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

Percentage Accurate: 82.0% → 99.8%

Time: 6.5s

Alternatives: 5

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: 82.0% 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: 99.8% accurate, 1.3× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 85.3%

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

   1. sub-neg 85.3%

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

   2. associate-/l* 92.6%

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

   3. *-commutative 92.6%

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

   4. associate-/l* 92.5%

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

   5. distribute-neg-frac 92.5%

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

   6. metadata-eval 92.5%

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

   7. associate-/l/ 85.3%

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

   8. div-sub 76.6%

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

   9. times-frac 92.6%

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

   10. *-inverses 92.6%

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

   11. *-rgt-identity 92.6%

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

   12. *-commutative 92.6%

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

   13. associate-*l/ 92.6%

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

   14. *-commutative 92.6%

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

   15. times-frac 99.9%

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

   16. *-inverses 99.9%

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

   17. *-lft-identity 99.9%

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

3. Simplified 99.9%

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

4. Final simplification 99.9%

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

Alternative 2: 88.5% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.8 \cdot 10^{-20} \lor \neg \left(z \leq 5.5 \cdot 10^{-79}\right):\\ \;\;\;\;x - \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{-2}{\frac{t}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -2.8e-20) (not (<= z 5.5e-79)))
   (- x (/ y z))
   (- x (/ -2.0 (/ t z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -2.8e-20) || !(z <= 5.5e-79)) {
		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 <= (-2.8d-20)) .or. (.not. (z <= 5.5d-79))) 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 <= -2.8e-20) || !(z <= 5.5e-79)) {
		tmp = x - (y / z);
	} else {
		tmp = x - (-2.0 / (t / z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -2.8e-20) or not (z <= 5.5e-79):
		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 <= -2.8e-20) || !(z <= 5.5e-79))
		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 <= -2.8e-20) || ~((z <= 5.5e-79)))
		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, -2.8e-20], N[Not[LessEqual[z, 5.5e-79]], $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 < -2.8000000000000003e-20 or 5.4999999999999997e-79 < z

   1. Initial program 78.5%

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

      1. sub-neg 78.5%

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

      2. associate-/l* 90.8%

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

      3. *-commutative 90.8%

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

      4. associate-/l* 90.8%

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

      5. distribute-neg-frac 90.8%

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

      6. metadata-eval 90.8%

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

      7. associate-/l/ 78.5%

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

      8. div-sub 78.4%

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

      9. times-frac 92.9%

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

      10. *-inverses 92.9%

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

      11. *-rgt-identity 92.9%

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

      12. *-commutative 92.9%

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

      13. associate-*l/ 92.9%

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

      14. *-commutative 92.9%

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

      15. times-frac 99.9%

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

      16. *-inverses 99.9%

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

      17. *-lft-identity 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in z around inf 91.7%

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

      1. +-commutative 91.7%

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

      2. mul-1-neg 91.7%

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

      3. sub-neg 91.7%

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

   6. Simplified 91.7%

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

   if -2.8000000000000003e-20 < z < 5.4999999999999997e-79

   1. Initial program 93.9%

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

      1. associate-/l* 94.8%

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

      2. *-commutative 94.8%

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

      3. associate-*r/ 94.8%

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

      4. div-sub 94.6%

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

      5. *-commutative 94.6%

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

      6. associate-/l* 99.0%

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

      7. associate-/r* 99.0%

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

      8. *-inverses 99.0%

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

      9. metadata-eval 99.0%

         \[\leadsto x - 2 \cdot \frac{y}{\frac{z}{\color{blue}{0.5}} - \frac{y \cdot t}{z}} \]

      10. *-commutative 99.0%

          \[\leadsto x - 2 \cdot \frac{y}{\frac{z}{0.5} - \frac{\color{blue}{t \cdot y}}{z}} \]

      11. associate-*l/ 99.0%

          \[\leadsto x - 2 \cdot \frac{y}{\frac{z}{0.5} - \color{blue}{\frac{t}{z} \cdot y}} \]

   3. Simplified 99.0%

      \[\leadsto \color{blue}{x - 2 \cdot \frac{y}{\frac{z}{0.5} - \frac{t}{z} \cdot y}} \]

