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

Percentage Accurate: 99.8% → 99.8%

Time: 7.7s

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: 99.8% 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, 1.0× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

   1. lift--.f64 N/A

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

   2. lift--.f64 N/A

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

   3. sub-neg N/A

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

   4. associate--l+ N/A

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

   5. lift-*.f64 N/A

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

   6. *-commutative N/A

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

   7. lower-fma.f64 N/A

      \[\leadsto \color{blue}{\mathsf{fma}\left(\log y, x, \left(\mathsf{neg}\left(z\right)\right) - y\right)} \]

   8. lower--.f64 N/A

      \[\leadsto \mathsf{fma}\left(\log y, x, \color{blue}{\left(\mathsf{neg}\left(z\right)\right) - y}\right) \]

   9. lower-neg.f64 99.9

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

4. Applied rewrites 99.9%

   \[\leadsto \color{blue}{\mathsf{fma}\left(\log y, x, \left(-z\right) - y\right)} \]
5. Add Preprocessing

Alternative 2: 85.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -0.0135 \lor \neg \left(x \leq 1.3 \cdot 10^{-13}\right):\\ \;\;\;\;x \cdot \log y - z\\ \mathbf{else}:\\ \;\;\;\;\left(-z\right) - y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -0.0135) (not (<= x 1.3e-13))) (- (* x (log y)) z) (- (- z) y)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -0.0135) || !(x <= 1.3e-13)) {
		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 ((x <= (-0.0135d0)) .or. (.not. (x <= 1.3d-13))) 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 ((x <= -0.0135) || !(x <= 1.3e-13)) {
		tmp = (x * Math.log(y)) - z;
	} else {
		tmp = -z - y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -0.0135) or not (x <= 1.3e-13):
		tmp = (x * math.log(y)) - z
	else:
		tmp = -z - y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -0.0135) || !(x <= 1.3e-13))
		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 ((x <= -0.0135) || ~((x <= 1.3e-13)))
		tmp = (x * log(y)) - z;
	else
		tmp = -z - y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -0.0135], N[Not[LessEqual[x, 1.3e-13]], $MachinePrecision]], N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision], N[((-z) - y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -0.0134999999999999998 or 1.3e-13 < x

   1. Initial program 99.8%

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

      1. lift--.f64 N/A

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

      2. lift--.f64 N/A

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

      3. sub-neg N/A

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

      4. associate--l+ N/A

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

      5. lift-*.f64 N/A

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

      6. *-commutative N/A

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

      7. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(\log y, x, \left(\mathsf{neg}\left(z\right)\right) - y\right)} \]

      8. lower--.f64 N/A

         \[\leadsto \mathsf{fma}\left(\log y, x, \color{blue}{\left(\mathsf{neg}\left(z\right)\right) - y}\right) \]

      9. lower-neg.f64 99.8

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

   4. Applied rewrites 99.8%

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

   6. Applied rewrites 99.5%

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

   7. Taylor expanded in y around 0

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

   9. Applied rewrites 27.7%

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

   11. Applied rewrites 79.7%

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

   if -0.0134999999999999998 < x < 1.3e-13

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 96.4

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

   5. Applied rewrites 96.4%

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

4. Final simplification 87.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -0.0135 \lor \neg \left(x \leq 1.3 \cdot 10^{-13}\right):\\ \;\;\;\;x \cdot \log y - z\\ \mathbf{else}:\\ \;\;\;\;\left(-z\right) - y\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 85.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7.6 \cdot 10^{+103}:\\ \;\;\;\;\left(-z\right) - y\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{+47}:\\ \;\;\;\;\mathsf{fma}\left(\log y, x, -y\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \log y - z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -7.6e+103)
   (- (- z) y)
   (if (<= z 2.4e+47) (fma (log y) x (- y)) (- (* x (log y)) z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -7.6e+103) {
		tmp = -z - y;
	} else if (z <= 2.4e+47) {
		tmp = fma(log(y), x, -y);
	} else {
		tmp = (x * log(y)) - z;
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -7.6e+103)
		tmp = Float64(Float64(-z) - y);
	elseif (z <= 2.4e+47)
		tmp = fma(log(y), x, Float64(-y));
	else
		tmp = Float64(Float64(x * log(y)) - z);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -7.6e+103], N[((-z) - y), $MachinePrecision], If[LessEqual[z, 2.4e+47], N[(N[Log[y], $MachinePrecision] * x + (-y)), $MachinePrecision], N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -7.5999999999999994e103

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 88.9

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

   5. Applied rewrites 88.9%

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

   if -7.5999999999999994e103 < z < 2.40000000000000019e47

   1. Initial program 99.8%

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

   3. Taylor expanded in z around 0

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

      1. sub-neg N/A

         \[\leadsto \color{blue}{x \cdot \log y + \left(\mathsf{neg}\left(y\right)\right)} \]

      2. *-commutative N/A

         \[\leadsto \color{blue}{\log y \cdot x} + \left(\mathsf{neg}\left(y\right)\right) \]

