Statistics.Distribution.Poisson:$clogProbability from math-functions-0.1.5.2

Percentage Accurate: 99.9% → 99.8%

Time: 9.8s

Alternatives: 10

Speedup: 1.0×

Specification

Math

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

FPCore

(FPCore (x y z) :precision binary64 (- (- (* x (log y)) z) y))

C

double code(double x, double y, double z) {
	return ((x * log(y)) - z) - y;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = ((x * log(y)) - z) - y
end function

Java

public static double code(double x, double y, double z) {
	return ((x * Math.log(y)) - z) - y;
}

Python

def code(x, y, z):
	return ((x * math.log(y)) - z) - y

Julia

function code(x, y, z)
	return Float64(Float64(Float64(x * log(y)) - z) - y)
end

MATLAB

function tmp = code(x, y, z)
	tmp = ((x * log(y)) - z) - y;
end

Wolfram

code[x_, y_, z_] := N[(N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision] - y), $MachinePrecision]

Initial Program: 99.9% accurate, 1.0× speedup

Math

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

FPCore

(FPCore (x y z) :precision binary64 (- (- (* x (log y)) z) y))

C

double code(double x, double y, double z) {
	return ((x * log(y)) - z) - y;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = ((x * log(y)) - z) - y
end function

Java

public static double code(double x, double y, double z) {
	return ((x * Math.log(y)) - z) - y;
}

Python

def code(x, y, z):
	return ((x * math.log(y)) - z) - y

Julia

function code(x, y, z)
	return Float64(Float64(Float64(x * log(y)) - z) - y)
end

MATLAB

function tmp = code(x, y, z)
	tmp = ((x * log(y)) - z) - y;
end

Wolfram

code[x_, y_, z_] := N[(N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision] - y), $MachinePrecision]

Alternative 1: 99.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \left(3 \cdot \left(x \cdot \log \left(\sqrt[3]{y}\right)\right) - z\right) - y \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (- (- (* 3.0 (* x (log (cbrt y)))) z) y))

C

double code(double x, double y, double z) {
	return ((3.0 * (x * log(cbrt(y)))) - z) - y;
}

Java

public static double code(double x, double y, double z) {
	return ((3.0 * (x * Math.log(Math.cbrt(y)))) - z) - y;
}

Julia

function code(x, y, z)
	return Float64(Float64(Float64(3.0 * Float64(x * log(cbrt(y)))) - z) - y)
end

Wolfram

code[x_, y_, z_] := N[(N[(N[(3.0 * N[(x * N[Log[N[Power[y, 1/3], $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision] - y), $MachinePrecision]

Derivation

1. Initial program 99.8%

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

   1. add-cube-cbrt 99.8%

      \[\leadsto \left(x \cdot \log \color{blue}{\left(\left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) \cdot \sqrt[3]{y}\right)} - z\right) - y \]

   2. log-prod 99.8%

      \[\leadsto \left(x \cdot \color{blue}{\left(\log \left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) + \log \left(\sqrt[3]{y}\right)\right)} - z\right) - y \]

   3. pow2 99.8%

      \[\leadsto \left(x \cdot \left(\log \color{blue}{\left({\left(\sqrt[3]{y}\right)}^{2}\right)} + \log \left(\sqrt[3]{y}\right)\right) - z\right) - y \]

4. Applied egg-rr 99.8%

   \[\leadsto \left(x \cdot \color{blue}{\left(\log \left({\left(\sqrt[3]{y}\right)}^{2}\right) + \log \left(\sqrt[3]{y}\right)\right)} - z\right) - y \]
5. Step-by-step derivation

   1. distribute-lft-in 99.8%

      \[\leadsto \left(\color{blue}{\left(x \cdot \log \left({\left(\sqrt[3]{y}\right)}^{2}\right) + x \cdot \log \left(\sqrt[3]{y}\right)\right)} - z\right) - y \]

   2. *-commutative 99.8%

      \[\leadsto \left(\left(\color{blue}{\log \left({\left(\sqrt[3]{y}\right)}^{2}\right) \cdot x} + x \cdot \log \left(\sqrt[3]{y}\right)\right) - z\right) - y \]

