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

Percentage Accurate: 81.6% → 97.2%

Time: 10.7s

Alternatives: 8

Speedup: 1.1×

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: 81.6% 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: 97.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.3 \cdot 10^{-143} \lor \neg \left(z \leq 1.35 \cdot 10^{-154}\right):\\ \;\;\;\;x + \frac{y \cdot 2}{t \cdot \frac{y}{z} - 2 \cdot z}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{z \cdot -2}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -3.3e-143) (not (<= z 1.35e-154)))
   (+ x (/ (* y 2.0) (- (* t (/ y z)) (* 2.0 z))))
   (- x (/ (* z -2.0) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -3.3e-143) || !(z <= 1.35e-154)) {
		tmp = x + ((y * 2.0) / ((t * (y / z)) - (2.0 * 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 <= (-3.3d-143)) .or. (.not. (z <= 1.35d-154))) then
        tmp = x + ((y * 2.0d0) / ((t * (y / z)) - (2.0d0 * 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 <= -3.3e-143) || !(z <= 1.35e-154)) {
		tmp = x + ((y * 2.0) / ((t * (y / z)) - (2.0 * z)));
	} else {
		tmp = x - ((z * -2.0) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -3.3e-143) or not (z <= 1.35e-154):
		tmp = x + ((y * 2.0) / ((t * (y / z)) - (2.0 * z)))
	else:
		tmp = x - ((z * -2.0) / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -3.3e-143) || !(z <= 1.35e-154))
		tmp = Float64(x + Float64(Float64(y * 2.0) / Float64(Float64(t * Float64(y / z)) - Float64(2.0 * 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 <= -3.3e-143) || ~((z <= 1.35e-154)))
		tmp = x + ((y * 2.0) / ((t * (y / z)) - (2.0 * z)));
	else
		tmp = x - ((z * -2.0) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -3.3e-143], N[Not[LessEqual[z, 1.35e-154]], $MachinePrecision]], N[(x + N[(N[(y * 2.0), $MachinePrecision] / N[(N[(t * N[(y / z), $MachinePrecision]), $MachinePrecision] - N[(2.0 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(N[(z * -2.0), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.3000000000000001e-143 or 1.34999999999999995e-154 < z

   1. Initial program 84.3%

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

   3. Simplified 92.6%

      \[\leadsto \color{blue}{x - \left(y \cdot 2\right) \cdot \frac{z}{z \cdot \left(2 \cdot z\right) - y \cdot t}} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. clear-num 92.6%