      3. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(\log y, x, \mathsf{neg}\left(y\right)\right)} \]

      4. lower-log.f64 N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{\log y}, x, \mathsf{neg}\left(y\right)\right) \]

      5. lower-neg.f64 88.4

         \[\leadsto \mathsf{fma}\left(\log y, x, \color{blue}{-y}\right) \]

   5. Applied rewrites 88.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\log y, x, -y\right)} \]

   if 2.40000000000000019e47 < z

   1. Initial program 99.9%

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

      1. lift--.f64 N/A

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

      2. lift--.f64 N/A

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

      3. sub-neg N/A

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

      4. associate--l+ N/A

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

      5. lift-*.f64 N/A

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

      6. *-commutative N/A

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

      7. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(\log y, x, \left(\mathsf{neg}\left(z\right)\right) - y\right)} \]

      8. lower--.f64 N/A

         \[\leadsto \mathsf{fma}\left(\log y, x, \color{blue}{\left(\mathsf{neg}\left(z\right)\right) - y}\right) \]

      9. lower-neg.f64 99.9

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

   4. Applied rewrites 99.9%

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

   6. Applied rewrites 99.8%

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

   7. Taylor expanded in y around 0

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

   9. Applied rewrites 27.5%

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

   11. Applied rewrites 96.8%

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

Alternative 4: 80.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -8 \cdot 10^{+152} \lor \neg \left(x \leq 1.3 \cdot 10^{+131}\right):\\ \;\;\;\;\log y \cdot x\\ \mathbf{else}:\\ \;\;\;\;\left(-z\right) - y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -8e+152) (not (<= x 1.3e+131))) (* (log y) x) (- (- z) y)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -8e+152) || !(x <= 1.3e+131)) {
		tmp = log(y) * x;
	} 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 <= (-8d+152)) .or. (.not. (x <= 1.3d+131))) then
        tmp = log(y) * x
    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 <= -8e+152) || !(x <= 1.3e+131)) {
		tmp = Math.log(y) * x;
	} else {
		tmp = -z - y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -8e+152) or not (x <= 1.3e+131):
		tmp = math.log(y) * x
	else:
		tmp = -z - y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -8e+152) || !(x <= 1.3e+131))
		tmp = Float64(log(y) * x);
	else
		tmp = Float64(Float64(-z) - y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -8e+152) || ~((x <= 1.3e+131)))
		tmp = log(y) * x;
	else
		tmp = -z - y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -8e+152], N[Not[LessEqual[x, 1.3e+131]], $MachinePrecision]], N[(N[Log[y], $MachinePrecision] * x), $MachinePrecision], N[((-z) - y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -8.0000000000000004e152 or 1.3e131 < x

   1. Initial program 99.8%

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

      1. lift--.f64 N/A

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

      2. lift--.f64 N/A

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

      3. sub-neg N/A

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

      4. associate--l+ N/A

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

      5. lift-*.f64 N/A

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

      6. *-commutative N/A

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

      7. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(\log y, x, \left(\mathsf{neg}\left(z\right)\right) - y\right)} \]

      8. lower--.f64 N/A

         \[\leadsto \mathsf{fma}\left(\log y, x, \color{blue}{\left(\mathsf{neg}\left(z\right)\right) - y}\right) \]

      9. lower-neg.f64 99.8

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

   4. Applied rewrites 99.8%

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

   6. Applied rewrites 99.4%

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

   7. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-log.f64 73.3

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

   9. Applied rewrites 73.3%

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

   if -8.0000000000000004e152 < x < 1.3e131

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 83.6

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

   5. Applied rewrites 83.6%

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

4. Final simplification 80.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -8 \cdot 10^{+152} \lor \neg \left(x \leq 1.3 \cdot 10^{+131}\right):\\ \;\;\;\;\log y \cdot x\\ \mathbf{else}:\\ \;\;\;\;\left(-z\right) - y\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 99.8% 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 6: 65.7% accurate, 18.7× 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

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

   1. mul-1-neg N/A

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

   2. lower-neg.f64 66.0

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

5. Applied rewrites 66.0%

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

Alternative 7: 33.9% accurate, 37.3× 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

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

   1. mul-1-neg N/A

      \[\leadsto \color{blue}{\mathsf{neg}\left(y\right)} \]

   2. lower-neg.f64 34.0

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

5. Applied rewrites 34.0%

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

Alternative 8: 2.3% accurate, 112.0× 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

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

   1. mul-1-neg N/A

      \[\leadsto \color{blue}{\mathsf{neg}\left(y\right)} \]

   2. lower-neg.f64 34.0

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

5. Applied rewrites 34.0%

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

7. Applied rewrites 16.9%

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

9. Applied rewrites 2.1%

   \[\leadsto y \]
10. Add Preprocessing

Reproduce

herbie shell --seed 2024313 
(FPCore (x y z)
  :name "Statistics.Distribution.Poisson:$clogProbability from math-functions-0.1.5.2"
  :precision binary64
  (- (- (* x (log y)) z) y))