   3. log-pow 99.8%

      \[\leadsto \left(\left(\color{blue}{\left(2 \cdot \log \left(\sqrt[3]{y}\right)\right)} \cdot x + x \cdot \log \left(\sqrt[3]{y}\right)\right) - z\right) - y \]

   4. associate-*l* 99.8%

      \[\leadsto \left(\left(\color{blue}{2 \cdot \left(\log \left(\sqrt[3]{y}\right) \cdot x\right)} + x \cdot \log \left(\sqrt[3]{y}\right)\right) - z\right) - y \]

   5. *-commutative 99.8%

      \[\leadsto \left(\left(2 \cdot \color{blue}{\left(x \cdot \log \left(\sqrt[3]{y}\right)\right)} + x \cdot \log \left(\sqrt[3]{y}\right)\right) - z\right) - y \]

6. Applied egg-rr 99.8%

   \[\leadsto \left(\color{blue}{\left(2 \cdot \left(x \cdot \log \left(\sqrt[3]{y}\right)\right) + x \cdot \log \left(\sqrt[3]{y}\right)\right)} - z\right) - y \]
7. Step-by-step derivation

   1. distribute-lft1-in 99.8%

      \[\leadsto \left(\color{blue}{\left(2 + 1\right) \cdot \left(x \cdot \log \left(\sqrt[3]{y}\right)\right)} - z\right) - y \]

   2. metadata-eval 99.8%

      \[\leadsto \left(\color{blue}{3} \cdot \left(x \cdot \log \left(\sqrt[3]{y}\right)\right) - z\right) - y \]

8. Simplified 99.8%

   \[\leadsto \left(\color{blue}{3 \cdot \left(x \cdot \log \left(\sqrt[3]{y}\right)\right)} - z\right) - y \]
9. Add Preprocessing

Alternative 2: 85.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(-z\right) - y\\ t_1 := x \cdot \log y\\ \mathbf{if}\;z \leq -1.55 \cdot 10^{+72}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 8.4 \cdot 10^{+14}:\\ \;\;\;\;t\_1 - y\\ \mathbf{elif}\;z \leq 8.8 \cdot 10^{+126}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;t\_1 - z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- (- z) y)) (t_1 (* x (log y))))
   (if (<= z -1.55e+72)
     t_0
     (if (<= z 8.4e+14) (- t_1 y) (if (<= z 8.8e+126) t_0 (- t_1 z))))))

C

double code(double x, double y, double z) {
	double t_0 = -z - y;
	double t_1 = x * log(y);
	double tmp;
	if (z <= -1.55e+72) {
		tmp = t_0;
	} else if (z <= 8.4e+14) {
		tmp = t_1 - y;
	} else if (z <= 8.8e+126) {
		tmp = t_0;
	} else {
		tmp = t_1 - z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = -z - y
    t_1 = x * log(y)
    if (z <= (-1.55d+72)) then
        tmp = t_0
    else if (z <= 8.4d+14) then
        tmp = t_1 - y
    else if (z <= 8.8d+126) then
        tmp = t_0
    else
        tmp = t_1 - z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = -z - y;
	double t_1 = x * Math.log(y);
	double tmp;
	if (z <= -1.55e+72) {
		tmp = t_0;
	} else if (z <= 8.4e+14) {
		tmp = t_1 - y;
	} else if (z <= 8.8e+126) {
		tmp = t_0;
	} else {
		tmp = t_1 - z;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = -z - y
	t_1 = x * math.log(y)
	tmp = 0
	if z <= -1.55e+72:
		tmp = t_0
	elif z <= 8.4e+14:
		tmp = t_1 - y
	elif z <= 8.8e+126:
		tmp = t_0
	else:
		tmp = t_1 - z
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(-z) - y)
	t_1 = Float64(x * log(y))
	tmp = 0.0
	if (z <= -1.55e+72)
		tmp = t_0;
	elseif (z <= 8.4e+14)
		tmp = Float64(t_1 - y);
	elseif (z <= 8.8e+126)
		tmp = t_0;
	else
		tmp = Float64(t_1 - z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = -z - y;
	t_1 = x * log(y);
	tmp = 0.0;
	if (z <= -1.55e+72)
		tmp = t_0;
	elseif (z <= 8.4e+14)
		tmp = t_1 - y;
	elseif (z <= 8.8e+126)
		tmp = t_0;
	else
		tmp = t_1 - z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[((-z) - y), $MachinePrecision]}, Block[{t$95$1 = N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.55e+72], t$95$0, If[LessEqual[z, 8.4e+14], N[(t$95$1 - y), $MachinePrecision], If[LessEqual[z, 8.8e+126], t$95$0, N[(t$95$1 - z), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.54999999999999994e72 or 8.4e14 < z < 8.79999999999999994e126

