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

Percentage Accurate: 99.9% → 99.9%

Time: 9.2s

Alternatives: 8

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: 99.9% 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 99.9%

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

Alternative 2: 84.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.8 \cdot 10^{+93} \lor \neg \left(z \leq 2 \cdot 10^{+41}\right):\\ \;\;\;\;\left(-z\right) - y\\ \mathbf{else}:\\ \;\;\;\;x \cdot \log y - y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -5.8e+93) (not (<= z 2e+41))) (- (- z) y) (- (* x (log y)) y)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -5.8e+93) || !(z <= 2e+41)) {
		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 <= (-5.8d+93)) .or. (.not. (z <= 2d+41))) 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 <= -5.8e+93) || !(z <= 2e+41)) {
		tmp = -z - y;
	} else {
		tmp = (x * Math.log(y)) - y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -5.8e+93) or not (z <= 2e+41):
		tmp = -z - y
	else:
		tmp = (x * math.log(y)) - y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -5.8e+93) || !(z <= 2e+41))
		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 <= -5.8e+93) || ~((z <= 2e+41)))
		tmp = -z - y;
	else
		tmp = (x * log(y)) - y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -5.8e+93], N[Not[LessEqual[z, 2e+41]], $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 < -5.7999999999999997e93 or 2.00000000000000001e41 < z

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 82.8%

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

      1. neg-mul-1 82.8%

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

   5. Simplified 82.8%

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

   if -5.7999999999999997e93 < z < 2.00000000000000001e41

   1. Initial program 99.8%

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

   3. Taylor expanded in z around 0 87.1%

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

4. Final simplification 85.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.8 \cdot 10^{+93} \lor \neg \left(z \leq 2 \cdot 10^{+41}\right):\\ \;\;\;\;\left(-z\right) - y\\ \mathbf{else}:\\ \;\;\;\;x \cdot \log y - y\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 78.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.8 \cdot 10^{+203} \lor \neg \left(x \leq 8.5 \cdot 10^{+105}\right):\\ \;\;\;\;x \cdot \log y\\ \mathbf{else}:\\ \;\;\;\;\left(-z\right) - y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -2.8e+203) (not (<= x 8.5e+105))) (* x (log y)) (- (- z) y)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -2.8e+203) || !(x <= 8.5e+105)) {
		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 <= (-2.8d+203)) .or. (.not. (x <= 8.5d+105))) 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 <= -2.8e+203) || !(x <= 8.5e+105)) {
		tmp = x * Math.log(y);
	} else {
		tmp = -z - y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -2.8e+203) or not (x <= 8.5e+105):
		tmp = x * math.log(y)
	else:
		tmp = -z - y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -2.8e+203) || !(x <= 8.5e+105))
		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 <= -2.8e+203) || ~((x <= 8.5e+105)))
		tmp = x * log(y);
	else
		tmp = -z - y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -2.8e+203], N[Not[LessEqual[x, 8.5e+105]], $MachinePrecision]], N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision], N[((-z) - y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -2.7999999999999999e203 or 8.49999999999999986e105 < x

   1. Initial program 99.7%

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

   3. Taylor expanded in y around inf 68.5%

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

      1. sub-neg 68.5%

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

      2. mul-1-neg 68.5%

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

      3. *-commutative 68.5%

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

      4. associate-/l* 68.5%

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

      5. distribute-lft-neg-in 68.5%

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

      6. log-rec 68.5%

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

      7. remove-double-neg 68.5%

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

      8. distribute-neg-in 68.5%

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

      9. metadata-eval 68.5%

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

      10. unsub-neg 68.5%

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

   5. Simplified 68.5%

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

   6. Taylor expanded in x around inf 68.5%

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

      1. associate-*r/ 68.5%

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

      2. distribute-lft-in 68.5%

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

      3. metadata-eval 68.5%

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

      4. mul-1-neg 68.5%

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

      5. sub-neg 68.5%

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

   8. Simplified 68.5%

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

   9. Taylor expanded in x around inf 68.8%

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

   if -2.7999999999999999e203 < x < 8.49999999999999986e105

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 83.2%

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

      1. neg-mul-1 83.2%

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

   5. Simplified 83.2%

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

4. Final simplification 79.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.8 \cdot 10^{+203} \lor \neg \left(x \leq 8.5 \cdot 10^{+105}\right):\\ \;\;\;\;x \cdot \log y\\ \mathbf{else}:\\ \;\;\;\;\left(-z\right) - y\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 85.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 1.25 \cdot 10^{+72}:\\ \;\;\;\;x \cdot \log y - z\\ \mathbf{else}:\\ \;\;\;\;\left(-z\right) - y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y 1.25e+72) (- (* x (log y)) z) (- (- z) y)))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= 1.25e+72) {
		tmp = (x * log(y)) - z;
	} 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 (y <= 1.25d+72) then
        tmp = (x * log(y)) - z
    else
        tmp = -z - y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= 1.25e+72) {
		tmp = (x * Math.log(y)) - z;
	} else {
		tmp = -z - y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= 1.25e+72:
		tmp = (x * math.log(y)) - z
	else:
		tmp = -z - y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= 1.25e+72)
		tmp = Float64(Float64(x * log(y)) - z);
	else
		tmp = Float64(Float64(-z) - y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= 1.25e+72)
		tmp = (x * log(y)) - z;
	else
		tmp = -z - y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, 1.25e+72], N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision], N[((-z) - y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 1.24999999999999998e72

