1, If[LessEqual[z, -2.7e-68], x, If[LessEqual[z, -1.8e-150], N[(z * N[((-x) / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.1e+47], t$95$1, If[LessEqual[z, 9.2e+85], x, If[LessEqual[z, 3.25e+125], N[(x * N[(y / t), $MachinePrecision]), $MachinePrecision], x]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -2.6999999999999998e57 or -1.2e19 < z < -7.50000000000000019e-6 or -1.8999999999999999e-61 < z < -2.7000000000000002e-68 or 4.1000000000000001e47 < z < 9.1999999999999996e85 or 3.2499999999999999e125 < z

   1. Initial program 75.7%

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

      1. associate-*l/ 71.3%

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

   3. Simplified 71.3%

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

   4. Taylor expanded in z around inf 69.1%

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

   if -2.6999999999999998e57 < z < -1.2e19

   1. Initial program 99.6%

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

      1. associate-*l/ 88.9%

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

   3. Simplified 88.9%

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

   4. Taylor expanded in x around 0 99.6%

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

      1. associate-*r/ 99.6%

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

   6. Simplified 99.6%

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

   7. Taylor expanded in y around 0 71.9%

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

      1. associate-*r/ 71.9%

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

      2. neg-mul-1 71.9%

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

   9. Simplified 71.9%

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

   10. Taylor expanded in z around 0 62.4%

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

       1. mul-1-neg 62.4%

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

       2. distribute-neg-frac 62.4%

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

   12. Simplified 62.4%

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

   if -7.50000000000000019e-6 < z < -1.8999999999999999e-61 or -1.8000000000000001e-150 < z < 4.1000000000000001e47

   1. Initial program 95.4%

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

      1. associate-*l/ 93.7%

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

   3. Simplified 93.7%

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

   4. Taylor expanded in z around 0 68.8%

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

      1. associate-/l* 70.8%

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

   6. Simplified 70.8%

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

   if -2.7000000000000002e-68 < z < -1.8000000000000001e-150

   1. Initial program 94.5%

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

      1. associate-*l/ 94.1%

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

   3. Simplified 94.1%

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

   4. Taylor expanded in t around inf 60.5%

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

      1. associate-/l* 57.5%

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

   6. Simplified 57.5%

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

   7. Taylor expanded in y around 0 44.0%

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

      1. mul-1-neg 44.0%

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

      2. associate-*l/ 46.7%

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

      3. distribute-rgt-neg-in 46.7%

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

   9. Simplified 46.7%

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

   if 9.1999999999999996e85 < z < 3.2499999999999999e125

   1. Initial program 80.8%

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

      1. associate-*l/ 53.2%

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

   3. Simplified 53.2%

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

   4. Taylor expanded in x around 0 80.8%

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

      1. associate-*r/ 99.7%

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

   6. Simplified 99.7%

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

   7. Taylor expanded in z around 0 51.9%

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

4. Final simplification 67.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.7 \cdot 10^{+57}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -1.2 \cdot 10^{+19}:\\ \;\;\;\;x \cdot \frac{-z}{t}\\ \mathbf{elif}\;z \leq -7.5 \cdot 10^{-6}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -1.9 \cdot 10^{-61}:\\ \;\;\;\;\frac{x}{\frac{t}{y}}\\ \mathbf{elif}\;z \leq -2.7 \cdot 10^{-68}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -1.8 \cdot 10^{-150}:\\ \;\;\;\;z \cdot \frac{-x}{t}\\ \mathbf{elif}\;z \leq 4.1 \cdot 10^{+47}:\\ \;\;\;\;\frac{x}{\frac{t}{y}}\\ \mathbf{elif}\;z \leq 9.2 \cdot 10^{+85}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 3.25 \cdot 10^{+125}:\\ \;\;\;\;x \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 4: 58.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{\frac{t}{y}}\\ \mathbf{if}\;z \leq -5.1 \cdot 10^{+57}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -3 \cdot 10^{+26}:\\ \;\;\;\;\frac{x}{\frac{-t}{z}}\\ \mathbf{elif}\;z \leq -7.5 \cdot 10^{-6}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -2.55 \cdot 10^{-61}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.05 \cdot 10^{-66}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -1.8 \cdot 10^{-150}:\\ \;\;\;\;z \cdot \frac{-x}{t}\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{+48}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{+83}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 3.25 \cdot 10^{+125}:\\ \;\;\;\;x \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ x (/ t y))))
   (if (<= z -5.1e+57)
     x
     (if (<= z -3e+26)
       (/ x (/ (- t) z))
       (if (<= z -7.5e-6)
         x
         (if (<= z -2.55e-61)
           t_1
           (if (<= z -1.05e-66)
             x
             (if (<= z -1.8e-150)
               (* z (/ (- x) t))
               (if (<= z 1.2e+48)
                 t_1
                 (if (<= z 6.5e+83)
                   x
                   (if (<= z 3.25e+125) (* x (/ y t)) x)))))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x / (t / y);
	double tmp;
	if (z <= -5.1e+57) {
		tmp = x;
	} else if (z <= -3e+26) {
		tmp = x / (-t / z);
	} else if (z <= -7.5e-6) {
		tmp = x;
	} else if (z <= -2.55e-61) {
		tmp = t_1;
	} else if (z <= -1.05e-66) {
		tmp = x;
	} else if (z <= -1.8e-150) {
		tmp = z * (-x / t);
	} else if (z <= 1.2e+48) {
		tmp = t_1;
	} else if (z <= 6.5e+83) {
		tmp = x;
	} else if (z <= 3.25e+125) {
		tmp = x * (y / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x / (t / y)
    if (z <= (-5.1d+57)) then
        tmp = x
    else if (z <= (-3d+26)) then
        tmp = x / (-t / z)
    else if (z <= (-7.5d-6)) then
        tmp = x
    else if (z <= (-2.55d-61)) then
        tmp = t_1
    else if (z <= (-1.05d-66)) then
        tmp = x
    else if (z <= (-1.8d-150)) then
        tmp = z * (-x / t)
    else if (z <= 1.2d+48) then
        tmp = t_1
    else if (z <= 6.5d+83) then
        tmp = x
    else if (z <= 3.25d+125) then
        tmp = x * (y / t)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x / (t / y);
	double tmp;
	if (z <= -5.1e+57) {
		tmp = x;
	} else if (z <= -3e+26) {
		tmp = x / (-t / z);
	} else if (z <= -7.5e-6) {
		tmp = x;
	} else if (z <= -2.55e-61) {
		tmp = t_1;
	} else if (z <= -1.05e-66) {
		tmp = x;
	} else if (z <= -1.8e-150) {
		tmp = z * (-x / t);
	} else if (z <= 1.2e+48) {
		tmp = t_1;
	} else if (z <= 6.5e+83) {
		tmp = x;
	} else if (z <= 3.25e+125) {
		tmp = x * (y / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x / (t / y)
	tmp = 0
	if z <= -5.1e+57:
		tmp = x
	elif z <= -3e+26:
		tmp = x / (-t / z)
	elif z <= -7.5e-6:
		tmp = x
	elif z <= -2.55e-61:
		tmp = t_1
	elif z <= -1.05e-66:
		tmp = x
	elif z <= -1.8e-150:
		tmp = z * (-x / t)
	elif z <= 1.2e+48:
		tmp = t_1
	elif z <= 6.5e+83:
		tmp = x
	elif z <= 3.25e+125:
		tmp = x * (y / t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x / Float64(t / y))
	tmp = 0.0
	if (z <= -5.1e+57)
		tmp = x;
	elseif (z <= -3e+26)
		tmp = Float64(x / Float64(Float64(-t) / z));
	elseif (z <= -7.5e-6)
		tmp = x;
	elseif (z <= -2.55e-61)
		tmp = t_1;
	elseif (z <= -1.05e-66)
		tmp = x;
	elseif (z <= -1.8e-150)
		tmp = Float64(z * Float64(Float64(-x) / t));
	elseif (z <= 1.2e+48)
		tmp = t_1;
	elseif (z <= 6.5e+83)
		tmp = x;
	elseif (z <= 3.25e+125)
		tmp = Float64(x * Float64(y / t));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x / (t / y);
	tmp = 0.0;
	if (z <= -5.1e+57)
		tmp = x;
	elseif (z <= -3e+26)
		tmp = x / (-t / z);
	elseif (z <= -7.5e-6)
		tmp = x;
	elseif (z <= -2.55e-61)
		tmp = t_1;
	elseif (z <= -1.05e-66)
		tmp = x;
	elseif (z <= -1.8e-150)
		tmp = z * (-x / t);
	elseif (z <= 1.2e+48)
		tmp = t_1;
	elseif (z <= 6.5e+83)
		tmp = x;
	elseif (z <= 3.25e+125)
		tmp = x * (y / t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x / N[(t / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -5.1e+57], x, If[LessEqual[z, -3e+26], N[(x / N[((-t) / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -7.5e-6], x, If[LessEqual[z, -2.55e-61], t$95$1, If[LessEqual[z, -1.05e-66], x, If[LessEqual[z, -1.8e-150], N[(z * N[((-x) / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.2e+48], t$95$1, If[LessEqual[z, 6.5e+83], x, If[LessEqual[z, 3.25e+125], N[(x * N[(y / t), $MachinePrecision]), $MachinePrecision], x]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -5.10000000000000023e57 or -2.99999999999999997e26 < z < -7.50000000000000019e-6 or -2.54999999999999984e-61 < z < -1.05e-66 or 1.2000000000000001e48 < z < 6.5000000000000003e83 or 3.2499999999999999e125 < z