   4. Taylor expanded in y around inf 92.3%

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

      1. associate-*r/ 92.3%

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

      2. associate-/l* 92.2%

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

   6. Simplified 92.2%

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

4. Final simplification 91.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.8 \cdot 10^{-20} \lor \neg \left(z \leq 5.5 \cdot 10^{-79}\right):\\ \;\;\;\;x - \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{-2}{\frac{t}{z}}\\ \end{array} \]

Alternative 3: 88.5% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7.5 \cdot 10^{-13} \lor \neg \left(z \leq 8.2 \cdot 10^{-79}\right):\\ \;\;\;\;x - \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{z}{t \cdot -0.5}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -7.5e-13) (not (<= z 8.2e-79)))
   (- x (/ y z))
   (- x (/ z (* t -0.5)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -7.5e-13) || !(z <= 8.2e-79)) {
		tmp = x - (y / z);
	} else {
		tmp = x - (z / (t * -0.5));
	}
	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-13)) .or. (.not. (z <= 8.2d-79))) then
        tmp = x - (y / z)
    else
        tmp = x - (z / (t * (-0.5d0)))
    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-13) || !(z <= 8.2e-79)) {
		tmp = x - (y / z);
	} else {
		tmp = x - (z / (t * -0.5));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -7.5e-13) or not (z <= 8.2e-79):
		tmp = x - (y / z)
	else:
		tmp = x - (z / (t * -0.5))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -7.5e-13) || !(z <= 8.2e-79))
		tmp = Float64(x - Float64(y / z));
	else
		tmp = Float64(x - Float64(z / Float64(t * -0.5)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -7.5e-13) || ~((z <= 8.2e-79)))
		tmp = x - (y / z);
	else
		tmp = x - (z / (t * -0.5));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -7.5e-13], N[Not[LessEqual[z, 8.2e-79]], $MachinePrecision]], N[(x - N[(y / z), $MachinePrecision]), $MachinePrecision], N[(x - N[(z / N[(t * -0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -7.5000000000000004e-13 or 8.19999999999999987e-79 < z

   1. Initial program 78.5%

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

      1. sub-neg 78.5%

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

      2. associate-/l* 90.8%

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

      3. *-commutative 90.8%

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

      4. associate-/l* 90.8%

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

      5. distribute-neg-frac 90.8%

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

      6. metadata-eval 90.8%

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

      7. associate-/l/ 78.5%

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

      8. div-sub 78.4%

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

      9. times-frac 92.9%

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

      10. *-inverses 92.9%

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

      11. *-rgt-identity 92.9%

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

      12. *-commutative 92.9%

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

      13. associate-*l/ 92.9%

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

      14. *-commutative 92.9%

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

      15. times-frac 99.9%

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

      16. *-inverses 99.9%

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

      17. *-lft-identity 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in z around inf 91.7%

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

      1. +-commutative 91.7%

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

      2. mul-1-neg 91.7%

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

      3. sub-neg 91.7%

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

   6. Simplified 91.7%

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

   if -7.5000000000000004e-13 < z < 8.19999999999999987e-79

   1. Initial program 93.9%

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

      1. *-commutative 93.9%

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

      2. associate-/l* 95.7%

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

      3. div-sub 95.6%

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

      4. sub-neg 95.6%

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

      5. *-commutative 95.6%

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

      6. associate-*l* 95.6%

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

      7. *-commutative 95.6%

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

      8. times-frac 95.6%

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

      9. metadata-eval 95.6%

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

      10. *-lft-identity 95.6%

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

      11. associate-*r/ 99.0%

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

      12. fma-def 99.2%

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

      13. associate-/r* 99.2%

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

      14. distribute-neg-frac 99.2%

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

      15. *-commutative 99.2%

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

      16. associate-/l* 99.9%

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

      17. *-inverses 99.9%

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

      18. /-rgt-identity 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in z around 0 92.3%

      \[\leadsto x - \frac{z}{\color{blue}{-0.5 \cdot t}} \]
   5. Step-by-step derivation

      1. *-commutative 92.3%

         \[\leadsto x - \frac{z}{\color{blue}{t \cdot -0.5}} \]