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

      2. un-div-inv 92.6%

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

      3. *-commutative 92.6%

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

      4. *-commutative 92.6%

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

      5. associate-*l* 92.6%

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

      6. pow2 92.6%

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

   6. Applied egg-rr 92.6%

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

   7. Taylor expanded in y around 0 95.2%

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

      1. mul-1-neg 95.2%

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

      2. +-commutative 95.2%

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

      3. unsub-neg 95.2%

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

      4. *-commutative 95.2%

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

      5. associate-/l* 96.7%

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

   9. Simplified 96.7%

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

   if -3.3000000000000001e-143 < z < 1.34999999999999995e-154

   1. Initial program 87.7%

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

   3. Simplified 85.0%

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

   5. Taylor expanded in y around inf 100.0%

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

      1. associate-*r/ 100.0%

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

      2. *-commutative 100.0%

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

   7. Simplified 100.0%

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

4. Final simplification 97.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.3 \cdot 10^{-143} \lor \neg \left(z \leq 1.35 \cdot 10^{-154}\right):\\ \;\;\;\;x + \frac{y \cdot 2}{t \cdot \frac{y}{z} - 2 \cdot z}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{z \cdot -2}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 97.1% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x + \frac{\left(y \cdot 2\right) \cdot z}{y \cdot t - z \cdot \left(2 \cdot z\right)} \leq 10^{+214}:\\ \;\;\;\;x - \left(y \cdot 2\right) \cdot \frac{z}{\mathsf{fma}\left(2 \cdot z, z, y \cdot \left(-t\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot 2}{t \cdot \frac{y}{z} - 2 \cdot z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (+ x (/ (* (* y 2.0) z) (- (* y t) (* z (* 2.0 z))))) 1e+214)
   (- x (* (* y 2.0) (/ z (fma (* 2.0 z) z (* y (- t))))))
   (+ x (/ (* y 2.0) (- (* t (/ y z)) (* 2.0 z))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x + (((y * 2.0) * z) / ((y * t) - (z * (2.0 * z))))) <= 1e+214) {
		tmp = x - ((y * 2.0) * (z / fma((2.0 * z), z, (y * -t))));
	} else {
		tmp = x + ((y * 2.0) / ((t * (y / z)) - (2.0 * z)));
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(x + Float64(Float64(Float64(y * 2.0) * z) / Float64(Float64(y * t) - Float64(z * Float64(2.0 * z))))) <= 1e+214)
		tmp = Float64(x - Float64(Float64(y * 2.0) * Float64(z / fma(Float64(2.0 * z), z, Float64(y * Float64(-t))))));
	else
		tmp = Float64(x + Float64(Float64(y * 2.0) / Float64(Float64(t * Float64(y / z)) - Float64(2.0 * z))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(x + N[(N[(N[(y * 2.0), $MachinePrecision] * z), $MachinePrecision] / N[(N[(y * t), $MachinePrecision] - N[(z * N[(2.0 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 1e+214], N[(x - N[(N[(y * 2.0), $MachinePrecision] * N[(z / N[(N[(2.0 * z), $MachinePrecision] * z + N[(y * (-t)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y * 2.0), $MachinePrecision] / N[(N[(t * N[(y / z), $MachinePrecision]), $MachinePrecision] - N[(2.0 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 x (/.f64 (*.f64 (*.f64 y #s(literal 2 binary64)) z) (-.f64 (*.f64 (*.f64 z #s(literal 2 binary64)) z) (*.f64 y t)))) < 9.9999999999999995e213

   1. Initial program 96.1%

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

   3. Simplified 96.2%

      \[\leadsto \color{blue}{x - \left(y \cdot 2\right) \cdot \frac{z}{z \cdot \left(2 \cdot z\right) - y \cdot t}} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. associate-*r* 96.2%

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

      2. fma-neg 96.2%

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

      3. *-commutative 96.2%

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

      4. distribute-rgt-neg-in 96.2%

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

   6. Applied egg-rr 96.2%

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

   if 9.9999999999999995e213 < (-.f64 x (/.f64 (*.f64 (*.f64 y #s(literal 2 binary64)) z) (-.f64 (*.f64 (*.f64 z #s(literal 2 binary64)) z) (*.f64 y t))))

   1. Initial program 28.9%

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

   3. Simplified 62.6%

      \[\leadsto \color{blue}{x - \left(y \cdot 2\right) \cdot \frac{z}{z \cdot \left(2 \cdot z\right) - y \cdot t}} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. clear-num 62.6%