   1. Initial program 75.7%

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

      1. associate-*l/ 71.3%

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

   3. Simplified 71.3%

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

   4. Taylor expanded in z around inf 69.1%

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

   if -5.10000000000000023e57 < z < -2.99999999999999997e26

   1. Initial program 99.6%

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

      1. associate-*l/ 88.9%

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

   3. Simplified 88.9%

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

   4. Taylor expanded in t around inf 61.3%

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

      1. associate-/l* 61.8%

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

   6. Simplified 61.8%

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

   7. Taylor expanded in y around 0 62.6%

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

      1. associate-*r/ 62.6%

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

      2. neg-mul-1 62.6%

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

   9. Simplified 62.6%

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

   if -7.50000000000000019e-6 < z < -2.54999999999999984e-61 or -1.8000000000000001e-150 < z < 1.2000000000000001e48

   1. Initial program 95.4%

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

      1. associate-*l/ 93.7%

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

   3. Simplified 93.7%

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

   4. Taylor expanded in z around 0 68.8%

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

      1. associate-/l* 70.8%

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

   6. Simplified 70.8%

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

   if -1.05e-66 < z < -1.8000000000000001e-150

   1. Initial program 94.5%

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

      1. associate-*l/ 94.1%

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

   3. Simplified 94.1%

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

   4. Taylor expanded in t around inf 60.5%

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

      1. associate-/l* 57.5%

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

   6. Simplified 57.5%

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

   7. Taylor expanded in y around 0 44.0%

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

      1. mul-1-neg 44.0%

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

      2. associate-*l/ 46.7%

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

      3. distribute-rgt-neg-in 46.7%

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

   9. Simplified 46.7%

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

   if 6.5000000000000003e83 < z < 3.2499999999999999e125

   1. Initial program 80.8%

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

      1. associate-*l/ 53.2%

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

   3. Simplified 53.2%

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

   4. Taylor expanded in x around 0 80.8%

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

      1. associate-*r/ 99.7%

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

   6. Simplified 99.7%

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

   7. Taylor expanded in z around 0 51.9%

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

4. Final simplification 67.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.1 \cdot 10^{+57}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -3 \cdot 10^{+26}:\\ \;\;\;\;\frac{x}{\frac{-t}{z}}\\ \mathbf{elif}\;z \leq -7.5 \cdot 10^{-6}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -2.55 \cdot 10^{-61}:\\ \;\;\;\;\frac{x}{\frac{t}{y}}\\ \mathbf{elif}\;z \leq -1.05 \cdot 10^{-66}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -1.8 \cdot 10^{-150}:\\ \;\;\;\;z \cdot \frac{-x}{t}\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{+48}:\\ \;\;\;\;\frac{x}{\frac{t}{y}}\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{+83}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 3.25 \cdot 10^{+125}:\\ \;\;\;\;x \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 5: 58.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{\frac{t}{y}}\\ \mathbf{if}\;z \leq -2.4 \cdot 10^{+57}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -1.9 \cdot 10^{+21}:\\ \;\;\;\;\frac{x}{\frac{-t}{z}}\\ \mathbf{elif}\;z \leq -7.5 \cdot 10^{-6}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -1.9 \cdot 10^{-61}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.16 \cdot 10^{-66}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -1.8 \cdot 10^{-150}:\\ \;\;\;\;\frac{z}{\frac{-t}{x}}\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{+47}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{+84}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 3.25 \cdot 10^{+125}:\\ \;\;\;\;x \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ x (/ t y))))
   (if (<= z -2.4e+57)
     x
     (if (<= z -1.9e+21)
       (/ x (/ (- t) z))
       (if (<= z -7.5e-6)
         x
         (if (<= z -1.9e-61)
           t_1
           (if (<= z -1.16e-66)
             x
             (if (<= z -1.8e-150)
               (/ z (/ (- t) x))
               (if (<= z 3.6e+47)
                 t_1
                 (if (<= z 6.5e+84)
                   x
                   (if (<= z 3.25e+125) (* x (/ y t)) x)))))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x / (t / y);
	double tmp;
	if (z <= -2.4e+57) {
		tmp = x;
	} else if (z <= -1.9e+21) {
		tmp = x / (-t / z);
	} else if (z <= -7.5e-6) {
		tmp = x;
	} else if (z <= -1.9e-61) {
		tmp = t_1;
	} else if (z <= -1.16e-66) {
		tmp = x;
	} else if (z <= -1.8e-150) {
		tmp = z / (-t / x);
	} else if (z <= 3.6e+47) {
		tmp = t_1;
	} else if (z <= 6.5e+84) {
		tmp = x;
	} else if (z <= 3.25e+125) {
		tmp = x * (y / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x / (t / y)
    if (z <= (-2.4d+57)) then
        tmp = x
    else if (z <= (-1.9d+21)) then
        tmp = x / (-t / z)
    else if (z <= (-7.5d-6)) then
        tmp = x
    else if (z <= (-1.9d-61)) then
        tmp = t_1
    else if (z <= (-1.16d-66)) then
        tmp = x
    else if (z <= (-1.8d-150)) then
        tmp = z / (-t / x)
    else if (z <= 3.6d+47) then
        tmp = t_1
    else if (z <= 6.5d+84) then
        tmp = x
    else if (z <= 3.25d+125) then
        tmp = x * (y / t)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x / (t / y);
	double tmp;
	if (z <= -2.4e+57) {
		tmp = x;
	} else if (z <= -1.9e+21) {
		tmp = x / (-t / z);
	} else if (z <= -7.5e-6) {
		tmp = x;
	} else if (z <= -1.9e-61) {
		tmp = t_1;
	} else if (z <= -1.16e-66) {
		tmp = x;
	} else if (z <= -1.8e-150) {
		tmp = z / (-t / x);
	} else if (z <= 3.6e+47) {
		tmp = t_1;
	} else if (z <= 6.5e+84) {
		tmp = x;
	} else if (z <= 3.25e+125) {
		tmp = x * (y / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x / (t / y)
	tmp = 0
	if z <= -2.4e+57:
		tmp = x
	elif z <= -1.9e+21:
		tmp = x / (-t / z)
	elif z <= -7.5e-6:
		tmp = x
	elif z <= -1.9e-61:
		tmp = t_1
	elif z <= -1.16e-66:
		tmp = x
	elif z <= -1.8e-150:
		tmp = z / (-t / x)
	elif z <= 3.6e+47:
		tmp = t_1
	elif z <= 6.5e+84:
		tmp = x
	elif z <= 3.25e+125:
		tmp = x * (y / t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x / Float64(t / y))
	tmp = 0.0
	if (z <= -2.4e+57)
		tmp = x;
	elseif (z <= -1.9e+21)
		tmp = Float64(x / Float64(Float64(-t) / z));
	elseif (z <= -7.5e-6)
		tmp = x;
	elseif (z <= -1.9e-61)
		tmp = t_1;
	elseif (z <= -1.16e-66)
		tmp = x;
	elseif (z <= -1.8e-150)
		tmp = Float64(z / Float64(Float64(-t) / x));
	elseif (z <= 3.6e+47)
		tmp = t_1;
	elseif (z <= 6.5e+84)
		tmp = x;
	elseif (z <= 3.25e+125)
		tmp = Float64(x * Float64(y / t));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x / (t / y);
	tmp = 0.0;
	if (z <= -2.4e+57)
		tmp = x;
	elseif (z <= -1.9e+21)
		tmp = x / (-t / z);
	elseif (z <= -7.5e-6)
		tmp = x;
	elseif (z <= -1.9e-61)
		tmp = t_1;
	elseif (z <= -1.16e-66)
		tmp = x;
	elseif (z <= -1.8e-150)
		tmp = z / (-t / x);
	elseif (z <= 3.6e+47)
		tmp = t_1;
	elseif (z <= 6.5e+84)
		tmp = x;
	elseif (z <= 3.25e+125)
		tmp = x * (y / t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x / N[(t / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.4e+57], x, If[LessEqual[z, -1.9e+21], N[(x / N[((-t) / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -7.5e-6], x, If[LessEqual[z, -1.9e-61], t$95$1, If[LessEqual[z, -1.16e-66], x, If[LessEqual[z, -1.8e-150], N[(z / N[((-t) / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.6e+47], t$95$1, If[LessEqual[z, 6.5e+84], x, If[LessEqual[z, 3.25e+125], N[(x * N[(y / t), $MachinePrecision]), $MachinePrecision], x]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -2.40000000000000005e57 or -1.9e21 < z < -7.50000000000000019e-6 or -1.8999999999999999e-61 < z < -1.16000000000000002e-66 or 3.60000000000000008e47 < z < 6.50000000000000027e84 or 3.2499999999999999e125 < z