   1. Initial program 99.8%

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

   3. Taylor expanded in y around inf 73.0%

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

      1. sub-neg 73.0%

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

      2. mul-1-neg 73.0%

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

      3. *-commutative 73.0%

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

      4. associate-/l* 72.9%

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

      5. distribute-lft-neg-in 72.9%

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

      6. log-rec 72.9%

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

      7. remove-double-neg 72.9%

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

      8. distribute-neg-in 72.9%

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

      9. metadata-eval 72.9%

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

      10. unsub-neg 72.9%

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

   5. Simplified 72.9%

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

      1. clear-num 72.9%

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

      2. un-div-inv 73.0%

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

   7. Applied egg-rr 73.0%

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

   8. Taylor expanded in y around 0 87.2%

      \[\leadsto \color{blue}{x \cdot \log y - z} \]
   9. Step-by-step derivation

      1. *-commutative 87.2%

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

   10. Simplified 87.2%

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

   if 1.24999999999999998e72 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 85.8%

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

      1. neg-mul-1 85.8%

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

   5. Simplified 85.8%

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

4. Final simplification 86.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 1.25 \cdot 10^{+72}:\\ \;\;\;\;x \cdot \log y - z\\ \mathbf{else}:\\ \;\;\;\;\left(-z\right) - y\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 52.5% accurate, 15.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 2.3 \cdot 10^{+34}:\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;-y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (if (<= y 2.3e+34) (- z) (- y)))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= 2.3e+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 (y <= 2.3d+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 (y <= 2.3e+34) {
		tmp = -z;
	} else {
		tmp = -y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= 2.3e+34:
		tmp = -z
	else:
		tmp = -y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= 2.3e+34)
		tmp = Float64(-z);
	else
		tmp = Float64(-y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= 2.3e+34)
		tmp = -z;
	else
		tmp = -y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, 2.3e+34], (-z), (-y)]

Derivation

1. Split input into 2 regimes

2. if y < 2.2999999999999998e34

   1. Initial program 99.8%

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

   3. Taylor expanded in y around inf 69.6%

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

      1. sub-neg 69.6%

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

      2. mul-1-neg 69.6%

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

      3. *-commutative 69.6%

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

      4. associate-/l* 69.5%

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

      5. distribute-lft-neg-in 69.5%

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

      6. log-rec 69.5%

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

      7. remove-double-neg 69.5%

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

      8. distribute-neg-in 69.5%

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

      9. metadata-eval 69.5%

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

      10. unsub-neg 69.5%

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

   5. Simplified 69.5%

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

      1. clear-num 69.5%

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

      2. un-div-inv 69.6%

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

   7. Applied egg-rr 69.6%

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

   8. Taylor expanded in z around inf 49.1%

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

      1. neg-mul-1 49.1%

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

   10. Simplified 49.1%

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

   if 2.2999999999999998e34 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 63.6%

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

      1. neg-mul-1 63.6%

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

   5. Simplified 63.6%

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

Alternative 6: 65.8% 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 99.9%

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

3. Taylor expanded in x around 0 68.6%

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

   1. neg-mul-1 68.6%

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

5. Simplified 68.6%

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

Alternative 7: 34.0% 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 99.9%

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

3. Taylor expanded in y around inf 33.8%

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

   1. neg-mul-1 33.8%

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

5. Simplified 33.8%

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

Alternative 8: 2.3% 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 99.9%

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

3. Taylor expanded in y around inf 33.8%

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

   1. neg-mul-1 33.8%

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

5. Simplified 33.8%

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

   1. neg-sub0 33.8%

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

   2. sub-neg 33.8%

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

   3. add-sqr-sqrt 0.0%

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

   4. sqrt-unprod 2.3%

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

   5. sqr-neg 2.3%

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

   6. sqrt-unprod 2.3%

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

   7. add-sqr-sqrt 2.3%

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

7. Applied egg-rr 2.3%

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

   1. +-lft-identity 2.3%

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

9. Simplified 2.3%

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

Reproduce

herbie shell --seed 2024131 
(FPCore (x y z)
  :name "Statistics.Distribution.Poisson:$clogProbability from math-functions-0.1.5.2"
  :precision binary64
  (- (- (* x (log y)) z) y))