   1. Initial program 99.9%

      \[\left(x \cdot \log y - z\right) - y \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 84.3%

      \[\leadsto \color{blue}{-1 \cdot \left(y + z\right)} \]
   4. Step-by-step derivation

      1. neg-mul-1 84.3%

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

      2. +-commutative 84.3%

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

      3. distribute-neg-in 84.3%

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

      4. sub-neg 84.3%

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

   5. Simplified 84.3%

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

   if -1.54999999999999994e72 < z < 8.4e14

   1. Initial program 99.8%

      \[\left(x \cdot \log y - z\right) - y \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 94.7%

      \[\leadsto \color{blue}{x \cdot \log y - y} \]

   if 8.79999999999999994e126 < z

   1. Initial program 99.8%

      \[\left(x \cdot \log y - z\right) - y \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 96.6%

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

Alternative 3: 85.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.5 \cdot 10^{+72} \lor \neg \left(z \leq 1.4 \cdot 10^{+14}\right):\\ \;\;\;\;\left(-z\right) - y\\ \mathbf{else}:\\ \;\;\;\;x \cdot \log y - y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -4.5e+72) (not (<= z 1.4e+14)))
   (- (- z) y)
   (- (* x (log y)) y)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -4.5e+72) || !(z <= 1.4e+14)) {
		tmp = -z - y;
	} else {
		tmp = (x * log(y)) - y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((z <= (-4.5d+72)) .or. (.not. (z <= 1.4d+14))) then
        tmp = -z - y
    else
        tmp = (x * log(y)) - y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -4.5e+72) || !(z <= 1.4e+14)) {
		tmp = -z - y;
	} else {
		tmp = (x * Math.log(y)) - y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -4.5e+72) or not (z <= 1.4e+14):
		tmp = -z - y
	else:
		tmp = (x * math.log(y)) - y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -4.5e+72) || !(z <= 1.4e+14))
		tmp = Float64(Float64(-z) - y);
	else
		tmp = Float64(Float64(x * log(y)) - y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -4.5e+72) || ~((z <= 1.4e+14)))
		tmp = -z - y;
	else
		tmp = (x * log(y)) - y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -4.5e+72], N[Not[LessEqual[z, 1.4e+14]], $MachinePrecision]], N[((-z) - y), $MachinePrecision], N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] - y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4.4999999999999998e72 or 1.4e14 < z

   1. Initial program 99.9%

      \[\left(x \cdot \log y - z\right) - y \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 81.7%

      \[\leadsto \color{blue}{-1 \cdot \left(y + z\right)} \]
   4. Step-by-step derivation

      1. neg-mul-1 81.7%

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

      2. +-commutative 81.7%

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

      3. distribute-neg-in 81.7%

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

      4. sub-neg 81.7%

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

   5. Simplified 81.7%

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

   if -4.4999999999999998e72 < z < 1.4e14

   1. Initial program 99.8%

      \[\left(x \cdot \log y - z\right) - y \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 94.7%