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

      2. un-div-inv 62.6%

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

      3. *-commutative 62.6%

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

      4. *-commutative 62.6%

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

      5. associate-*l* 62.6%

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

      6. pow2 62.6%

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

   6. Applied egg-rr 62.6%

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

   7. Taylor expanded in y around 0 79.3%

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

      1. mul-1-neg 79.3%

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

      2. +-commutative 79.3%

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

      3. unsub-neg 79.3%

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

      4. *-commutative 79.3%

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

      5. associate-/l* 97.5%

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

   9. Simplified 97.5%

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

4. Final simplification 96.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{\left(y \cdot 2\right) \cdot z}{y \cdot t - z \cdot \left(2 \cdot z\right)} \leq 10^{+214}:\\ \;\;\;\;x - \left(y \cdot 2\right) \cdot \frac{z}{\mathsf{fma}\left(2 \cdot z, z, y \cdot \left(-t\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot 2}{t \cdot \frac{y}{z} - 2 \cdot z}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 97.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot t - z \cdot \left(2 \cdot z\right)\\ \mathbf{if}\;x + \frac{\left(y \cdot 2\right) \cdot z}{t\_1} \leq 10^{+214}:\\ \;\;\;\;x + \left(y \cdot 2\right) \cdot \frac{z}{t\_1}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot 2}{t \cdot \frac{y}{z} - 2 \cdot z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (* y t) (* z (* 2.0 z)))))
   (if (<= (+ x (/ (* (* y 2.0) z) t_1)) 1e+214)
     (+ x (* (* y 2.0) (/ z t_1)))
     (+ x (/ (* y 2.0) (- (* t (/ y z)) (* 2.0 z)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (y * t) - (z * (2.0 * z));
	double tmp;
	if ((x + (((y * 2.0) * z) / t_1)) <= 1e+214) {
		tmp = x + ((y * 2.0) * (z / t_1));
	} else {
		tmp = x + ((y * 2.0) / ((t * (y / z)) - (2.0 * 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) :: t_1
    real(8) :: tmp
    t_1 = (y * t) - (z * (2.0d0 * z))
    if ((x + (((y * 2.0d0) * z) / t_1)) <= 1d+214) then
        tmp = x + ((y * 2.0d0) * (z / t_1))
    else
        tmp = x + ((y * 2.0d0) / ((t * (y / z)) - (2.0d0 * z)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (y * t) - (z * (2.0 * z));
	double tmp;
	if ((x + (((y * 2.0) * z) / t_1)) <= 1e+214) {
		tmp = x + ((y * 2.0) * (z / t_1));
	} else {
		tmp = x + ((y * 2.0) / ((t * (y / z)) - (2.0 * z)));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (y * t) - (z * (2.0 * z))
	tmp = 0
	if (x + (((y * 2.0) * z) / t_1)) <= 1e+214:
		tmp = x + ((y * 2.0) * (z / t_1))
	else:
		tmp = x + ((y * 2.0) / ((t * (y / z)) - (2.0 * z)))
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(y * t) - Float64(z * Float64(2.0 * z)))
	tmp = 0.0
	if (Float64(x + Float64(Float64(Float64(y * 2.0) * z) / t_1)) <= 1e+214)
		tmp = Float64(x + Float64(Float64(y * 2.0) * Float64(z / t_1)));
	else
		tmp = Float64(x + Float64(Float64(y * 2.0) / Float64(Float64(t * Float64(y / z)) - Float64(2.0 * z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (y * t) - (z * (2.0 * z));
	tmp = 0.0;
	if ((x + (((y * 2.0) * z) / t_1)) <= 1e+214)
		tmp = x + ((y * 2.0) * (z / t_1));
	else
		tmp = x + ((y * 2.0) / ((t * (y / z)) - (2.0 * z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(y * t), $MachinePrecision] - N[(z * N[(2.0 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x + N[(N[(N[(y * 2.0), $MachinePrecision] * z), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision], 1e+214], N[(x + N[(N[(y * 2.0), $MachinePrecision] * N[(z / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y * 2.0), $MachinePrecision] / N[(N[(t * N[(y / z), $MachinePrecision]), $MachinePrecision] - N[(2.0 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 x (/.f64 (*.f64 (*.f64 y #s(literal 2 binary64)) z) (-.f64 (*.f64 (*.f64 z #s(literal 2 binary64)) z) (*.f64 y t)))) < 9.9999999999999995e213

   1. Initial program 96.1%

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

   3. Simplified 96.2%

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

   if 9.9999999999999995e213 < (-.f64 x (/.f64 (*.f64 (*.f64 y #s(literal 2 binary64)) z) (-.f64 (*.f64 (*.f64 z #s(literal 2 binary64)) z) (*.f64 y t))))

   1. Initial program 28.9%

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

   3. Simplified 62.6%

      \[\leadsto \color{blue}{x - \left(y \cdot 2\right) \cdot \frac{z}{z \cdot \left(2 \cdot z\right) - y \cdot t}} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. clear-num 62.6%

