Numeric.AD.Rank1.Halley:findZero from ad-4.2.4

Percentage Accurate: 81.7% → 98.3%

Time: 8.7s

Alternatives: 6

Speedup: 1.5×

Specification

Math

\[\begin{array}{l} \\ x - \frac{\left(y \cdot 2\right) \cdot z}{\left(z \cdot 2\right) \cdot z - y \cdot t} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (- x (/ (* (* y 2.0) z) (- (* (* z 2.0) z) (* y t)))))

C

double code(double x, double y, double z, double t) {
	return x - (((y * 2.0) * z) / (((z * 2.0) * z) - (y * t)));
}

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 * 2.0d0) * z) / (((z * 2.0d0) * z) - (y * t)))
end function

Java

public static double code(double x, double y, double z, double t) {
	return x - (((y * 2.0) * z) / (((z * 2.0) * z) - (y * t)));
}

Python

def code(x, y, z, t):
	return x - (((y * 2.0) * z) / (((z * 2.0) * z) - (y * t)))

Julia

function code(x, y, z, t)
	return Float64(x - Float64(Float64(Float64(y * 2.0) * z) / Float64(Float64(Float64(z * 2.0) * z) - Float64(y * t))))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = x - (((y * 2.0) * z) / (((z * 2.0) * z) - (y * t)));
end

Wolfram

code[x_, y_, z_, t_] := N[(x - N[(N[(N[(y * 2.0), $MachinePrecision] * z), $MachinePrecision] / N[(N[(N[(z * 2.0), $MachinePrecision] * z), $MachinePrecision] - N[(y * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Initial Program: 81.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x - \frac{\left(y \cdot 2\right) \cdot z}{\left(z \cdot 2\right) \cdot z - y \cdot t} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (- x (/ (* (* y 2.0) z) (- (* (* z 2.0) z) (* y t)))))

C

double code(double x, double y, double z, double t) {
	return x - (((y * 2.0) * z) / (((z * 2.0) * z) - (y * t)));
}

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 * 2.0d0) * z) / (((z * 2.0d0) * z) - (y * t)))
end function

Java

public static double code(double x, double y, double z, double t) {
	return x - (((y * 2.0) * z) / (((z * 2.0) * z) - (y * t)));
}

Python

def code(x, y, z, t):
	return x - (((y * 2.0) * z) / (((z * 2.0) * z) - (y * t)))

Julia

function code(x, y, z, t)
	return Float64(x - Float64(Float64(Float64(y * 2.0) * z) / Float64(Float64(Float64(z * 2.0) * z) - Float64(y * t))))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = x - (((y * 2.0) * z) / (((z * 2.0) * z) - (y * t)));
end

Wolfram

code[x_, y_, z_, t_] := N[(x - N[(N[(N[(y * 2.0), $MachinePrecision] * z), $MachinePrecision] / N[(N[(N[(z * 2.0), $MachinePrecision] * z), $MachinePrecision] - N[(y * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Alternative 1: 98.3% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \mathsf{fma}\left(\frac{y}{z \cdot -2 + \frac{y}{\frac{z}{t}}}, 2, x\right) \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (fma (/ y (+ (* z -2.0) (/ y (/ z t)))) 2.0 x))

C

double code(double x, double y, double z, double t) {
	return fma((y / ((z * -2.0) + (y / (z / t)))), 2.0, x);
}

Julia

function code(x, y, z, t)
	return fma(Float64(y / Float64(Float64(z * -2.0) + Float64(y / Float64(z / t)))), 2.0, x)
end

Wolfram

code[x_, y_, z_, t_] := N[(N[(y / N[(N[(z * -2.0), $MachinePrecision] + N[(y / N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * 2.0 + x), $MachinePrecision]

Derivation

1. Initial program 79.3%

   \[x - \frac{\left(y \cdot 2\right) \cdot z}{\left(z \cdot 2\right) \cdot z - y \cdot t} \]

3. Simplified 98.5%

   \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y}{z \cdot -2 + \frac{y}{\frac{z}{t}}}, 2, x\right)} \]

4. Final simplification 98.5%

   \[\leadsto \mathsf{fma}\left(\frac{y}{z \cdot -2 + \frac{y}{\frac{z}{t}}}, 2, x\right) \]