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

4. Final simplification 89.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.5 \cdot 10^{+72} \lor \neg \left(z \leq 1.4 \cdot 10^{+14}\right):\\ \;\;\;\;\left(-z\right) - y\\ \mathbf{else}:\\ \;\;\;\;x \cdot \log y - y\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 79.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.2 \cdot 10^{+134} \lor \neg \left(x \leq 1.35 \cdot 10^{+126}\right):\\ \;\;\;\;x \cdot \log y\\ \mathbf{else}:\\ \;\;\;\;\left(-z\right) - y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -1.2e+134) (not (<= x 1.35e+126))) (* x (log y)) (- (- z) y)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.2e+134) || !(x <= 1.35e+126)) {
		tmp = x * log(y);
	} else {
		tmp = -z - y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((x <= (-1.2d+134)) .or. (.not. (x <= 1.35d+126))) then
        tmp = x * log(y)
    else
        tmp = -z - y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.2e+134) || !(x <= 1.35e+126)) {
		tmp = x * Math.log(y);
	} else {
		tmp = -z - y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -1.2e+134) or not (x <= 1.35e+126):
		tmp = x * math.log(y)
	else:
		tmp = -z - y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -1.2e+134) || !(x <= 1.35e+126))
		tmp = Float64(x * log(y));
	else
		tmp = Float64(Float64(-z) - y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -1.2e+134) || ~((x <= 1.35e+126)))
		tmp = x * log(y);
	else
		tmp = -z - y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -1.2e+134], N[Not[LessEqual[x, 1.35e+126]], $MachinePrecision]], N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision], N[((-z) - y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.20000000000000003e134 or 1.35000000000000001e126 < x

   1. Initial program 99.6%

      \[\left(x \cdot \log y - z\right) - y \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 62.5%

      \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \frac{x \cdot \log \left(\frac{1}{y}\right)}{y} - \left(1 + \frac{z}{y}\right)\right)} \]
   4. Step-by-step derivation

      1. sub-neg 62.5%

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

      2. mul-1-neg 62.5%

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

      3. log-rec 62.5%

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

      4. mul-1-neg 62.5%

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

      5. associate-/l* 62.5%

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

      6. distribute-rgt-neg-in 62.5%

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

      7. mul-1-neg 62.5%

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

      8. distribute-frac-neg 62.5%

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

      9. remove-double-neg 62.5%

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

      10. distribute-neg-in 62.5%

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

      11. metadata-eval 62.5%

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

      12. unsub-neg 62.5%

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

   5. Simplified 62.5%

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

   6. Taylor expanded in x around inf 73.0%

      \[\leadsto \color{blue}{x \cdot \log y} \]

   if -1.20000000000000003e134 < x < 1.35000000000000001e126

   1. Initial program 99.9%

      \[\left(x \cdot \log y - z\right) - y \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 85.4%

      \[\leadsto \color{blue}{-1 \cdot \left(y + z\right)} \]
   4. Step-by-step derivation

      1. neg-mul-1 85.4%

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

      2. +-commutative 85.4%

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

      3. distribute-neg-in 85.4%

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

      4. sub-neg 85.4%

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

   5. Simplified 85.4%

      \[\leadsto \color{blue}{\left(-z\right) - y} \]
3. Recombined 2 regimes into one program.

4. Final simplification 81.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.2 \cdot 10^{+134} \lor \neg \left(x \leq 1.35 \cdot 10^{+126}\right):\\ \;\;\;\;x \cdot \log y\\ \mathbf{else}:\\ \;\;\;\;\left(-z\right) - y\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 99.9% accurate, 1.0× speedup

Math

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

FPCore

(FPCore (x y z) :precision binary64 (- (- (* x (log y)) z) y))

C

double code(double x, double y, double z) {
	return ((x * log(y)) - z) - y;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = ((x * log(y)) - z) - y
end function

Java

public static double code(double x, double y, double z) {
	return ((x * Math.log(y)) - z) - y;
}

Python

def code(x, y, z):
	return ((x * math.log(y)) - z) - y

Julia

function code(x, y, z)
	return Float64(Float64(Float64(x * log(y)) - z) - y)
end

MATLAB

function tmp = code(x, y, z)
	tmp = ((x * log(y)) - z) - y;
end

Wolfram

code[x_, y_, z_] := N[(N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision] - y), $MachinePrecision]

Derivation

1. Initial program 99.8%

   \[\left(x \cdot \log y - z\right) - y \]
2. Add Preprocessing
3. Add Preprocessing