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

      2. un-div-inv 62.6%

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

      3. *-commutative 62.6%

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

      4. *-commutative 62.6%

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

      5. associate-*l* 62.6%

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

      6. pow2 62.6%

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

   6. Applied egg-rr 62.6%

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

   7. Taylor expanded in y around 0 79.3%

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

      1. mul-1-neg 79.3%

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

      2. +-commutative 79.3%

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

      3. unsub-neg 79.3%

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

      4. *-commutative 79.3%

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

      5. associate-/l* 97.5%

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

   9. Simplified 97.5%

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

4. Final simplification 96.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{\left(y \cdot 2\right) \cdot z}{y \cdot t - z \cdot \left(2 \cdot z\right)} \leq 10^{+214}:\\ \;\;\;\;x + \left(y \cdot 2\right) \cdot \frac{z}{y \cdot t - z \cdot \left(2 \cdot z\right)}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot 2}{t \cdot \frac{y}{z} - 2 \cdot z}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 89.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.85 \cdot 10^{-31} \lor \neg \left(z \leq 1.9 \cdot 10^{-15}\right):\\ \;\;\;\;x - \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{z \cdot -2}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1.85e-31) (not (<= z 1.9e-15)))
   (- x (/ y z))
   (- x (/ (* z -2.0) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.85e-31) || !(z <= 1.9e-15)) {
		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 <= (-1.85d-31)) .or. (.not. (z <= 1.9d-15))) 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 <= -1.85e-31) || !(z <= 1.9e-15)) {
		tmp = x - (y / z);
	} else {
		tmp = x - ((z * -2.0) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -1.85e-31) or not (z <= 1.9e-15):
		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 <= -1.85e-31) || !(z <= 1.9e-15))
		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 <= -1.85e-31) || ~((z <= 1.9e-15)))
		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, -1.85e-31], N[Not[LessEqual[z, 1.9e-15]], $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 < -1.8499999999999999e-31 or 1.9000000000000001e-15 < z

   1. Initial program 79.2%

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

   3. Simplified 90.4%

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

   5. Taylor expanded in y around 0 89.3%

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

   if -1.8499999999999999e-31 < z < 1.9000000000000001e-15

   1. Initial program 92.5%

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

   3. Simplified 91.0%

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

   5. Taylor expanded in y around inf 94.2%

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

      1. associate-*r/ 94.2%

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

      2. *-commutative 94.2%

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

   7. Simplified 94.2%

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

4. Final simplification 91.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.85 \cdot 10^{-31} \lor \neg \left(z \leq 1.9 \cdot 10^{-15}\right):\\ \;\;\;\;x - \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{z \cdot -2}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 82.5% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.6 \cdot 10^{-50} \lor \neg \left(z \leq 5.6 \cdot 10^{-36}\right):\\ \;\;\;\;x - \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -3.6e-50) (not (<= z 5.6e-36))) (- x (/ y z)) x))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -3.6e-50) || !(z <= 5.6e-36)) {
		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 <= (-3.6d-50)) .or. (.not. (z <= 5.6d-36))) 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 <= -3.6e-50) || !(z <= 5.6e-36)) {
		tmp = x - (y / z);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -3.6e-50) or not (z <= 5.6e-36):
		tmp = x - (y / z)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -3.6e-50) || !(z <= 5.6e-36))
		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 <= -3.6e-50) || ~((z <= 5.6e-36)))
		tmp = x - (y / z);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -3.6e-50], N[Not[LessEqual[z, 5.6e-36]], $MachinePrecision]], N[(x - N[(y / z), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -3.59999999999999979e-50 or 5.6000000000000002e-36 < z