Alternative 2: 94.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{z \cdot \left(y \cdot 2\right)}{z \cdot \left(z \cdot 2\right) - y \cdot t} \leq 5 \cdot 10^{+193}:\\ \;\;\;\;x + \left(z \cdot -2\right) \cdot \frac{y}{2 \cdot \left(z \cdot z\right) - y \cdot t}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ (* z (* y 2.0)) (- (* z (* z 2.0)) (* y t))) 5e+193)
   (+ x (* (* z -2.0) (/ y (- (* 2.0 (* z z)) (* y t)))))
   (- x (/ y z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((z * (y * 2.0)) / ((z * (z * 2.0)) - (y * t))) <= 5e+193) {
		tmp = x + ((z * -2.0) * (y / ((2.0 * (z * z)) - (y * t))));
	} else {
		tmp = x - (y / z);
	}
	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 * (y * 2.0d0)) / ((z * (z * 2.0d0)) - (y * t))) <= 5d+193) then
        tmp = x + ((z * (-2.0d0)) * (y / ((2.0d0 * (z * z)) - (y * t))))
    else
        tmp = x - (y / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (((z * (y * 2.0)) / ((z * (z * 2.0)) - (y * t))) <= 5e+193) {
		tmp = x + ((z * -2.0) * (y / ((2.0 * (z * z)) - (y * t))));
	} else {
		tmp = x - (y / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((z * (y * 2.0)) / ((z * (z * 2.0)) - (y * t))) <= 5e+193:
		tmp = x + ((z * -2.0) * (y / ((2.0 * (z * z)) - (y * t))))
	else:
		tmp = x - (y / z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(Float64(z * Float64(y * 2.0)) / Float64(Float64(z * Float64(z * 2.0)) - Float64(y * t))) <= 5e+193)
		tmp = Float64(x + Float64(Float64(z * -2.0) * Float64(y / Float64(Float64(2.0 * Float64(z * z)) - Float64(y * t)))));
	else
		tmp = Float64(x - Float64(y / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((z * (y * 2.0)) / ((z * (z * 2.0)) - (y * t))) <= 5e+193)
		tmp = x + ((z * -2.0) * (y / ((2.0 * (z * z)) - (y * t))));
	else
		tmp = x - (y / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(N[(z * N[(y * 2.0), $MachinePrecision]), $MachinePrecision] / N[(N[(z * N[(z * 2.0), $MachinePrecision]), $MachinePrecision] - N[(y * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 5e+193], N[(x + N[(N[(z * -2.0), $MachinePrecision] * N[(y / N[(N[(2.0 * N[(z * z), $MachinePrecision]), $MachinePrecision] - N[(y * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(y / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 (*.f64 y 2) z) (-.f64 (*.f64 (*.f64 z 2) z) (*.f64 y t))) < 4.99999999999999972e193

   1. Initial program 94.3%

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

      1. sub-neg 94.3%

         \[\leadsto \color{blue}{x + \left(-\frac{\left(y \cdot 2\right) \cdot z}{\left(z \cdot 2\right) \cdot z - y \cdot t}\right)} \]

      2. associate-*l* 94.3%

         \[\leadsto x + \left(-\frac{\color{blue}{y \cdot \left(2 \cdot z\right)}}{\left(z \cdot 2\right) \cdot z - y \cdot t}\right) \]

      3. *-commutative 94.3%

         \[\leadsto x + \left(-\frac{y \cdot \color{blue}{\left(z \cdot 2\right)}}{\left(z \cdot 2\right) \cdot z - y \cdot t}\right) \]

      4. associate-*l/ 96.3%

         \[\leadsto x + \left(-\color{blue}{\frac{y}{\left(z \cdot 2\right) \cdot z - y \cdot t} \cdot \left(z \cdot 2\right)}\right) \]

      5. distribute-rgt-neg-in 96.3%

         \[\leadsto x + \color{blue}{\frac{y}{\left(z \cdot 2\right) \cdot z - y \cdot t} \cdot \left(-z \cdot 2\right)} \]

      6. *-commutative 96.3%

         \[\leadsto x + \frac{y}{\color{blue}{\left(2 \cdot z\right)} \cdot z - y \cdot t} \cdot \left(-z \cdot 2\right) \]

      7. associate-*l* 96.3%

         \[\leadsto x + \frac{y}{\color{blue}{2 \cdot \left(z \cdot z\right)} - y \cdot t} \cdot \left(-z \cdot 2\right) \]

      8. distribute-rgt-neg-in 96.3%

         \[\leadsto x + \frac{y}{2 \cdot \left(z \cdot z\right) - y \cdot t} \cdot \color{blue}{\left(z \cdot \left(-2\right)\right)} \]

      9. metadata-eval 96.3%

         \[\leadsto x + \frac{y}{2 \cdot \left(z \cdot z\right) - y \cdot t} \cdot \left(z \cdot \color{blue}{-2}\right) \]

   3. Simplified 96.3%

      \[\leadsto \color{blue}{x + \frac{y}{2 \cdot \left(z \cdot z\right) - y \cdot t} \cdot \left(z \cdot -2\right)} \]

   if 4.99999999999999972e193 < (/.f64 (*.f64 (*.f64 y 2) z) (-.f64 (*.f64 (*.f64 z 2) z) (*.f64 y t)))

   1. Initial program 0.2%

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

      1. sub-neg 0.2%

         \[\leadsto \color{blue}{x + \left(-\frac{\left(y \cdot 2\right) \cdot z}{\left(z \cdot 2\right) \cdot z - y \cdot t}\right)} \]

      2. associate-*l* 0.2%

         \[\leadsto x + \left(-\frac{\color{blue}{y \cdot \left(2 \cdot z\right)}}{\left(z \cdot 2\right) \cdot z - y \cdot t}\right) \]