   1. Initial program 75.7%

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

      1. associate-*l/ 71.3%

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

   3. Simplified 71.3%

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

   4. Taylor expanded in z around inf 69.1%

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

   if -2.40000000000000005e57 < z < -1.9e21

   1. Initial program 99.6%

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

      1. associate-*l/ 88.9%

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

   3. Simplified 88.9%

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

   4. Taylor expanded in t around inf 61.3%

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

      1. associate-/l* 61.8%

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

   6. Simplified 61.8%

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

   7. Taylor expanded in y around 0 62.6%

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

      1. associate-*r/ 62.6%

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

      2. neg-mul-1 62.6%

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

   9. Simplified 62.6%

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

   if -7.50000000000000019e-6 < z < -1.8999999999999999e-61 or -1.8000000000000001e-150 < z < 3.60000000000000008e47

   1. Initial program 95.4%

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

      1. associate-*l/ 93.7%

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

   3. Simplified 93.7%

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

   4. Taylor expanded in z around 0 68.8%

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

      1. associate-/l* 70.8%

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

   6. Simplified 70.8%

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

   if -1.16000000000000002e-66 < z < -1.8000000000000001e-150

   1. Initial program 94.5%

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

      1. associate-*l/ 94.1%

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

   3. Simplified 94.1%

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

   4. Taylor expanded in x around 0 94.5%

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

      1. associate-*r/ 99.1%

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

   6. Simplified 99.1%

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

   7. Taylor expanded in y around 0 48.3%

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

      1. associate-*r/ 48.3%

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

      2. neg-mul-1 48.3%

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

   9. Simplified 48.3%

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

   10. Taylor expanded in z around 0 46.1%

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

       1. mul-1-neg 46.1%

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

       2. distribute-neg-frac 46.1%

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

   12. Simplified 46.1%

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

       1. *-commutative 46.1%

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

       2. frac-2neg 46.1%

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

       3. remove-double-neg 46.1%

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

       4. associate-*l/ 44.0%

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

   14. Applied egg-rr 44.0%

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

       1. associate-/l* 46.7%

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

       2. distribute-frac-neg 46.7%

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

   16. Simplified 46.7%

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

   if 6.50000000000000027e84 < z < 3.2499999999999999e125

   1. Initial program 80.8%

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

      1. associate-*l/ 53.2%

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

   3. Simplified 53.2%

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

   4. Taylor expanded in x around 0 80.8%

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

      1. associate-*r/ 99.7%

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

   6. Simplified 99.7%

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

   7. Taylor expanded in z around 0 51.9%

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

4. Final simplification 67.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.4 \cdot 10^{+57}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -1.9 \cdot 10^{+21}:\\ \;\;\;\;\frac{x}{\frac{-t}{z}}\\ \mathbf{elif}\;z \leq -7.5 \cdot 10^{-6}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -1.9 \cdot 10^{-61}:\\ \;\;\;\;\frac{x}{\frac{t}{y}}\\ \mathbf{elif}\;z \leq -1.16 \cdot 10^{-66}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -1.8 \cdot 10^{-150}:\\ \;\;\;\;\frac{z}{\frac{-t}{x}}\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{+47}:\\ \;\;\;\;\frac{x}{\frac{t}{y}}\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{+84}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 3.25 \cdot 10^{+125}:\\ \;\;\;\;x \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 6: 66.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{y}{t - z}\\ \mathbf{if}\;z \leq -6 \cdot 10^{+57}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -6 \cdot 10^{+23}:\\ \;\;\;\;\frac{x}{\frac{-t}{z}}\\ \mathbf{elif}\;z \leq -680000000:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -8.2 \cdot 10^{-104}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -6.6 \cdot 10^{-280}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{t}\\ \mathbf{elif}\;z \leq 6.6 \cdot 10^{+48} \lor \neg \left(z \leq 7 \cdot 10^{+84}\right) \land z \leq 1.8 \cdot 10^{+128}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (/ y (- t z)))))
   (if (<= z -6e+57)
     x
     (if (<= z -6e+23)
       (/ x (/ (- t) z))
       (if (<= z -680000000.0)
         x
         (if (<= z -8.2e-104)
           t_1
           (if (<= z -6.6e-280)
             (* (- y z) (/ x t))
             (if (or (<= z 6.6e+48) (and (not (<= z 7e+84)) (<= z 1.8e+128)))
               t_1
               x))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (y / (t - z));
	double tmp;
	if (z <= -6e+57) {
		tmp = x;
	} else if (z <= -6e+23) {
		tmp = x / (-t / z);
	} else if (z <= -680000000.0) {
		tmp = x;
	} else if (z <= -8.2e-104) {
		tmp = t_1;
	} else if (z <= -6.6e-280) {
		tmp = (y - z) * (x / t);
	} else if ((z <= 6.6e+48) || (!(z <= 7e+84) && (z <= 1.8e+128))) {
		tmp = t_1;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (y / (t - z))
    if (z <= (-6d+57)) then
        tmp = x
    else if (z <= (-6d+23)) then
        tmp = x / (-t / z)
    else if (z <= (-680000000.0d0)) then
        tmp = x
    else if (z <= (-8.2d-104)) then
        tmp = t_1
    else if (z <= (-6.6d-280)) then
        tmp = (y - z) * (x / t)
    else if ((z <= 6.6d+48) .or. (.not. (z <= 7d+84)) .and. (z <= 1.8d+128)) then
        tmp = t_1
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x * (y / (t - z));
	double tmp;
	if (z <= -6e+57) {
		tmp = x;
	} else if (z <= -6e+23) {
		tmp = x / (-t / z);
	} else if (z <= -680000000.0) {
		tmp = x;
	} else if (z <= -8.2e-104) {
		tmp = t_1;
	} else if (z <= -6.6e-280) {
		tmp = (y - z) * (x / t);
	} else if ((z <= 6.6e+48) || (!(z <= 7e+84) && (z <= 1.8e+128))) {
		tmp = t_1;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (y / (t - z))
	tmp = 0
	if z <= -6e+57:
		tmp = x
	elif z <= -6e+23:
		tmp = x / (-t / z)
	elif z <= -680000000.0:
		tmp = x
	elif z <= -8.2e-104:
		tmp = t_1
	elif z <= -6.6e-280:
		tmp = (y - z) * (x / t)
	elif (z <= 6.6e+48) or (not (z <= 7e+84) and (z <= 1.8e+128)):
		tmp = t_1
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(y / Float64(t - z)))
	tmp = 0.0
	if (z <= -6e+57)
		tmp = x;
	elseif (z <= -6e+23)
		tmp = Float64(x / Float64(Float64(-t) / z));
	elseif (z <= -680000000.0)
		tmp = x;
	elseif (z <= -8.2e-104)
		tmp = t_1;
	elseif (z <= -6.6e-280)
		tmp = Float64(Float64(y - z) * Float64(x / t));
	elseif ((z <= 6.6e+48) || (!(z <= 7e+84) && (z <= 1.8e+128)))
		tmp = t_1;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (y / (t - z));
	tmp = 0.0;
	if (z <= -6e+57)
		tmp = x;
	elseif (z <= -6e+23)
		tmp = x / (-t / z);
	elseif (z <= -680000000.0)
		tmp = x;
	elseif (z <= -8.2e-104)
		tmp = t_1;
	elseif (z <= -6.6e-280)
		tmp = (y - z) * (x / t);
	elseif ((z <= 6.6e+48) || (~((z <= 7e+84)) && (z <= 1.8e+128)))
		tmp = t_1;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(y / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -6e+57], x, If[LessEqual[z, -6e+23], N[(x / N[((-t) / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -680000000.0], x, If[LessEqual[z, -8.2e-104], t$95$1, If[LessEqual[z, -6.6e-280], N[(N[(y - z), $MachinePrecision] * N[(x / t), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, 6.6e+48], And[N[Not[LessEqual[z, 7e+84]], $MachinePrecision], LessEqual[z, 1.8e+128]]], t$95$1, x]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -5.9999999999999999e57 or -6.0000000000000002e23 < z < -6.8e8 or 6.60000000000000045e48 < z < 6.9999999999999998e84 or 1.80000000000000014e128 < z

   1. Initial program 74.3%

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

      1. associate-*l/ 69.6%

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

   3. Simplified 69.6%

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

   4. Taylor expanded in z around inf 70.4%

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

   if -5.9999999999999999e57 < z < -6.0000000000000002e23

   1. Initial program 99.6%

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

      1. associate-*l/ 88.9%

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

   3. Simplified 88.9%

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

   4. Taylor expanded in t around inf 61.3%

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

      1. associate-/l* 61.8%

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

   6. Simplified 61.8%

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

   7. Taylor expanded in y around 0 62.6%

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

      1. associate-*r/ 62.6%

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

      2. neg-mul-1 62.6%

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

   9. Simplified 62.6%

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

   if -6.8e8 < z < -8.19999999999999968e-104 or -6.59999999999999982e-280 < z < 6.60000000000000045e48 or 6.9999999999999998e84 < z < 1.80000000000000014e128