Alternative 6: 52.8% accurate, 8.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1 \cdot 10^{+62} \lor \neg \left(z \leq 1.6 \cdot 10^{+34}\right):\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;-y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -1e+62) (not (<= z 1.6e+34))) (- z) (- y)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1e+62) || !(z <= 1.6e+34)) {
		tmp = -z;
	} else {
		tmp = -y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((z <= (-1d+62)) .or. (.not. (z <= 1.6d+34))) then
        tmp = -z
    else
        tmp = -y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1e+62) || !(z <= 1.6e+34)) {
		tmp = -z;
	} else {
		tmp = -y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -1e+62) or not (z <= 1.6e+34):
		tmp = -z
	else:
		tmp = -y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -1e+62) || !(z <= 1.6e+34))
		tmp = Float64(-z);
	else
		tmp = Float64(-y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -1e+62) || ~((z <= 1.6e+34)))
		tmp = -z;
	else
		tmp = -y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -1e+62], N[Not[LessEqual[z, 1.6e+34]], $MachinePrecision]], (-z), (-y)]

Derivation

1. Split input into 2 regimes

2. if z < -1.00000000000000004e62 or 1.5999999999999999e34 < z

   1. Initial program 99.9%

      \[\left(x \cdot \log y - z\right) - y \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 61.8%

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

      1. neg-mul-1 61.8%

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

   5. Simplified 61.8%

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

   if -1.00000000000000004e62 < z < 1.5999999999999999e34

   1. Initial program 99.8%

      \[\left(x \cdot \log y - z\right) - y \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 53.6%

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

      1. neg-mul-1 53.6%

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

   5. Simplified 53.6%

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

4. Final simplification 57.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1 \cdot 10^{+62} \lor \neg \left(z \leq 1.6 \cdot 10^{+34}\right):\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;-y\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 66.4% accurate, 26.8× speedup

Math

\[\begin{array}{l} \\ \left(-z\right) - y \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (- (- z) y))

C

double code(double x, double y, double z) {
	return -z - y;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = -z - y
end function

Java

public static double code(double x, double y, double z) {
	return -z - y;
}

Python

def code(x, y, z):
	return -z - y

Julia

function code(x, y, z)
	return Float64(Float64(-z) - y)
end

MATLAB

function tmp = code(x, y, z)
	tmp = -z - y;
end

Wolfram

code[x_, y_, z_] := N[((-z) - y), $MachinePrecision]

Derivation

1. Initial program 99.8%

   \[\left(x \cdot \log y - z\right) - y \]
2. Add Preprocessing

3. Taylor expanded in x around 0 67.5%

   \[\leadsto \color{blue}{-1 \cdot \left(y + z\right)} \]
4. Step-by-step derivation

   1. neg-mul-1 67.5%

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

   2. +-commutative 67.5%

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

   3. distribute-neg-in 67.5%

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

   4. sub-neg 67.5%

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

5. Simplified 67.5%

   \[\leadsto \color{blue}{\left(-z\right) - y} \]
6. Add Preprocessing

Alternative 8: 35.0% accurate, 53.5× speedup

Math

\[\begin{array}{l} \\ -y \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (- y))

C

double code(double x, double y, double z) {
	return -y;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = -y
end function

Java

public static double code(double x, double y, double z) {
	return -y;
}

Python

def code(x, y, z):
	return -y

Julia

function code(x, y, z)
	return Float64(-y)
end

MATLAB

function tmp = code(x, y, z)
	tmp = -y;
end

Wolfram

code[x_, y_, z_] := (-y)

Derivation

1. Initial program 99.8%

   \[\left(x \cdot \log y - z\right) - y \]
2. Add Preprocessing

3. Taylor expanded in y around inf 39.4%

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

   1. neg-mul-1 39.4%

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

5. Simplified 39.4%

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

Alternative 9: 2.3% accurate, 107.0× speedup

Math

\[\begin{array}{l} \\ z \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 z)

C

double code(double x, double y, double z) {
	return z;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = z
end function