      3. *-commutative 0.2%

         \[\leadsto x + \left(-\frac{y \cdot \color{blue}{\left(z \cdot 2\right)}}{\left(z \cdot 2\right) \cdot z - y \cdot t}\right) \]

      4. associate-*l/ 45.3%

         \[\leadsto x + \left(-\color{blue}{\frac{y}{\left(z \cdot 2\right) \cdot z - y \cdot t} \cdot \left(z \cdot 2\right)}\right) \]

      5. distribute-rgt-neg-in 45.3%

         \[\leadsto x + \color{blue}{\frac{y}{\left(z \cdot 2\right) \cdot z - y \cdot t} \cdot \left(-z \cdot 2\right)} \]

      6. *-commutative 45.3%

         \[\leadsto x + \frac{y}{\color{blue}{\left(2 \cdot z\right)} \cdot z - y \cdot t} \cdot \left(-z \cdot 2\right) \]

      7. associate-*l* 45.3%

         \[\leadsto x + \frac{y}{\color{blue}{2 \cdot \left(z \cdot z\right)} - y \cdot t} \cdot \left(-z \cdot 2\right) \]

      8. distribute-rgt-neg-in 45.3%

         \[\leadsto x + \frac{y}{2 \cdot \left(z \cdot z\right) - y \cdot t} \cdot \color{blue}{\left(z \cdot \left(-2\right)\right)} \]

      9. metadata-eval 45.3%

         \[\leadsto x + \frac{y}{2 \cdot \left(z \cdot z\right) - y \cdot t} \cdot \left(z \cdot \color{blue}{-2}\right) \]

   3. Simplified 45.3%

      \[\leadsto \color{blue}{x + \frac{y}{2 \cdot \left(z \cdot z\right) - y \cdot t} \cdot \left(z \cdot -2\right)} \]

   4. Taylor expanded in y around 0 86.4%

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

      1. mul-1-neg 86.4%

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

      2. sub-neg 86.4%

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

   6. Simplified 86.4%

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

4. Final simplification 94.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z \cdot \left(y \cdot 2\right)}{z \cdot \left(z \cdot 2\right) - y \cdot t} \leq 5 \cdot 10^{+193}:\\ \;\;\;\;x + \left(z \cdot -2\right) \cdot \frac{y}{2 \cdot \left(z \cdot z\right) - y \cdot t}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{z}\\ \end{array} \]

Alternative 3: 89.0% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4 \cdot 10^{+59} \lor \neg \left(z \leq 7.5 \cdot 10^{-16}\right):\\ \;\;\;\;x - \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{-2}{\frac{t}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -4e+59) (not (<= z 7.5e-16)))
   (- x (/ y z))
   (- x (/ -2.0 (/ t z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -4e+59) || !(z <= 7.5e-16)) {
		tmp = x - (y / z);
	} else {
		tmp = x - (-2.0 / (t / z));
	}
	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 <= (-4d+59)) .or. (.not. (z <= 7.5d-16))) then
        tmp = x - (y / z)
    else
        tmp = x - ((-2.0d0) / (t / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -4e+59) || !(z <= 7.5e-16)) {
		tmp = x - (y / z);
	} else {
		tmp = x - (-2.0 / (t / z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -4e+59) or not (z <= 7.5e-16):
		tmp = x - (y / z)
	else:
		tmp = x - (-2.0 / (t / z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -4e+59) || !(z <= 7.5e-16))
		tmp = Float64(x - Float64(y / z));
	else
		tmp = Float64(x - Float64(-2.0 / Float64(t / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -4e+59) || ~((z <= 7.5e-16)))
		tmp = x - (y / z);
	else
		tmp = x - (-2.0 / (t / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -4e+59], N[Not[LessEqual[z, 7.5e-16]], $MachinePrecision]], N[(x - N[(y / z), $MachinePrecision]), $MachinePrecision], N[(x - N[(-2.0 / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.99999999999999989e59 or 7.5e-16 < z

   1. Initial program 62.6%

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

      1. sub-neg 62.6%

         \[\leadsto \color{blue}{x + \left(-\frac{\left(y \cdot 2\right) \cdot z}{\left(z \cdot 2\right) \cdot z - y \cdot t}\right)} \]

      2. associate-*l* 62.6%

         \[\leadsto x + \left(-\frac{\color{blue}{y \cdot \left(2 \cdot z\right)}}{\left(z \cdot 2\right) \cdot z - y \cdot t}\right) \]

      3. *-commutative 62.6%

         \[\leadsto x + \left(-\frac{y \cdot \color{blue}{\left(z \cdot 2\right)}}{\left(z \cdot 2\right) \cdot z - y \cdot t}\right) \]

      4. associate-*l/ 80.0%

         \[\leadsto x + \left(-\color{blue}{\frac{y}{\left(z \cdot 2\right) \cdot z - y \cdot t} \cdot \left(z \cdot 2\right)}\right) \]