   1. Initial program 93.8%

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

      1. associate-*l/ 90.3%

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

   3. Simplified 90.3%

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

   4. Taylor expanded in y around inf 77.0%

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

      1. *-commutative 77.0%

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

      2. associate-/l* 73.8%

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

      3. associate-/r/ 82.0%

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

   6. Simplified 82.0%

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

   if -8.19999999999999968e-104 < z < -6.59999999999999982e-280

   1. Initial program 96.4%

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

      1. associate-*l/ 94.5%

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

   3. Simplified 94.5%

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

   4. Taylor expanded in t around inf 84.9%

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

      1. associate-/l* 77.2%

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

      2. associate-/r/ 84.4%

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

   6. Simplified 84.4%

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

4. Final simplification 77.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6 \cdot 10^{+57}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -6 \cdot 10^{+23}:\\ \;\;\;\;\frac{x}{\frac{-t}{z}}\\ \mathbf{elif}\;z \leq -680000000:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -8.2 \cdot 10^{-104}:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \mathbf{elif}\;z \leq -6.6 \cdot 10^{-280}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{t}\\ \mathbf{elif}\;z \leq 6.6 \cdot 10^{+48} \lor \neg \left(z \leq 7 \cdot 10^{+84}\right) \land z \leq 1.8 \cdot 10^{+128}:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 7: 65.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{x}{t - z}\\ t_2 := x \cdot \frac{y - z}{t}\\ \mathbf{if}\;z \leq -3.8 \cdot 10^{+57}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -2.6 \cdot 10^{+19}:\\ \;\;\;\;\frac{x}{\frac{-t}{z}}\\ \mathbf{elif}\;z \leq -680000000:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -5 \cdot 10^{-98}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{-299}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 5.4 \cdot 10^{+47}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.55 \cdot 10^{+83}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 4 \cdot 10^{+125}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (/ x (- t z)))) (t_2 (* x (/ (- y z) t))))
   (if (<= z -3.8e+57)
     x
     (if (<= z -2.6e+19)
       (/ x (/ (- t) z))
       (if (<= z -680000000.0)
         x
         (if (<= z -5e-98)
           t_1
           (if (<= z 1.05e-299)
             t_2
             (if (<= z 5.4e+47)
               t_1
               (if (<= z 1.55e+83) x (if (<= z 4e+125) t_2 x))))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = y * (x / (t - z));
	double t_2 = x * ((y - z) / t);
	double tmp;
	if (z <= -3.8e+57) {
		tmp = x;
	} else if (z <= -2.6e+19) {
		tmp = x / (-t / z);
	} else if (z <= -680000000.0) {
		tmp = x;
	} else if (z <= -5e-98) {
		tmp = t_1;
	} else if (z <= 1.05e-299) {
		tmp = t_2;
	} else if (z <= 5.4e+47) {
		tmp = t_1;
	} else if (z <= 1.55e+83) {
		tmp = x;
	} else if (z <= 4e+125) {
		tmp = t_2;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = y * (x / (t - z))
    t_2 = x * ((y - z) / t)
    if (z <= (-3.8d+57)) then
        tmp = x
    else if (z <= (-2.6d+19)) then
        tmp = x / (-t / z)
    else if (z <= (-680000000.0d0)) then
        tmp = x
    else if (z <= (-5d-98)) then
        tmp = t_1
    else if (z <= 1.05d-299) then
        tmp = t_2
    else if (z <= 5.4d+47) then
        tmp = t_1
    else if (z <= 1.55d+83) then
        tmp = x
    else if (z <= 4d+125) then
        tmp = t_2
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = y * (x / (t - z));
	double t_2 = x * ((y - z) / t);
	double tmp;
	if (z <= -3.8e+57) {
		tmp = x;
	} else if (z <= -2.6e+19) {
		tmp = x / (-t / z);
	} else if (z <= -680000000.0) {
		tmp = x;
	} else if (z <= -5e-98) {
		tmp = t_1;
	} else if (z <= 1.05e-299) {
		tmp = t_2;
	} else if (z <= 5.4e+47) {
		tmp = t_1;
	} else if (z <= 1.55e+83) {
		tmp = x;
	} else if (z <= 4e+125) {
		tmp = t_2;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = y * (x / (t - z))
	t_2 = x * ((y - z) / t)
	tmp = 0
	if z <= -3.8e+57:
		tmp = x
	elif z <= -2.6e+19:
		tmp = x / (-t / z)
	elif z <= -680000000.0:
		tmp = x
	elif z <= -5e-98:
		tmp = t_1
	elif z <= 1.05e-299:
		tmp = t_2
	elif z <= 5.4e+47:
		tmp = t_1
	elif z <= 1.55e+83:
		tmp = x
	elif z <= 4e+125:
		tmp = t_2
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(y * Float64(x / Float64(t - z)))
	t_2 = Float64(x * Float64(Float64(y - z) / t))
	tmp = 0.0
	if (z <= -3.8e+57)
		tmp = x;
	elseif (z <= -2.6e+19)
		tmp = Float64(x / Float64(Float64(-t) / z));
	elseif (z <= -680000000.0)
		tmp = x;
	elseif (z <= -5e-98)
		tmp = t_1;
	elseif (z <= 1.05e-299)
		tmp = t_2;
	elseif (z <= 5.4e+47)
		tmp = t_1;
	elseif (z <= 1.55e+83)
		tmp = x;
	elseif (z <= 4e+125)
		tmp = t_2;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = y * (x / (t - z));
	t_2 = x * ((y - z) / t);
	tmp = 0.0;
	if (z <= -3.8e+57)
		tmp = x;
	elseif (z <= -2.6e+19)
		tmp = x / (-t / z);
	elseif (z <= -680000000.0)
		tmp = x;
	elseif (z <= -5e-98)
		tmp = t_1;
	elseif (z <= 1.05e-299)
		tmp = t_2;
	elseif (z <= 5.4e+47)
		tmp = t_1;
	elseif (z <= 1.55e+83)
		tmp = x;
	elseif (z <= 4e+125)
		tmp = t_2;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(y * N[(x / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(N[(y - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.8e+57], x, If[LessEqual[z, -2.6e+19], N[(x / N[((-t) / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -680000000.0], x, If[LessEqual[z, -5e-98], t$95$1, If[LessEqual[z, 1.05e-299], t$95$2, If[LessEqual[z, 5.4e+47], t$95$1, If[LessEqual[z, 1.55e+83], x, If[LessEqual[z, 4e+125], t$95$2, x]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -3.7999999999999999e57 or -2.6e19 < z < -6.8e8 or 5.39999999999999991e47 < z < 1.54999999999999996e83 or 3.9999999999999997e125 < z

   1. Initial program 74.6%

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

      1. associate-*l/ 69.9%

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

   3. Simplified 69.9%

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

   4. Taylor expanded in z around inf 69.7%

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

   if -3.7999999999999999e57 < z < -2.6e19

   1. Initial program 99.6%

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

      1. associate-*l/ 88.9%

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

   3. Simplified 88.9%

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

   4. Taylor expanded in t around inf 61.3%

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

      1. associate-/l* 61.8%

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

   6. Simplified 61.8%

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

   7. Taylor expanded in y around 0 62.6%

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

      1. associate-*r/ 62.6%

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

      2. neg-mul-1 62.6%

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

   9. Simplified 62.6%

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

   if -6.8e8 < z < -5.00000000000000018e-98 or 1.05000000000000005e-299 < z < 5.39999999999999991e47

   1. Initial program 94.5%

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

      1. associate-*l/ 96.2%

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

   3. Simplified 96.2%

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

   4. Taylor expanded in y around inf 75.7%

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

      1. associate-*l/ 78.3%

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

      2. *-commutative 78.3%

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

   6. Simplified 78.3%

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

   if -5.00000000000000018e-98 < z < 1.05000000000000005e-299 or 1.54999999999999996e83 < z < 3.9999999999999997e125

