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

Percentage Accurate: 81.4% → 96.0%

Time: 11.4s

Alternatives: 5

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: 81.4% 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: 96.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.55 \lor \neg \left(z \leq 1.6 \cdot 10^{-105}\right):\\ \;\;\;\;x + y \cdot \frac{2}{t \cdot \frac{y}{z} - z \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{z \cdot -2}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1.55) (not (<= z 1.6e-105)))
   (+ x (* y (/ 2.0 (- (* t (/ y z)) (* z 2.0)))))
   (- x (/ (* z -2.0) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.55) || !(z <= 1.6e-105)) {
		tmp = x + (y * (2.0 / ((t * (y / z)) - (z * 2.0))));
	} 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 <= (-1.55d0)) .or. (.not. (z <= 1.6d-105))) then
        tmp = x + (y * (2.0d0 / ((t * (y / z)) - (z * 2.0d0))))
    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 <= -1.55) || !(z <= 1.6e-105)) {
		tmp = x + (y * (2.0 / ((t * (y / z)) - (z * 2.0))));
	} else {
		tmp = x - ((z * -2.0) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -1.55) or not (z <= 1.6e-105):
		tmp = x + (y * (2.0 / ((t * (y / z)) - (z * 2.0))))
	else:
		tmp = x - ((z * -2.0) / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -1.55) || !(z <= 1.6e-105))
		tmp = Float64(x + Float64(y * Float64(2.0 / Float64(Float64(t * Float64(y / z)) - Float64(z * 2.0)))));
	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 <= -1.55) || ~((z <= 1.6e-105)))
		tmp = x + (y * (2.0 / ((t * (y / z)) - (z * 2.0))));
	else
		tmp = x - ((z * -2.0) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -1.55], N[Not[LessEqual[z, 1.6e-105]], $MachinePrecision]], N[(x + N[(y * N[(2.0 / N[(N[(t * N[(y / z), $MachinePrecision]), $MachinePrecision] - N[(z * 2.0), $MachinePrecision]), $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 < -1.55000000000000004 or 1.59999999999999991e-105 < z

   1. Initial program 71.8%

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

      1. associate-/l* 85.8%

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

      2. associate-*r* 85.8%

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

      3. associate-*l* 85.8%

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

      4. *-commutative 85.8%

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

      5. clear-num 85.8%

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

      6. un-div-inv 85.8%

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

      7. *-commutative 85.8%

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

      8. associate-*l* 85.8%

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

      9. pow2 85.8%

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

   4. Applied egg-rr 85.8%

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

   5. Taylor expanded in y around 0 95.3%

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

      1. +-commutative 95.3%

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

      2. mul-1-neg 95.3%

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

      3. *-commutative 95.3%

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

      4. associate-*r/ 98.1%

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

      5. unsub-neg 98.1%

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

      6. *-commutative 98.1%

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

      7. associate-*r/ 95.3%

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

      8. *-commutative 95.3%

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

      9. associate-/l* 98.2%

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

   7. Simplified 98.2%

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

   if -1.55000000000000004 < z < 1.59999999999999991e-105

   1. Initial program 90.9%

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

   3. Simplified 93.1%

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

   5. Taylor expanded in y around inf 96.8%

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

      1. associate-*r/ 96.8%

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

      2. *-commutative 96.8%

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

   7. Simplified 96.8%

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

4. Final simplification 97.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.55 \lor \neg \left(z \leq 1.6 \cdot 10^{-105}\right):\\ \;\;\;\;x + y \cdot \frac{2}{t \cdot \frac{y}{z} - z \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{z \cdot -2}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 73.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1 \cdot 10^{-109}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -1 \cdot 10^{-137} \lor \neg \left(x \leq -5.8 \cdot 10^{-186}\right) \land x \leq 3.5 \cdot 10^{-301}:\\ \;\;\;\;\frac{y}{-z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -1e-109)
   x
   (if (or (<= x -1e-137) (and (not (<= x -5.8e-186)) (<= x 3.5e-301)))
     (/ y (- z))
     x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -1e-109) {
		tmp = x;
	} else if ((x <= -1e-137) || (!(x <= -5.8e-186) && (x <= 3.5e-301))) {
		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 <= (-1d-109)) then
        tmp = x
    else if ((x <= (-1d-137)) .or. (.not. (x <= (-5.8d-186))) .and. (x <= 3.5d-301)) 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 <= -1e-109) {
		tmp = x;
	} else if ((x <= -1e-137) || (!(x <= -5.8e-186) && (x <= 3.5e-301))) {
		tmp = y / -z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -1e-109:
		tmp = x
	elif (x <= -1e-137) or (not (x <= -5.8e-186) and (x <= 3.5e-301)):
		tmp = y / -z
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -1e-109)
		tmp = x;
	elseif ((x <= -1e-137) || (!(x <= -5.8e-186) && (x <= 3.5e-301)))
		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 <= -1e-109)
		tmp = x;
	elseif ((x <= -1e-137) || (~((x <= -5.8e-186)) && (x <= 3.5e-301)))
		tmp = y / -z;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -1e-109], x, If[Or[LessEqual[x, -1e-137], And[N[Not[LessEqual[x, -5.8e-186]], $MachinePrecision], LessEqual[x, 3.5e-301]]], N[(y / (-z)), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if x < -9.9999999999999999e-110 or -9.99999999999999978e-138 < x < -5.80000000000000038e-186 or 3.49999999999999992e-301 < x