      5. distribute-rgt-neg-in 80.0%

         \[\leadsto x + \color{blue}{\frac{y}{\left(z \cdot 2\right) \cdot z - y \cdot t} \cdot \left(-z \cdot 2\right)} \]

      6. *-commutative 80.0%

         \[\leadsto x + \frac{y}{\color{blue}{\left(2 \cdot z\right)} \cdot z - y \cdot t} \cdot \left(-z \cdot 2\right) \]

      7. associate-*l* 80.0%

         \[\leadsto x + \frac{y}{\color{blue}{2 \cdot \left(z \cdot z\right)} - y \cdot t} \cdot \left(-z \cdot 2\right) \]

      8. distribute-rgt-neg-in 80.0%

         \[\leadsto x + \frac{y}{2 \cdot \left(z \cdot z\right) - y \cdot t} \cdot \color{blue}{\left(z \cdot \left(-2\right)\right)} \]

      9. metadata-eval 80.0%

         \[\leadsto x + \frac{y}{2 \cdot \left(z \cdot z\right) - y \cdot t} \cdot \left(z \cdot \color{blue}{-2}\right) \]

   3. Simplified 80.0%

      \[\leadsto \color{blue}{x + \frac{y}{2 \cdot \left(z \cdot z\right) - y \cdot t} \cdot \left(z \cdot -2\right)} \]

   4. Taylor expanded in y around 0 90.5%

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

      1. mul-1-neg 90.5%

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

      2. sub-neg 90.5%

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

   6. Simplified 90.5%

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

   if -3.99999999999999989e59 < z < 7.5e-16

   1. Initial program 94.4%

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

      1. associate-/l* 94.1%

         \[\leadsto x - \color{blue}{\frac{y \cdot 2}{\frac{\left(z \cdot 2\right) \cdot z - y \cdot t}{z}}} \]

      2. associate-*l* 94.1%

         \[\leadsto x - \frac{y \cdot 2}{\frac{\color{blue}{z \cdot \left(2 \cdot z\right)} - y \cdot t}{z}} \]

   3. Simplified 94.1%

      \[\leadsto \color{blue}{x - \frac{y \cdot 2}{\frac{z \cdot \left(2 \cdot z\right) - y \cdot t}{z}}} \]

   4. Taylor expanded in z around 0 83.2%

      \[\leadsto x - \frac{y \cdot 2}{\color{blue}{-1 \cdot \frac{t \cdot y}{z}}} \]
   5. Step-by-step derivation

      1. associate-*r/ 83.2%

         \[\leadsto x - \frac{y \cdot 2}{\color{blue}{\frac{-1 \cdot \left(t \cdot y\right)}{z}}} \]

      2. mul-1-neg 83.2%

         \[\leadsto x - \frac{y \cdot 2}{\frac{\color{blue}{-t \cdot y}}{z}} \]

      3. *-commutative 83.2%

         \[\leadsto x - \frac{y \cdot 2}{\frac{-\color{blue}{y \cdot t}}{z}} \]

      4. distribute-rgt-neg-in 83.2%

         \[\leadsto x - \frac{y \cdot 2}{\frac{\color{blue}{y \cdot \left(-t\right)}}{z}} \]

   6. Simplified 83.2%

      \[\leadsto x - \frac{y \cdot 2}{\color{blue}{\frac{y \cdot \left(-t\right)}{z}}} \]

   7. Taylor expanded in y around 0 90.5%

      \[\leadsto x - \color{blue}{-2 \cdot \frac{z}{t}} \]
   8. Step-by-step derivation

      1. *-lft-identity 90.5%

         \[\leadsto x - -2 \cdot \frac{\color{blue}{1 \cdot z}}{t} \]

      2. associate-*l/ 90.3%

         \[\leadsto x - -2 \cdot \color{blue}{\left(\frac{1}{t} \cdot z\right)} \]

      3. *-inverses 90.3%

         \[\leadsto x - -2 \cdot \left(\frac{\color{blue}{\frac{y}{y}}}{t} \cdot z\right) \]

      4. associate-/r* 84.5%

         \[\leadsto x - -2 \cdot \left(\color{blue}{\frac{y}{y \cdot t}} \cdot z\right) \]

      5. *-commutative 84.5%

         \[\leadsto x - -2 \cdot \left(\frac{y}{\color{blue}{t \cdot y}} \cdot z\right) \]

      6. associate-*l/ 84.1%

         \[\leadsto x - -2 \cdot \color{blue}{\frac{y \cdot z}{t \cdot y}} \]

      7. /-rgt-identity 84.1%

         \[\leadsto x - -2 \cdot \frac{\color{blue}{\frac{y}{1}} \cdot z}{t \cdot y} \]

      8. associate-/r/ 84.1%

         \[\leadsto x - -2 \cdot \frac{\color{blue}{\frac{y}{\frac{1}{z}}}}{t \cdot y} \]