   1. Initial program 80.3%

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

   3. Simplified 90.7%

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

   5. Taylor expanded in y around 0 85.6%

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

   if -3.59999999999999979e-50 < z < 5.6000000000000002e-36

   1. Initial program 92.3%

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

   3. Simplified 90.6%

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

   5. Taylor expanded in x around inf 71.1%

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

4. Final simplification 79.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.6 \cdot 10^{-50} \lor \neg \left(z \leq 5.6 \cdot 10^{-36}\right):\\ \;\;\;\;x - \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 74.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 6.6 \cdot 10^{-300}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 10^{-124}:\\ \;\;\;\;2 \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x 6.6e-300) x (if (<= x 1e-124) (* 2.0 (/ z t)) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= 6.6e-300) {
		tmp = x;
	} else if (x <= 1e-124) {
		tmp = 2.0 * (z / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (x <= 6.6d-300) then
        tmp = x
    else if (x <= 1d-124) then
        tmp = 2.0d0 * (z / t)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= 6.6e-300) {
		tmp = x;
	} else if (x <= 1e-124) {
		tmp = 2.0 * (z / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= 6.6e-300:
		tmp = x
	elif x <= 1e-124:
		tmp = 2.0 * (z / t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= 6.6e-300)
		tmp = x;
	elseif (x <= 1e-124)
		tmp = Float64(2.0 * Float64(z / t));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= 6.6e-300)
		tmp = x;
	elseif (x <= 1e-124)
		tmp = 2.0 * (z / t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, 6.6e-300], x, If[LessEqual[x, 1e-124], N[(2.0 * N[(z / t), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if x < 6.6000000000000004e-300 or 9.99999999999999933e-125 < x

   1. Initial program 87.0%

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

   3. Simplified 94.0%

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

   5. Taylor expanded in x around inf 79.4%

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

   if 6.6000000000000004e-300 < x < 9.99999999999999933e-125

   1. Initial program 74.1%

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

   3. Simplified 71.8%

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

   5. Taylor expanded in y around inf 61.6%

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

      1. associate-*r/ 61.6%

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

      2. *-commutative 61.6%

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

   7. Simplified 61.6%

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

   8. Taylor expanded in x around 0 55.5%

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

Alternative 7: 72.8% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 1.26 \cdot 10^{-297}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 1.7 \cdot 10^{-100}:\\ \;\;\;\;\frac{y}{-z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x 1.26e-297) x (if (<= x 1.7e-100) (/ y (- z)) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= 1.26e-297) {
		tmp = x;
	} else if (x <= 1.7e-100) {
		tmp = 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 (x <= 1.26d-297) then
        tmp = x
    else if (x <= 1.7d-100) then
        tmp = 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 (x <= 1.26e-297) {
		tmp = x;
	} else if (x <= 1.7e-100) {
		tmp = y / -z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= 1.26e-297:
		tmp = x
	elif x <= 1.7e-100:
		tmp = y / -z
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= 1.26e-297)
		tmp = x;
	elseif (x <= 1.7e-100)
		tmp = Float64(y / Float64(-z));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= 1.26e-297)
		tmp = x;
	elseif (x <= 1.7e-100)
		tmp = y / -z;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, 1.26e-297], x, If[LessEqual[x, 1.7e-100], N[(y / (-z)), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if x < 1.2599999999999999e-297 or 1.69999999999999988e-100 < x

   1. Initial program 86.7%

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

   3. Simplified 93.8%

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

   5. Taylor expanded in x around inf 80.2%

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

   if 1.2599999999999999e-297 < x < 1.69999999999999988e-100

   1. Initial program 77.4%

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

   3. Simplified 75.5%

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

   5. Taylor expanded in y around 0 46.4%

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

   6. Taylor expanded in x around 0 40.0%

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

      1. mul-1-neg 40.0%

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

      2. distribute-frac-neg2 40.0%

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

   8. Simplified 40.0%

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

Alternative 8: 75.6% 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 85.1%

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

3. Simplified 90.7%

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

5. Taylor expanded in x around inf 69.7%

   \[\leadsto \color{blue}{x} \]
6. Add Preprocessing

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 2024098 
(FPCore (x y z t)
  :name "Numeric.AD.Rank1.Halley:findZero from ad-4.2.4"
  :precision binary64

  :alt
  (- x (/ 1.0 (- (/ z y) (/ (/ t 2.0) z))))

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