   1. Initial program 94.2%

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

      1. associate-*l/ 83.0%

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

   3. Simplified 83.0%

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

   4. Taylor expanded in x around 0 94.2%

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

      1. associate-*r/ 94.5%

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

   6. Simplified 94.5%

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

   7. Taylor expanded in t around inf 81.2%

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

4. Final simplification 75.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.8 \cdot 10^{+57}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -2.6 \cdot 10^{+19}:\\ \;\;\;\;\frac{x}{\frac{-t}{z}}\\ \mathbf{elif}\;z \leq -680000000:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -5 \cdot 10^{-98}:\\ \;\;\;\;y \cdot \frac{x}{t - z}\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{-299}:\\ \;\;\;\;x \cdot \frac{y - z}{t}\\ \mathbf{elif}\;z \leq 5.4 \cdot 10^{+47}:\\ \;\;\;\;y \cdot \frac{x}{t - z}\\ \mathbf{elif}\;z \leq 1.55 \cdot 10^{+83}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 4 \cdot 10^{+125}:\\ \;\;\;\;x \cdot \frac{y - z}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 8: 65.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{x}{t - z}\\ \mathbf{if}\;z \leq -4.5 \cdot 10^{+57}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -2.3 \cdot 10^{+26}:\\ \;\;\;\;\frac{x}{\frac{-t}{z}}\\ \mathbf{elif}\;z \leq -680000000:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -3.8 \cdot 10^{-106}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 6.8 \cdot 10^{-57}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{t}\\ \mathbf{elif}\;z \leq 6.6 \cdot 10^{+48}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{+82}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 7.8 \cdot 10^{+126}:\\ \;\;\;\;x \cdot \frac{y - z}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (/ x (- t z)))))
   (if (<= z -4.5e+57)
     x
     (if (<= z -2.3e+26)
       (/ x (/ (- t) z))
       (if (<= z -680000000.0)
         x
         (if (<= z -3.8e-106)
           t_1
           (if (<= z 6.8e-57)
             (* (- y z) (/ x t))
             (if (<= z 6.6e+48)
               t_1
               (if (<= z 1.15e+82)
                 x
                 (if (<= z 7.8e+126) (* x (/ (- y z) t)) x))))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = y * (x / (t - z));
	double tmp;
	if (z <= -4.5e+57) {
		tmp = x;
	} else if (z <= -2.3e+26) {
		tmp = x / (-t / z);
	} else if (z <= -680000000.0) {
		tmp = x;
	} else if (z <= -3.8e-106) {
		tmp = t_1;
	} else if (z <= 6.8e-57) {
		tmp = (y - z) * (x / t);
	} else if (z <= 6.6e+48) {
		tmp = t_1;
	} else if (z <= 1.15e+82) {
		tmp = x;
	} else if (z <= 7.8e+126) {
		tmp = x * ((y - z) / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * (x / (t - z))
    if (z <= (-4.5d+57)) then
        tmp = x
    else if (z <= (-2.3d+26)) then
        tmp = x / (-t / z)
    else if (z <= (-680000000.0d0)) then
        tmp = x
    else if (z <= (-3.8d-106)) then
        tmp = t_1
    else if (z <= 6.8d-57) then
        tmp = (y - z) * (x / t)
    else if (z <= 6.6d+48) then
        tmp = t_1
    else if (z <= 1.15d+82) then
        tmp = x
    else if (z <= 7.8d+126) then
        tmp = x * ((y - z) / t)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = y * (x / (t - z));
	double tmp;
	if (z <= -4.5e+57) {
		tmp = x;
	} else if (z <= -2.3e+26) {
		tmp = x / (-t / z);
	} else if (z <= -680000000.0) {
		tmp = x;
	} else if (z <= -3.8e-106) {
		tmp = t_1;
	} else if (z <= 6.8e-57) {
		tmp = (y - z) * (x / t);
	} else if (z <= 6.6e+48) {
		tmp = t_1;
	} else if (z <= 1.15e+82) {
		tmp = x;
	} else if (z <= 7.8e+126) {
		tmp = x * ((y - z) / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = y * (x / (t - z))
	tmp = 0
	if z <= -4.5e+57:
		tmp = x
	elif z <= -2.3e+26:
		tmp = x / (-t / z)
	elif z <= -680000000.0:
		tmp = x
	elif z <= -3.8e-106:
		tmp = t_1
	elif z <= 6.8e-57:
		tmp = (y - z) * (x / t)
	elif z <= 6.6e+48:
		tmp = t_1
	elif z <= 1.15e+82:
		tmp = x
	elif z <= 7.8e+126:
		tmp = x * ((y - z) / t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(y * Float64(x / Float64(t - z)))
	tmp = 0.0
	if (z <= -4.5e+57)
		tmp = x;
	elseif (z <= -2.3e+26)
		tmp = Float64(x / Float64(Float64(-t) / z));
	elseif (z <= -680000000.0)
		tmp = x;
	elseif (z <= -3.8e-106)
		tmp = t_1;
	elseif (z <= 6.8e-57)
		tmp = Float64(Float64(y - z) * Float64(x / t));
	elseif (z <= 6.6e+48)
		tmp = t_1;
	elseif (z <= 1.15e+82)
		tmp = x;
	elseif (z <= 7.8e+126)
		tmp = Float64(x * Float64(Float64(y - z) / t));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = y * (x / (t - z));
	tmp = 0.0;
	if (z <= -4.5e+57)
		tmp = x;
	elseif (z <= -2.3e+26)
		tmp = x / (-t / z);
	elseif (z <= -680000000.0)
		tmp = x;
	elseif (z <= -3.8e-106)
		tmp = t_1;
	elseif (z <= 6.8e-57)
		tmp = (y - z) * (x / t);
	elseif (z <= 6.6e+48)
		tmp = t_1;
	elseif (z <= 1.15e+82)
		tmp = x;
	elseif (z <= 7.8e+126)
		tmp = x * ((y - z) / t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(y * N[(x / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -4.5e+57], x, If[LessEqual[z, -2.3e+26], N[(x / N[((-t) / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -680000000.0], x, If[LessEqual[z, -3.8e-106], t$95$1, If[LessEqual[z, 6.8e-57], N[(N[(y - z), $MachinePrecision] * N[(x / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6.6e+48], t$95$1, If[LessEqual[z, 1.15e+82], x, If[LessEqual[z, 7.8e+126], N[(x * N[(N[(y - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], x]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -4.49999999999999996e57 or -2.3000000000000001e26 < z < -6.8e8 or 6.60000000000000045e48 < z < 1.14999999999999994e82 or 7.79999999999999986e126 < z