   6. Simplified 92.3%

      \[\leadsto x - \frac{z}{\color{blue}{t \cdot -0.5}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 92.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.5 \cdot 10^{-13} \lor \neg \left(z \leq 8.2 \cdot 10^{-79}\right):\\ \;\;\;\;x - \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{z}{t \cdot -0.5}\\ \end{array} \]

Alternative 4: 81.0% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.2 \cdot 10^{+59} \lor \neg \left(z \leq 6.2 \cdot 10^{-107}\right):\\ \;\;\;\;x - \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -2.2e+59) (not (<= z 6.2e-107))) (- x (/ y z)) x))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -2.2e+59) || !(z <= 6.2e-107)) {
		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 <= (-2.2d+59)) .or. (.not. (z <= 6.2d-107))) 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 <= -2.2e+59) || !(z <= 6.2e-107)) {
		tmp = x - (y / z);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -2.2e+59) or not (z <= 6.2e-107):
		tmp = x - (y / z)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -2.2e+59) || !(z <= 6.2e-107))
		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 <= -2.2e+59) || ~((z <= 6.2e-107)))
		tmp = x - (y / z);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -2.2e+59], N[Not[LessEqual[z, 6.2e-107]], $MachinePrecision]], N[(x - N[(y / z), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -2.2e59 or 6.20000000000000043e-107 < z

   1. Initial program 78.3%

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

      1. sub-neg 78.3%

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

      2. associate-/l* 90.4%

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

      3. *-commutative 90.4%

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

      4. associate-/l* 90.4%

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

      5. distribute-neg-frac 90.4%

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

      6. metadata-eval 90.4%

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

      7. associate-/l/ 78.3%

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

      8. div-sub 78.2%

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

      9. times-frac 93.4%

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

      10. *-inverses 93.4%

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

      11. *-rgt-identity 93.4%

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

      12. *-commutative 93.4%

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

      13. associate-*l/ 93.3%

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

      14. *-commutative 93.3%

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

      15. times-frac 99.9%

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

      16. *-inverses 99.9%

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

      17. *-lft-identity 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in z around inf 93.3%

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

      1. +-commutative 93.3%

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

      2. mul-1-neg 93.3%

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

      3. sub-neg 93.3%

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

   6. Simplified 93.3%

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

   if -2.2e59 < z < 6.20000000000000043e-107

   1. Initial program 93.4%

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

      1. sub-neg 93.4%

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

      2. associate-/l* 95.0%

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

      3. *-commutative 95.0%

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

      4. associate-/l* 95.1%

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

      5. distribute-neg-frac 95.1%

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

      6. metadata-eval 95.1%

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

      7. associate-/l/ 93.4%

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

      8. div-sub 74.8%

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

      9. times-frac 91.7%

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

      10. *-inverses 91.7%

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

      11. *-rgt-identity 91.7%

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

      12. *-commutative 91.7%

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

      13. associate-*l/ 91.7%

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

      14. *-commutative 91.7%

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

      15. times-frac 99.9%

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

      16. *-inverses 99.9%

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

      17. *-lft-identity 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in x around inf 79.1%

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

4. Final simplification 86.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.2 \cdot 10^{+59} \lor \neg \left(z \leq 6.2 \cdot 10^{-107}\right):\\ \;\;\;\;x - \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 5: 75.9% 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 85.3%

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

   1. sub-neg 85.3%

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

   2. associate-/l* 92.6%

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

   3. *-commutative 92.6%

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

   4. associate-/l* 92.5%

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

   5. distribute-neg-frac 92.5%

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

   6. metadata-eval 92.5%

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

   7. associate-/l/ 85.3%

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

   8. div-sub 76.6%

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

   9. times-frac 92.6%

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

   10. *-inverses 92.6%

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

   11. *-rgt-identity 92.6%

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

   12. *-commutative 92.6%

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

   13. associate-*l/ 92.6%

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

   14. *-commutative 92.6%

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

   15. times-frac 99.9%

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

   16. *-inverses 99.9%

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

   17. *-lft-identity 99.9%

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

3. Simplified 99.9%

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

4. Taylor expanded in x around inf 79.3%

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

5. Final simplification 79.3%

   \[\leadsto x \]

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 2023207 
(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)))))