      9. metadata-eval 84.1%

         \[\leadsto x - \color{blue}{\left(-2\right)} \cdot \frac{\frac{y}{\frac{1}{z}}}{t \cdot y} \]

      10. associate-/r* 83.2%

          \[\leadsto x - \left(-2\right) \cdot \color{blue}{\frac{y}{\frac{1}{z} \cdot \left(t \cdot y\right)}} \]

      11. associate-*l/ 83.2%

          \[\leadsto x - \left(-2\right) \cdot \frac{y}{\color{blue}{\frac{1 \cdot \left(t \cdot y\right)}{z}}} \]

      12. *-lft-identity 83.2%

          \[\leadsto x - \left(-2\right) \cdot \frac{y}{\frac{\color{blue}{t \cdot y}}{z}} \]

      13. associate-*l/ 88.2%

          \[\leadsto x - \left(-2\right) \cdot \frac{y}{\color{blue}{\frac{t}{z} \cdot y}} \]

      14. *-commutative 88.2%

          \[\leadsto x - \left(-2\right) \cdot \frac{y}{\color{blue}{y \cdot \frac{t}{z}}} \]

      15. distribute-lft-neg-in 88.2%

          \[\leadsto x - \color{blue}{\left(-2 \cdot \frac{y}{y \cdot \frac{t}{z}}\right)} \]

      16. associate-*r/ 88.2%

          \[\leadsto x - \left(-\color{blue}{\frac{2 \cdot y}{y \cdot \frac{t}{z}}}\right) \]

      17. *-commutative 88.2%

          \[\leadsto x - \left(-\frac{\color{blue}{y \cdot 2}}{y \cdot \frac{t}{z}}\right) \]

      18. associate-/r* 90.4%

          \[\leadsto x - \left(-\color{blue}{\frac{\frac{y \cdot 2}{y}}{\frac{t}{z}}}\right) \]

      19. distribute-neg-frac 90.4%

          \[\leadsto x - \color{blue}{\frac{-\frac{y \cdot 2}{y}}{\frac{t}{z}}} \]

   9. Simplified 90.4%

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

4. Final simplification 90.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4 \cdot 10^{+59} \lor \neg \left(z \leq 7.5 \cdot 10^{-16}\right):\\ \;\;\;\;x - \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{-2}{\frac{t}{z}}\\ \end{array} \]

Alternative 4: 89.0% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1 \cdot 10^{+59} \lor \neg \left(z \leq 7.8 \cdot 10^{-17}\right):\\ \;\;\;\;x - \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{z \cdot -2}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1e+59) (not (<= z 7.8e-17)))
   (- x (/ y z))
   (- x (/ (* z -2.0) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1e+59) || !(z <= 7.8e-17)) {
		tmp = x - (y / z);
	} else {
		tmp = x - ((z * -2.0) / 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 ((z <= (-1d+59)) .or. (.not. (z <= 7.8d-17))) then
        tmp = x - (y / z)
    else
        tmp = x - ((z * (-2.0d0)) / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1e+59) || !(z <= 7.8e-17)) {
		tmp = x - (y / z);
	} else {
		tmp = x - ((z * -2.0) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -1e+59) or not (z <= 7.8e-17):
		tmp = x - (y / z)
	else:
		tmp = x - ((z * -2.0) / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -1e+59) || !(z <= 7.8e-17))
		tmp = Float64(x - Float64(y / z));
	else
		tmp = Float64(x - Float64(Float64(z * -2.0) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -1e+59) || ~((z <= 7.8e-17)))
		tmp = x - (y / z);
	else
		tmp = x - ((z * -2.0) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -1e+59], N[Not[LessEqual[z, 7.8e-17]], $MachinePrecision]], N[(x - N[(y / z), $MachinePrecision]), $MachinePrecision], N[(x - N[(N[(z * -2.0), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -9.99999999999999972e58 or 7.79999999999999979e-17 < z

   1. Initial program 62.6%

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

      1. sub-neg 62.6%

         \[\leadsto \color{blue}{x + \left(-\frac{\left(y \cdot 2\right) \cdot z}{\left(z \cdot 2\right) \cdot z - y \cdot t}\right)} \]

      2. associate-*l* 62.6%

         \[\leadsto x + \left(-\frac{\color{blue}{y \cdot \left(2 \cdot z\right)}}{\left(z \cdot 2\right) \cdot z - y \cdot t}\right) \]

      3. *-commutative 62.6%

         \[\leadsto x + \left(-\frac{y \cdot \color{blue}{\left(z \cdot 2\right)}}{\left(z \cdot 2\right) \cdot z - y \cdot t}\right) \]

      4. associate-*l/ 80.0%

         \[\leadsto x + \left(-\color{blue}{\frac{y}{\left(z \cdot 2\right) \cdot z - y \cdot t} \cdot \left(z \cdot 2\right)}\right) \]

      5. distribute-rgt-neg-in 80.0%

         \[\leadsto x + \color{blue}{\frac{y}{\left(z \cdot 2\right) \cdot z - y \cdot t} \cdot \left(-z \cdot 2\right)} \]