   1. Initial program 74.6%

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

      1. associate-*l/ 69.9%

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

   3. Simplified 69.9%

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

   4. Taylor expanded in z around inf 69.7%

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

   if -4.49999999999999996e57 < z < -2.3000000000000001e26

   1. Initial program 99.6%

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

      1. associate-*l/ 88.9%

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

   3. Simplified 88.9%

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

   4. Taylor expanded in t around inf 61.3%

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

      1. associate-/l* 61.8%

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

   6. Simplified 61.8%

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

   7. Taylor expanded in y around 0 62.6%

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

      1. associate-*r/ 62.6%

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

      2. neg-mul-1 62.6%

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

   9. Simplified 62.6%

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

   if -6.8e8 < z < -3.7999999999999999e-106 or 6.80000000000000032e-57 < z < 6.60000000000000045e48

   1. Initial program 90.6%

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

      1. associate-*l/ 92.0%

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

   3. Simplified 92.0%

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

   4. Taylor expanded in y around inf 72.6%

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

      1. associate-*l/ 76.8%

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

      2. *-commutative 76.8%

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

   6. Simplified 76.8%

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

   if -3.7999999999999999e-106 < z < 6.80000000000000032e-57

   1. Initial program 96.8%

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

      1. associate-*l/ 94.6%

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

   3. Simplified 94.6%

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

   4. Taylor expanded in t around inf 81.9%

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

      1. associate-/l* 78.6%

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

      2. associate-/r/ 81.0%

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

   6. Simplified 81.0%

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

   if 1.14999999999999994e82 < z < 7.79999999999999986e126

   1. Initial program 80.8%

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

      1. associate-*l/ 53.2%

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

   3. Simplified 53.2%

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

   4. Taylor expanded in x around 0 80.8%

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

      1. associate-*r/ 99.7%

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

   6. Simplified 99.7%

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

   7. Taylor expanded in t around inf 70.6%

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

4. Final simplification 75.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.5 \cdot 10^{+57}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -2.3 \cdot 10^{+26}:\\ \;\;\;\;\frac{x}{\frac{-t}{z}}\\ \mathbf{elif}\;z \leq -680000000:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -3.8 \cdot 10^{-106}:\\ \;\;\;\;y \cdot \frac{x}{t - z}\\ \mathbf{elif}\;z \leq 6.8 \cdot 10^{-57}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{t}\\ \mathbf{elif}\;z \leq 6.6 \cdot 10^{+48}:\\ \;\;\;\;y \cdot \frac{x}{t - z}\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{+82}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 7.8 \cdot 10^{+126}:\\ \;\;\;\;x \cdot \frac{y - z}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 9: 66.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6 \cdot 10^{+57}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 6.6 \cdot 10^{+48} \lor \neg \left(z \leq 3.8 \cdot 10^{+85}\right) \land z \leq 4.3 \cdot 10^{+125}:\\ \;\;\;\;x \cdot \frac{y - z}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -6e+57)
   x
   (if (or (<= z 6.6e+48) (and (not (<= z 3.8e+85)) (<= z 4.3e+125)))
     (* x (/ (- y z) t))
     x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -6e+57) {
		tmp = x;
	} else if ((z <= 6.6e+48) || (!(z <= 3.8e+85) && (z <= 4.3e+125))) {
		tmp = x * ((y - z) / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-6d+57)) then
        tmp = x
    else if ((z <= 6.6d+48) .or. (.not. (z <= 3.8d+85)) .and. (z <= 4.3d+125)) then
        tmp = x * ((y - z) / t)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -6e+57) {
		tmp = x;
	} else if ((z <= 6.6e+48) || (!(z <= 3.8e+85) && (z <= 4.3e+125))) {
		tmp = x * ((y - z) / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -6e+57:
		tmp = x
	elif (z <= 6.6e+48) or (not (z <= 3.8e+85) and (z <= 4.3e+125)):
		tmp = x * ((y - z) / t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -6e+57)
		tmp = x;
	elseif ((z <= 6.6e+48) || (!(z <= 3.8e+85) && (z <= 4.3e+125)))
		tmp = Float64(x * Float64(Float64(y - z) / t));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -6e+57)
		tmp = x;
	elseif ((z <= 6.6e+48) || (~((z <= 3.8e+85)) && (z <= 4.3e+125)))
		tmp = x * ((y - z) / t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -6e+57], x, If[Or[LessEqual[z, 6.6e+48], And[N[Not[LessEqual[z, 3.8e+85]], $MachinePrecision], LessEqual[z, 4.3e+125]]], N[(x * N[(N[(y - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if z < -5.9999999999999999e57 or 6.60000000000000045e48 < z < 3.79999999999999992e85 or 4.30000000000000035e125 < z