Java

public static double code(double x, double y, double z) {
	return z;
}

Python

def code(x, y, z):
	return z

Julia

function code(x, y, z)
	return z
end

MATLAB

function tmp = code(x, y, z)
	tmp = z;
end

Wolfram

code[x_, y_, z_] := z

Derivation

1. Initial program 99.8%

   \[\left(x \cdot \log y - z\right) - y \]
2. Add Preprocessing

3. Taylor expanded in z around inf 30.2%

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

   1. neg-mul-1 30.2%

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

5. Simplified 30.2%

   \[\leadsto \color{blue}{-z} \]
6. Step-by-step derivation

   1. neg-sub0 30.2%

      \[\leadsto \color{blue}{0 - z} \]

   2. sub-neg 30.2%

      \[\leadsto \color{blue}{0 + \left(-z\right)} \]

   3. add-sqr-sqrt 13.7%

      \[\leadsto 0 + \color{blue}{\sqrt{-z} \cdot \sqrt{-z}} \]

   4. sqrt-unprod 6.4%

      \[\leadsto 0 + \color{blue}{\sqrt{\left(-z\right) \cdot \left(-z\right)}} \]

   5. sqr-neg 6.4%

      \[\leadsto 0 + \sqrt{\color{blue}{z \cdot z}} \]

   6. sqrt-unprod 1.0%

      \[\leadsto 0 + \color{blue}{\sqrt{z} \cdot \sqrt{z}} \]

   7. add-sqr-sqrt 2.5%

      \[\leadsto 0 + \color{blue}{z} \]

7. Applied egg-rr 2.5%

   \[\leadsto \color{blue}{0 + z} \]
8. Step-by-step derivation

   1. +-lft-identity 2.5%

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

9. Simplified 2.5%

   \[\leadsto \color{blue}{z} \]
10. Add Preprocessing

Alternative 10: 2.2% accurate, 107.0× speedup

Math

\[\begin{array}{l} \\ y \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 y)

C

double code(double x, double y, double z) {
	return y;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = y
end function

Java

public static double code(double x, double y, double z) {
	return y;
}

Python

def code(x, y, z):
	return y

Julia

function code(x, y, z)
	return y
end

MATLAB

function tmp = code(x, y, z)
	tmp = y;
end

Wolfram

code[x_, y_, z_] := y

Derivation

1. Initial program 99.8%

   \[\left(x \cdot \log y - z\right) - y \]
2. Add Preprocessing

3. Taylor expanded in y around inf 39.4%

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

   1. neg-mul-1 39.4%

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

5. Simplified 39.4%

   \[\leadsto \color{blue}{-y} \]
6. Step-by-step derivation

   1. neg-sub0 39.4%

      \[\leadsto \color{blue}{0 - y} \]

   2. sub-neg 39.4%

      \[\leadsto \color{blue}{0 + \left(-y\right)} \]

   3. add-sqr-sqrt 0.0%

      \[\leadsto 0 + \color{blue}{\sqrt{-y} \cdot \sqrt{-y}} \]

   4. sqrt-unprod 2.1%

      \[\leadsto 0 + \color{blue}{\sqrt{\left(-y\right) \cdot \left(-y\right)}} \]

   5. sqr-neg 2.1%

      \[\leadsto 0 + \sqrt{\color{blue}{y \cdot y}} \]

   6. sqrt-unprod 2.2%

      \[\leadsto 0 + \color{blue}{\sqrt{y} \cdot \sqrt{y}} \]

   7. add-sqr-sqrt 2.2%

      \[\leadsto 0 + \color{blue}{y} \]

7. Applied egg-rr 2.2%

   \[\leadsto \color{blue}{0 + y} \]
8. Step-by-step derivation

   1. +-lft-identity 2.2%

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

9. Simplified 2.2%

   \[\leadsto \color{blue}{y} \]
10. Add Preprocessing

Reproduce

herbie shell --seed 2024135 
(FPCore (x y z)
  :name "Statistics.Distribution.Poisson:$clogProbability from math-functions-0.1.5.2"
  :precision binary64
  (- (- (* x (log y)) z) y))