      6. *-commutative 80.0%

         \[\leadsto x + \frac{y}{\color{blue}{\left(2 \cdot z\right)} \cdot z - y \cdot t} \cdot \left(-z \cdot 2\right) \]

      7. associate-*l* 80.0%

         \[\leadsto x + \frac{y}{\color{blue}{2 \cdot \left(z \cdot z\right)} - y \cdot t} \cdot \left(-z \cdot 2\right) \]

      8. distribute-rgt-neg-in 80.0%

         \[\leadsto x + \frac{y}{2 \cdot \left(z \cdot z\right) - y \cdot t} \cdot \color{blue}{\left(z \cdot \left(-2\right)\right)} \]

      9. metadata-eval 80.0%

         \[\leadsto x + \frac{y}{2 \cdot \left(z \cdot z\right) - y \cdot t} \cdot \left(z \cdot \color{blue}{-2}\right) \]

   3. Simplified 80.0%

      \[\leadsto \color{blue}{x + \frac{y}{2 \cdot \left(z \cdot z\right) - y \cdot t} \cdot \left(z \cdot -2\right)} \]

   4. Taylor expanded in y around 0 90.5%

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

      1. mul-1-neg 90.5%

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

      2. sub-neg 90.5%

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

   6. Simplified 90.5%

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

   if -9.99999999999999972e58 < z < 7.79999999999999979e-17

   1. Initial program 94.4%

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

      1. sub-neg 94.4%

         \[\leadsto \color{blue}{x + \left(-\frac{\left(y \cdot 2\right) \cdot z}{\left(z \cdot 2\right) \cdot z - y \cdot t}\right)} \]

      2. associate-*l* 94.4%

         \[\leadsto x + \left(-\frac{\color{blue}{y \cdot \left(2 \cdot z\right)}}{\left(z \cdot 2\right) \cdot z - y \cdot t}\right) \]

      3. *-commutative 94.4%

         \[\leadsto x + \left(-\frac{y \cdot \color{blue}{\left(z \cdot 2\right)}}{\left(z \cdot 2\right) \cdot z - y \cdot t}\right) \]

      4. associate-*l/ 95.4%

         \[\leadsto x + \left(-\color{blue}{\frac{y}{\left(z \cdot 2\right) \cdot z - y \cdot t} \cdot \left(z \cdot 2\right)}\right) \]

      5. distribute-rgt-neg-in 95.4%

         \[\leadsto x + \color{blue}{\frac{y}{\left(z \cdot 2\right) \cdot z - y \cdot t} \cdot \left(-z \cdot 2\right)} \]

      6. *-commutative 95.4%

         \[\leadsto x + \frac{y}{\color{blue}{\left(2 \cdot z\right)} \cdot z - y \cdot t} \cdot \left(-z \cdot 2\right) \]

      7. associate-*l* 95.4%

         \[\leadsto x + \frac{y}{\color{blue}{2 \cdot \left(z \cdot z\right)} - y \cdot t} \cdot \left(-z \cdot 2\right) \]

      8. distribute-rgt-neg-in 95.4%

         \[\leadsto x + \frac{y}{2 \cdot \left(z \cdot z\right) - y \cdot t} \cdot \color{blue}{\left(z \cdot \left(-2\right)\right)} \]

      9. metadata-eval 95.4%

         \[\leadsto x + \frac{y}{2 \cdot \left(z \cdot z\right) - y \cdot t} \cdot \left(z \cdot \color{blue}{-2}\right) \]

   3. Simplified 95.4%

      \[\leadsto \color{blue}{x + \frac{y}{2 \cdot \left(z \cdot z\right) - y \cdot t} \cdot \left(z \cdot -2\right)} \]

   4. Taylor expanded in y around inf 90.5%

      \[\leadsto \color{blue}{x + 2 \cdot \frac{z}{t}} \]
   5. Step-by-step derivation

      1. metadata-eval 90.5%

         \[\leadsto x + \color{blue}{\left(--2\right)} \cdot \frac{z}{t} \]

      2. cancel-sign-sub-inv 90.5%

         \[\leadsto \color{blue}{x - -2 \cdot \frac{z}{t}} \]

      3. associate-*r/ 90.5%

         \[\leadsto x - \color{blue}{\frac{-2 \cdot z}{t}} \]

      4. *-commutative 90.5%

         \[\leadsto x - \frac{\color{blue}{z \cdot -2}}{t} \]

   6. Simplified 90.5%

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

4. Final simplification 90.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1 \cdot 10^{+59} \lor \neg \left(z \leq 7.8 \cdot 10^{-17}\right):\\ \;\;\;\;x - \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{z \cdot -2}{t}\\ \end{array} \]