   1. Initial program 73.3%

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

      1. associate-*l/ 68.4%

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

   3. Simplified 68.4%

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

   4. Taylor expanded in z around inf 69.2%

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

   if -5.9999999999999999e57 < z < 6.60000000000000045e48 or 3.79999999999999992e85 < z < 4.30000000000000035e125

   1. Initial program 94.8%

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

      1. associate-*l/ 91.4%

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

   3. Simplified 91.4%

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

   4. Taylor expanded in x around 0 94.8%

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

      1. associate-*r/ 96.4%

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

   6. Simplified 96.4%

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

   7. Taylor expanded in t around inf 71.1%

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

4. Final simplification 70.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6 \cdot 10^{+57}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 6.6 \cdot 10^{+48} \lor \neg \left(z \leq 3.8 \cdot 10^{+85}\right) \land z \leq 4.3 \cdot 10^{+125}:\\ \;\;\;\;x \cdot \frac{y - z}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 10: 60.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7.5 \cdot 10^{-6}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{+47} \lor \neg \left(z \leq 1.35 \cdot 10^{+83}\right) \land z \leq 3.25 \cdot 10^{+125}:\\ \;\;\;\;x \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -7.5e-6)
   x
   (if (or (<= z 1.35e+47) (and (not (<= z 1.35e+83)) (<= z 3.25e+125)))
     (* x (/ y t))
     x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -7.5e-6) {
		tmp = x;
	} else if ((z <= 1.35e+47) || (!(z <= 1.35e+83) && (z <= 3.25e+125))) {
		tmp = x * (y / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-7.5d-6)) then
        tmp = x
    else if ((z <= 1.35d+47) .or. (.not. (z <= 1.35d+83)) .and. (z <= 3.25d+125)) then
        tmp = x * (y / t)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -7.5e-6) {
		tmp = x;
	} else if ((z <= 1.35e+47) || (!(z <= 1.35e+83) && (z <= 3.25e+125))) {
		tmp = x * (y / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -7.5e-6:
		tmp = x
	elif (z <= 1.35e+47) or (not (z <= 1.35e+83) and (z <= 3.25e+125)):
		tmp = x * (y / t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -7.5e-6)
		tmp = x;
	elseif ((z <= 1.35e+47) || (!(z <= 1.35e+83) && (z <= 3.25e+125)))
		tmp = Float64(x * Float64(y / t));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -7.5e-6)
		tmp = x;
	elseif ((z <= 1.35e+47) || (~((z <= 1.35e+83)) && (z <= 3.25e+125)))
		tmp = x * (y / t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -7.5e-6], x, If[Or[LessEqual[z, 1.35e+47], And[N[Not[LessEqual[z, 1.35e+83]], $MachinePrecision], LessEqual[z, 3.25e+125]]], N[(x * N[(y / t), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if z < -7.50000000000000019e-6 or 1.34999999999999998e47 < z < 1.35000000000000003e83 or 3.2499999999999999e125 < z

   1. Initial program 76.8%

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

      1. associate-*l/ 71.9%

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

   3. Simplified 71.9%

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

   4. Taylor expanded in z around inf 64.5%

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

   if -7.50000000000000019e-6 < z < 1.34999999999999998e47 or 1.35000000000000003e83 < z < 3.2499999999999999e125

   1. Initial program 94.3%

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

      1. associate-*l/ 91.0%

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

   3. Simplified 91.0%

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

   4. Taylor expanded in x around 0 94.3%

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

      1. associate-*r/ 96.0%

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

   6. Simplified 96.0%

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

   7. Taylor expanded in z around 0 63.7%

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

4. Final simplification 64.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.5 \cdot 10^{-6}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{+47} \lor \neg \left(z \leq 1.35 \cdot 10^{+83}\right) \land z \leq 3.25 \cdot 10^{+125}:\\ \;\;\;\;x \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 11: 60.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7.5 \cdot 10^{-6}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 6 \cdot 10^{+46}:\\ \;\;\;\;\frac{x}{\frac{t}{y}}\\ \mathbf{elif}\;z \leq 2.65 \cdot 10^{+85}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 7.8 \cdot 10^{+126}:\\ \;\;\;\;x \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -7.5e-6)
   x
   (if (<= z 6e+46)
     (/ x (/ t y))
     (if (<= z 2.65e+85) x (if (<= z 7.8e+126) (* x (/ y t)) x)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -7.5e-6) {
		tmp = x;
	} else if (z <= 6e+46) {
		tmp = x / (t / y);
	} else if (z <= 2.65e+85) {
		tmp = x;
	} else if (z <= 7.8e+126) {
		tmp = x * (y / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-7.5d-6)) then
        tmp = x
    else if (z <= 6d+46) then
        tmp = x / (t / y)
    else if (z <= 2.65d+85) then
        tmp = x
    else if (z <= 7.8d+126) then
        tmp = x * (y / t)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -7.5e-6) {
		tmp = x;
	} else if (z <= 6e+46) {
		tmp = x / (t / y);
	} else if (z <= 2.65e+85) {
		tmp = x;
	} else if (z <= 7.8e+126) {
		tmp = x * (y / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -7.5e-6:
		tmp = x
	elif z <= 6e+46:
		tmp = x / (t / y)
	elif z <= 2.65e+85:
		tmp = x
	elif z <= 7.8e+126:
		tmp = x * (y / t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -7.5e-6)
		tmp = x;
	elseif (z <= 6e+46)
		tmp = Float64(x / Float64(t / y));
	elseif (z <= 2.65e+85)
		tmp = x;
	elseif (z <= 7.8e+126)
		tmp = Float64(x * Float64(y / t));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -7.5e-6)
		tmp = x;
	elseif (z <= 6e+46)
		tmp = x / (t / y);
	elseif (z <= 2.65e+85)
		tmp = x;
	elseif (z <= 7.8e+126)
		tmp = x * (y / t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -7.5e-6], x, If[LessEqual[z, 6e+46], N[(x / N[(t / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.65e+85], x, If[LessEqual[z, 7.8e+126], N[(x * N[(y / t), $MachinePrecision]), $MachinePrecision], x]]]]

Derivation

1. Split input into 3 regimes

2. if z < -7.50000000000000019e-6 or 6.00000000000000047e46 < z < 2.65e85 or 7.79999999999999986e126 < z