   1. Initial program 81.4%

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

   3. Simplified 92.2%

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

   5. Taylor expanded in x around inf 82.1%

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

   if -9.9999999999999999e-110 < x < -9.99999999999999978e-138 or -5.80000000000000038e-186 < x < 3.49999999999999992e-301

   1. Initial program 64.1%

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

   3. Simplified 68.6%

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

   5. Taylor expanded in y around 0 69.3%

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

   6. Taylor expanded in x around 0 62.5%

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

      1. mul-1-neg 62.5%

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

   8. Simplified 62.5%

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

4. Final simplification 78.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1 \cdot 10^{-109}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -1 \cdot 10^{-137} \lor \neg \left(x \leq -5.8 \cdot 10^{-186}\right) \land x \leq 3.5 \cdot 10^{-301}:\\ \;\;\;\;\frac{y}{-z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 90.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.6 \cdot 10^{+48} \lor \neg \left(z \leq 1.15 \cdot 10^{+21}\right):\\ \;\;\;\;x - \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{z \cdot -2}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -2.6e+48) (not (<= z 1.15e+21)))
   (- x (/ y z))
   (- x (/ (* z -2.0) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -2.6e+48) || !(z <= 1.15e+21)) {
		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 <= (-2.6d+48)) .or. (.not. (z <= 1.15d+21))) 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 <= -2.6e+48) || !(z <= 1.15e+21)) {
		tmp = x - (y / z);
	} else {
		tmp = x - ((z * -2.0) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -2.6e+48) or not (z <= 1.15e+21):
		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 <= -2.6e+48) || !(z <= 1.15e+21))
		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 <= -2.6e+48) || ~((z <= 1.15e+21)))
		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, -2.6e+48], N[Not[LessEqual[z, 1.15e+21]], $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 < -2.59999999999999995e48 or 1.15e21 < z

   1. Initial program 66.6%

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

   3. Simplified 83.6%

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

   5. Taylor expanded in y around 0 95.0%

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

   if -2.59999999999999995e48 < z < 1.15e21

   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 93.9%

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

   5. Taylor expanded in y around inf 92.0%

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

      1. associate-*r/ 92.0%

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

      2. *-commutative 92.0%

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

   7. Simplified 92.0%

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

4. Final simplification 93.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.6 \cdot 10^{+48} \lor \neg \left(z \leq 1.15 \cdot 10^{+21}\right):\\ \;\;\;\;x - \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{z \cdot -2}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 82.5% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.3 \cdot 10^{+93} \lor \neg \left(z \leq 2.25 \cdot 10^{+21}\right):\\ \;\;\;\;x - \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1.3e+93) (not (<= z 2.25e+21))) (- x (/ y z)) x))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.3e+93) || !(z <= 2.25e+21)) {
		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 <= (-1.3d+93)) .or. (.not. (z <= 2.25d+21))) 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 <= -1.3e+93) || !(z <= 2.25e+21)) {
		tmp = x - (y / z);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -1.3e+93) or not (z <= 2.25e+21):
		tmp = x - (y / z)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -1.3e+93) || !(z <= 2.25e+21))
		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 <= -1.3e+93) || ~((z <= 2.25e+21)))
		tmp = x - (y / z);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -1.3e+93], N[Not[LessEqual[z, 2.25e+21]], $MachinePrecision]], N[(x - N[(y / z), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -1.3e93 or 2.25e21 < z

   1. Initial program 65.7%

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

   3. Simplified 82.4%

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

   5. Taylor expanded in y around 0 96.2%

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

   if -1.3e93 < z < 2.25e21

   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 94.3%

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

   5. Taylor expanded in x around inf 69.0%

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

4. Final simplification 82.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.3 \cdot 10^{+93} \lor \neg \left(z \leq 2.25 \cdot 10^{+21}\right):\\ \;\;\;\;x - \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 75.8% 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 78.6%

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

3. Simplified 88.4%

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

5. Taylor expanded in x around inf 71.0%

   \[\leadsto \color{blue}{x} \]
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 2024091 
(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)))))