Alternative 5: 81.5% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.2 \cdot 10^{-47} \lor \neg \left(z \leq 2.3 \cdot 10^{-26}\right):\\ \;\;\;\;x - \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -4.2e-47) (not (<= z 2.3e-26))) (- x (/ y z)) x))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -4.2e-47) || !(z <= 2.3e-26)) {
		tmp = x - (y / z);
	} 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 <= (-4.2d-47)) .or. (.not. (z <= 2.3d-26))) then
        tmp = x - (y / z)
    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 <= -4.2e-47) || !(z <= 2.3e-26)) {
		tmp = x - (y / z);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -4.2e-47) or not (z <= 2.3e-26):
		tmp = x - (y / z)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -4.2e-47) || !(z <= 2.3e-26))
		tmp = Float64(x - Float64(y / z));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -4.2e-47) || ~((z <= 2.3e-26)))
		tmp = x - (y / z);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -4.2e-47], N[Not[LessEqual[z, 2.3e-26]], $MachinePrecision]], N[(x - N[(y / z), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -4.2000000000000001e-47 or 2.30000000000000009e-26 < z

   1. Initial program 68.3%

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

      1. sub-neg 68.3%

         \[\leadsto \color{blue}{x + \left(-\frac{\left(y \cdot 2\right) \cdot z}{\left(z \cdot 2\right) \cdot z - y \cdot t}\right)} \]

      2. associate-*l* 68.3%

         \[\leadsto x + \left(-\frac{\color{blue}{y \cdot \left(2 \cdot z\right)}}{\left(z \cdot 2\right) \cdot z - y \cdot t}\right) \]

      3. *-commutative 68.3%

         \[\leadsto x + \left(-\frac{y \cdot \color{blue}{\left(z \cdot 2\right)}}{\left(z \cdot 2\right) \cdot z - y \cdot t}\right) \]

      4. associate-*l/ 82.7%

         \[\leadsto x + \left(-\color{blue}{\frac{y}{\left(z \cdot 2\right) \cdot z - y \cdot t} \cdot \left(z \cdot 2\right)}\right) \]

      5. distribute-rgt-neg-in 82.7%

         \[\leadsto x + \color{blue}{\frac{y}{\left(z \cdot 2\right) \cdot z - y \cdot t} \cdot \left(-z \cdot 2\right)} \]

      6. *-commutative 82.7%

         \[\leadsto x + \frac{y}{\color{blue}{\left(2 \cdot z\right)} \cdot z - y \cdot t} \cdot \left(-z \cdot 2\right) \]

      7. associate-*l* 82.7%

         \[\leadsto x + \frac{y}{\color{blue}{2 \cdot \left(z \cdot z\right)} - y \cdot t} \cdot \left(-z \cdot 2\right) \]

      8. distribute-rgt-neg-in 82.7%

         \[\leadsto x + \frac{y}{2 \cdot \left(z \cdot z\right) - y \cdot t} \cdot \color{blue}{\left(z \cdot \left(-2\right)\right)} \]

      9. metadata-eval 82.7%

         \[\leadsto x + \frac{y}{2 \cdot \left(z \cdot z\right) - y \cdot t} \cdot \left(z \cdot \color{blue}{-2}\right) \]

   3. Simplified 82.7%

      \[\leadsto \color{blue}{x + \frac{y}{2 \cdot \left(z \cdot z\right) - y \cdot t} \cdot \left(z \cdot -2\right)} \]

   4. Taylor expanded in y around 0 84.6%

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

      1. mul-1-neg 84.6%

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

      2. sub-neg 84.6%

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

   6. Simplified 84.6%

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

   if -4.2000000000000001e-47 < z < 2.30000000000000009e-26

   1. Initial program 94.0%

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

      1. sub-neg 94.0%

         \[\leadsto \color{blue}{x + \left(-\frac{\left(y \cdot 2\right) \cdot z}{\left(z \cdot 2\right) \cdot z - y \cdot t}\right)} \]

      2. associate-*l* 94.0%

         \[\leadsto x + \left(-\frac{\color{blue}{y \cdot \left(2 \cdot z\right)}}{\left(z \cdot 2\right) \cdot z - y \cdot t}\right) \]

      3. *-commutative 94.0%

         \[\leadsto x + \left(-\frac{y \cdot \color{blue}{\left(z \cdot 2\right)}}{\left(z \cdot 2\right) \cdot z - y \cdot t}\right) \]

      4. associate-*l/ 95.3%

         \[\leadsto x + \left(-\color{blue}{\frac{y}{\left(z \cdot 2\right) \cdot z - y \cdot t} \cdot \left(z \cdot 2\right)}\right) \]

      5. distribute-rgt-neg-in 95.3%

         \[\leadsto x + \color{blue}{\frac{y}{\left(z \cdot 2\right) \cdot z - y \cdot t} \cdot \left(-z \cdot 2\right)} \]

      6. *-commutative 95.3%

         \[\leadsto x + \frac{y}{\color{blue}{\left(2 \cdot z\right)} \cdot z - y \cdot t} \cdot \left(-z \cdot 2\right) \]

