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

Percentage Accurate: 81.9% → 99.9%

Time: 8.6s

Alternatives: 5

Speedup: 1.9×

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: 81.9% 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: 99.9% accurate, 1.3× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 85.9%

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

3. Simplified 99.6%

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

   1. fma-udef 99.6%

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

   2. clear-num 99.5%

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

   3. associate-*l/ 99.5%

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

   4. metadata-eval 99.5%

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

   5. fma-def 99.5%

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

   6. *-commutative 99.5%

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

5. Applied egg-rr 99.5%

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

6. Taylor expanded in z around 0 99.9%

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

7. Final simplification 99.9%

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

Alternative 2: 90.0% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.5 \cdot 10^{-38} \lor \neg \left(z \leq 3.3 \cdot 10^{-20}\right):\\ \;\;\;\;x - \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{2}{\frac{t}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -2.5e-38) (not (<= z 3.3e-20)))
   (- x (/ y z))
   (+ x (/ 2.0 (/ t z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -2.5e-38) || !(z <= 3.3e-20)) {
		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 <= (-2.5d-38)) .or. (.not. (z <= 3.3d-20))) 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 <= -2.5e-38) || !(z <= 3.3e-20)) {
		tmp = x - (y / z);
	} else {
		tmp = x + (2.0 / (t / z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -2.5e-38) or not (z <= 3.3e-20):
		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 <= -2.5e-38) || !(z <= 3.3e-20))
		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 <= -2.5e-38) || ~((z <= 3.3e-20)))
		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, -2.5e-38], N[Not[LessEqual[z, 3.3e-20]], $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 < -2.50000000000000017e-38 or 3.3e-20 < z

   1. Initial program 80.8%

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

   3. Simplified 93.7%

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

   4. Taylor expanded in y around 0 91.8%

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

      1. mul-1-neg 91.8%

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

      2. sub-neg 91.8%

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

   6. Simplified 91.8%

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

   if -2.50000000000000017e-38 < z < 3.3e-20

   1. Initial program 91.7%

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

   3. Simplified 99.9%

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

      1. fma-udef 99.9%

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

      2. clear-num 99.9%

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

      3. associate-*l/ 99.9%

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

      4. metadata-eval 99.9%

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

      5. fma-def 99.9%

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

      6. *-commutative 99.9%

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

   5. Applied egg-rr 99.9%

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

   6. Taylor expanded in z around 0 95.2%

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

4. Final simplification 93.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.5 \cdot 10^{-38} \lor \neg \left(z \leq 3.3 \cdot 10^{-20}\right):\\ \;\;\;\;x - \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{2}{\frac{t}{z}}\\ \end{array} \]

Alternative 3: 90.1% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{-38} \lor \neg \left(z \leq 4.5 \cdot 10^{-20}\right):\\ \;\;\;\;x - \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{-2 \cdot z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -2e-38) (not (<= z 4.5e-20)))
   (- x (/ y z))
   (- x (/ (* -2.0 z) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -2e-38) || !(z <= 4.5e-20)) {
		tmp = x - (y / z);
	} else {
		tmp = x - ((-2.0 * 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 ((z <= (-2d-38)) .or. (.not. (z <= 4.5d-20))) then
        tmp = x - (y / z)
    else
        tmp = x - (((-2.0d0) * z) / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -2e-38) || !(z <= 4.5e-20)) {
		tmp = x - (y / z);
	} else {
		tmp = x - ((-2.0 * z) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -2e-38) or not (z <= 4.5e-20):
		tmp = x - (y / z)
	else:
		tmp = x - ((-2.0 * z) / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -2e-38) || !(z <= 4.5e-20))
		tmp = Float64(x - Float64(y / z));
	else
		tmp = Float64(x - Float64(Float64(-2.0 * z) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -2e-38) || ~((z <= 4.5e-20)))
		tmp = x - (y / z);
	else
		tmp = x - ((-2.0 * z) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -2e-38], N[Not[LessEqual[z, 4.5e-20]], $MachinePrecision]], N[(x - N[(y / z), $MachinePrecision]), $MachinePrecision], N[(x - N[(N[(-2.0 * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.9999999999999999e-38 or 4.5000000000000001e-20 < z

   1. Initial program 80.8%

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

   3. Simplified 93.7%

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

   4. Taylor expanded in y around 0 91.8%

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

      1. mul-1-neg 91.8%

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

      2. sub-neg 91.8%

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

   6. Simplified 91.8%

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

   if -1.9999999999999999e-38 < z < 4.5000000000000001e-20

   1. Initial program 91.7%

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

   2. Taylor expanded in y around inf 95.3%

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

      1. associate-*r/ 95.3%

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

      2. *-commutative 95.3%

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

   4. Simplified 95.3%

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

4. Final simplification 93.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{-38} \lor \neg \left(z \leq 4.5 \cdot 10^{-20}\right):\\ \;\;\;\;x - \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{-2 \cdot z}{t}\\ \end{array} \]

Alternative 4: 82.8% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7.2 \cdot 10^{-39} \lor \neg \left(z \leq 1.25 \cdot 10^{-35}\right):\\ \;\;\;\;x - \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -7.2e-39) (not (<= z 1.25e-35))) (- x (/ y z)) x))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -7.2e-39) || !(z <= 1.25e-35)) {
		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 <= (-7.2d-39)) .or. (.not. (z <= 1.25d-35))) 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 <= -7.2e-39) || !(z <= 1.25e-35)) {
		tmp = x - (y / z);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -7.2e-39) or not (z <= 1.25e-35):
		tmp = x - (y / z)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -7.2e-39) || !(z <= 1.25e-35))
		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 <= -7.2e-39) || ~((z <= 1.25e-35)))
		tmp = x - (y / z);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -7.2e-39], N[Not[LessEqual[z, 1.25e-35]], $MachinePrecision]], N[(x - N[(y / z), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -7.2000000000000001e-39 or 1.24999999999999991e-35 < z

   1. Initial program 81.6%

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

   3. Simplified 93.9%

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

   4. Taylor expanded in y around 0 90.1%

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

      1. mul-1-neg 90.1%

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

      2. sub-neg 90.1%

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

   6. Simplified 90.1%

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

   if -7.2000000000000001e-39 < z < 1.24999999999999991e-35

   1. Initial program 91.3%

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

   3. Simplified 94.5%

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

   4. Taylor expanded in x around inf 79.9%

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

4. Final simplification 85.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.2 \cdot 10^{-39} \lor \neg \left(z \leq 1.25 \cdot 10^{-35}\right):\\ \;\;\;\;x - \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 5: 76.1% 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 85.9%

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

3. Simplified 94.2%

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

4. Taylor expanded in x around inf 80.3%

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

5. Final simplification 80.3%

   \[\leadsto x \]

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 2023301 
(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)))))