   1. Initial program 76.8%

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

      1. associate-*l/ 71.9%

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

   3. Simplified 71.9%

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

   4. Taylor expanded in z around inf 64.5%

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

   if -7.50000000000000019e-6 < z < 6.00000000000000047e46

   1. Initial program 95.3%

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

      1. associate-*l/ 93.9%

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

   3. Simplified 93.9%

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

   4. Taylor expanded in z around 0 63.2%

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

      1. associate-/l* 64.8%

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

   6. Simplified 64.8%

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

   if 2.65e85 < z < 7.79999999999999986e126

   1. Initial program 80.8%

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

      1. associate-*l/ 53.2%

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

   3. Simplified 53.2%

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

   4. Taylor expanded in x around 0 80.8%

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

      1. associate-*r/ 99.7%

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

   6. Simplified 99.7%

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

   7. Taylor expanded in z around 0 51.9%

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

4. Final simplification 64.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.5 \cdot 10^{-6}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 6 \cdot 10^{+46}:\\ \;\;\;\;\frac{x}{\frac{t}{y}}\\ \mathbf{elif}\;z \leq 2.65 \cdot 10^{+85}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 7.8 \cdot 10^{+126}:\\ \;\;\;\;x \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 12: 75.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.9 \cdot 10^{-97} \lor \neg \left(y \leq 20000000\right):\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{z}{z - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -3.9e-97) (not (<= y 20000000.0)))
   (* x (/ y (- t z)))
   (* x (/ z (- z t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -3.9e-97) || !(y <= 20000000.0)) {
		tmp = x * (y / (t - z));
	} else {
		tmp = x * (z / (z - t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= (-3.9d-97)) .or. (.not. (y <= 20000000.0d0))) then
        tmp = x * (y / (t - z))
    else
        tmp = x * (z / (z - t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -3.9e-97) || !(y <= 20000000.0)) {
		tmp = x * (y / (t - z));
	} else {
		tmp = x * (z / (z - t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -3.9e-97) or not (y <= 20000000.0):
		tmp = x * (y / (t - z))
	else:
		tmp = x * (z / (z - t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -3.9e-97) || !(y <= 20000000.0))
		tmp = Float64(x * Float64(y / Float64(t - z)));
	else
		tmp = Float64(x * Float64(z / Float64(z - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -3.9e-97) || ~((y <= 20000000.0)))
		tmp = x * (y / (t - z));
	else
		tmp = x * (z / (z - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -3.9e-97], N[Not[LessEqual[y, 20000000.0]], $MachinePrecision]], N[(x * N[(y / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(z / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -3.8999999999999998e-97 or 2e7 < y

   1. Initial program 86.0%

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

      1. associate-*l/ 84.9%

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

   3. Simplified 84.9%

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

   4. Taylor expanded in y around inf 71.4%

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

      1. *-commutative 71.4%

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

      2. associate-/l* 67.1%

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

      3. associate-/r/ 75.4%

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

   6. Simplified 75.4%

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

   if -3.8999999999999998e-97 < y < 2e7

   1. Initial program 87.1%

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

      1. associate-*l/ 79.4%

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

   3. Simplified 79.4%

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

   4. Taylor expanded in y around 0 78.3%

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

      1. associate-*r/ 78.3%

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

      2. mul-1-neg 78.3%

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

      3. distribute-rgt-neg-out 78.3%

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

      4. associate-/l* 88.7%

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

   6. Simplified 88.7%

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

      1. frac-2neg 88.7%

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

      2. div-inv 88.5%

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

      3. sub-neg 88.5%

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

      4. distribute-neg-in 88.5%

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

      5. remove-double-neg 88.5%

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

      6. remove-double-neg 88.5%

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

   8. Applied egg-rr 88.5%

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

      1. associate-*r/ 88.7%

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

      2. *-rgt-identity 88.7%

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

      3. +-commutative 88.7%

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

      4. unsub-neg 88.7%

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

   10. Simplified 88.7%

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

       1. clear-num 87.9%

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

       2. associate-/r/ 88.7%

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

       3. clear-num 89.7%

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

   12. Applied egg-rr 89.7%

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

4. Final simplification 81.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.9 \cdot 10^{-97} \lor \neg \left(y \leq 20000000\right):\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{z}{z - t}\\ \end{array} \]

Alternative 13: 75.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.1 \cdot 10^{-97}:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \mathbf{elif}\;y \leq 22000000:\\ \;\;\;\;x \cdot \frac{z}{z - t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{t - z}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -4.1e-97)
   (* x (/ y (- t z)))
   (if (<= y 22000000.0) (* x (/ z (- z t))) (/ x (/ (- t z) y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -4.1e-97) {
		tmp = x * (y / (t - z));
	} else if (y <= 22000000.0) {
		tmp = x * (z / (z - t));
	} else {
		tmp = x / ((t - z) / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-4.1d-97)) then
        tmp = x * (y / (t - z))
    else if (y <= 22000000.0d0) then
        tmp = x * (z / (z - t))
    else
        tmp = x / ((t - z) / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -4.1e-97) {
		tmp = x * (y / (t - z));
	} else if (y <= 22000000.0) {
		tmp = x * (z / (z - t));
	} else {
		tmp = x / ((t - z) / y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -4.1e-97:
		tmp = x * (y / (t - z))
	elif y <= 22000000.0:
		tmp = x * (z / (z - t))
	else:
		tmp = x / ((t - z) / y)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -4.1e-97)
		tmp = Float64(x * Float64(y / Float64(t - z)));
	elseif (y <= 22000000.0)
		tmp = Float64(x * Float64(z / Float64(z - t)));
	else
		tmp = Float64(x / Float64(Float64(t - z) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -4.1e-97)
		tmp = x * (y / (t - z));
	elseif (y <= 22000000.0)
		tmp = x * (z / (z - t));
	else
		tmp = x / ((t - z) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -4.1e-97], N[(x * N[(y / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 22000000.0], N[(x * N[(z / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(N[(t - z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.09999999999999993e-97

   1. Initial program 85.1%

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

      1. associate-*l/ 83.2%

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

   3. Simplified 83.2%

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

   4. Taylor expanded in y around inf 66.9%

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

      1. *-commutative 66.9%

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

      2. associate-/l* 64.0%

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

      3. associate-/r/ 69.4%

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

   6. Simplified 69.4%

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

   if -4.09999999999999993e-97 < y < 2.2e7

   1. Initial program 87.1%

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

      1. associate-*l/ 79.4%

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

   3. Simplified 79.4%

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

   4. Taylor expanded in y around 0 78.3%

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

      1. associate-*r/ 78.3%

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

      2. mul-1-neg 78.3%

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

      3. distribute-rgt-neg-out 78.3%

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

      4. associate-/l* 88.7%

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

   6. Simplified 88.7%

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

      1. frac-2neg 88.7%

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

      2. div-inv 88.5%

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

      3. sub-neg 88.5%

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

      4. distribute-neg-in 88.5%

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

      5. remove-double-neg 88.5%

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

      6. remove-double-neg 88.5%

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

   8. Applied egg-rr 88.5%

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

      1. associate-*r/ 88.7%

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

      2. *-rgt-identity 88.7%

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

      3. +-commutative 88.7%

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

      4. unsub-neg 88.7%

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

   10. Simplified 88.7%

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

       1. clear-num 87.9%

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

       2. associate-/r/ 88.7%

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

       3. clear-num 89.7%

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

   12. Applied egg-rr 89.7%

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

   if 2.2e7 < y

   1. Initial program 87.3%

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

      1. associate-*l/ 87.2%

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

   3. Simplified 87.2%

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

   4. Taylor expanded in x around 0 87.3%

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

      1. associate-*r/ 98.2%

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

   6. Simplified 98.2%

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

   7. Taylor expanded in y around inf 77.7%

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

      1. associate-/l* 84.6%

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

   9. Simplified 84.6%

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

4. Final simplification 81.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.1 \cdot 10^{-97}:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \mathbf{elif}\;y \leq 22000000:\\ \;\;\;\;x \cdot \frac{z}{z - t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{t - z}{y}}\\ \end{array} \]

Alternative 14: 35.0% accurate, 9.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 86.5%

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

   1. associate-*l/ 82.5%

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

3. Simplified 82.5%

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

4. Taylor expanded in z around inf 33.4%

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

5. Final simplification 33.4%

   \[\leadsto x \]

Developer target: 96.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{x}{\frac{t - z}{y - z}} \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2023279 
(FPCore (x y z t)
  :name "Graphics.Rendering.Chart.Plot.AreaSpots:renderAreaSpots4D from Chart-1.5.3"
  :precision binary64

  :herbie-target
  (/ x (/ (- t z) (- y z)))

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