      7. associate-*l* 95.3%

         \[\leadsto x + \frac{y}{\color{blue}{2 \cdot \left(z \cdot z\right)} - y \cdot t} \cdot \left(-z \cdot 2\right) \]

      8. distribute-rgt-neg-in 95.3%

         \[\leadsto x + \frac{y}{2 \cdot \left(z \cdot z\right) - y \cdot t} \cdot \color{blue}{\left(z \cdot \left(-2\right)\right)} \]

      9. metadata-eval 95.3%

         \[\leadsto x + \frac{y}{2 \cdot \left(z \cdot z\right) - y \cdot t} \cdot \left(z \cdot \color{blue}{-2}\right) \]

   3. Simplified 95.3%

      \[\leadsto \color{blue}{x + \frac{y}{2 \cdot \left(z \cdot z\right) - y \cdot t} \cdot \left(z \cdot -2\right)} \]

   4. Taylor expanded in x around inf 77.6%

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

4. Final simplification 81.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.2 \cdot 10^{-47} \lor \neg \left(z \leq 2.3 \cdot 10^{-26}\right):\\ \;\;\;\;x - \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 6: 74.9% accurate, 17.0× 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 79.3%

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

   1. sub-neg 79.3%

      \[\leadsto \color{blue}{x + \left(-\frac{\left(y \cdot 2\right) \cdot z}{\left(z \cdot 2\right) \cdot z - y \cdot t}\right)} \]

   2. associate-*l* 79.3%

      \[\leadsto x + \left(-\frac{\color{blue}{y \cdot \left(2 \cdot z\right)}}{\left(z \cdot 2\right) \cdot z - y \cdot t}\right) \]

   3. *-commutative 79.3%

      \[\leadsto x + \left(-\frac{y \cdot \color{blue}{\left(z \cdot 2\right)}}{\left(z \cdot 2\right) \cdot z - y \cdot t}\right) \]

   4. associate-*l/ 88.1%

      \[\leadsto x + \left(-\color{blue}{\frac{y}{\left(z \cdot 2\right) \cdot z - y \cdot t} \cdot \left(z \cdot 2\right)}\right) \]

   5. distribute-rgt-neg-in 88.1%

      \[\leadsto x + \color{blue}{\frac{y}{\left(z \cdot 2\right) \cdot z - y \cdot t} \cdot \left(-z \cdot 2\right)} \]

   6. *-commutative 88.1%

      \[\leadsto x + \frac{y}{\color{blue}{\left(2 \cdot z\right)} \cdot z - y \cdot t} \cdot \left(-z \cdot 2\right) \]

   7. associate-*l* 88.1%

      \[\leadsto x + \frac{y}{\color{blue}{2 \cdot \left(z \cdot z\right)} - y \cdot t} \cdot \left(-z \cdot 2\right) \]

   8. distribute-rgt-neg-in 88.1%

      \[\leadsto x + \frac{y}{2 \cdot \left(z \cdot z\right) - y \cdot t} \cdot \color{blue}{\left(z \cdot \left(-2\right)\right)} \]

   9. metadata-eval 88.1%

      \[\leadsto x + \frac{y}{2 \cdot \left(z \cdot z\right) - y \cdot t} \cdot \left(z \cdot \color{blue}{-2}\right) \]

3. Simplified 88.1%

   \[\leadsto \color{blue}{x + \frac{y}{2 \cdot \left(z \cdot z\right) - y \cdot t} \cdot \left(z \cdot -2\right)} \]

4. Taylor expanded in x around inf 71.7%

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

5. Final simplification 71.7%

   \[\leadsto x \]

Developer target: 99.9% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ x - \frac{1}{\frac{z}{y} - \frac{\frac{t}{2}}{z}} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (- x (/ 1.0 (- (/ z y) (/ (/ t 2.0) z)))))

C

double code(double x, double y, double z, double t) {
	return x - (1.0 / ((z / y) - ((t / 2.0) / 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 - (1.0d0 / ((z / y) - ((t / 2.0d0) / z)))
end function

Java

public static double code(double x, double y, double z, double t) {
	return x - (1.0 / ((z / y) - ((t / 2.0) / z)));
}

Python

def code(x, y, z, t):
	return x - (1.0 / ((z / y) - ((t / 2.0) / z)))

Julia

function code(x, y, z, t)
	return Float64(x - Float64(1.0 / Float64(Float64(z / y) - Float64(Float64(t / 2.0) / z))))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = x - (1.0 / ((z / y) - ((t / 2.0) / z)));
end

Wolfram

code[x_, y_, z_, t_] := N[(x - N[(1.0 / N[(N[(z / y), $MachinePrecision] - N[(N[(t / 2.0), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Reproduce

herbie shell --seed 2023310 
(FPCore (x y z t)
  :name "Numeric.AD.Rank1.Halley:findZero from ad-4.2.4"
  :precision binary64

  :herbie-target
  (- x (/ 1.0 (- (/ z y) (/ (/ t 2.0) z))))

  (- x (/ (* (* y 2.0) z) (- (* (* z 2.0) z) (* y t)))))