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

Percentage Accurate: 99.9% → 99.9%

Time: 7.6s

Alternatives: 9

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

\[\begin{array}{l} \\ \left(x \cdot \left(-\log \left(\frac{1}{y}\right)\right) - z\right) - y \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (- (- (* x (- (log (/ 1.0 y)))) z) y))

C

double code(double x, double y, double z) {
	return ((x * -log((1.0 / 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((1.0d0 / y))) - z) - y
end function

Java

public static double code(double x, double y, double z) {
	return ((x * -Math.log((1.0 / y))) - z) - y;
}

Python

def code(x, y, z):
	return ((x * -math.log((1.0 / y))) - z) - y

Julia

function code(x, y, z)
	return Float64(Float64(Float64(x * Float64(-log(Float64(1.0 / y)))) - z) - y)
end

MATLAB

function tmp = code(x, y, z)
	tmp = ((x * -log((1.0 / y))) - z) - y;
end

Wolfram

code[x_, y_, z_] := N[(N[(N[(x * (-N[Log[N[(1.0 / y), $MachinePrecision]], $MachinePrecision])), $MachinePrecision] - z), $MachinePrecision] - y), $MachinePrecision]

Derivation

1. Initial program 99.9%

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

3. Taylor expanded in y around inf 99.9%

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

4. Final simplification 99.9%

   \[\leadsto \left(x \cdot \left(-\log \left(\frac{1}{y}\right)\right) - z\right) - y \]
5. Add Preprocessing

Alternative 2: 84.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{+111} \lor \neg \left(z \leq 9.8 \cdot 10^{+122}\right):\\ \;\;\;\;\left(-z\right) - y\\ \mathbf{else}:\\ \;\;\;\;x \cdot \log y - y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -2e+111) (not (<= z 9.8e+122)))
   (- (- z) y)
   (- (* x (log y)) y)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -2e+111) || !(z <= 9.8e+122)) {
		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 <= (-2d+111)) .or. (.not. (z <= 9.8d+122))) 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 <= -2e+111) || !(z <= 9.8e+122)) {
		tmp = -z - y;
	} else {
		tmp = (x * Math.log(y)) - y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -2e+111) or not (z <= 9.8e+122):
		tmp = -z - y
	else:
		tmp = (x * math.log(y)) - y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -2e+111) || !(z <= 9.8e+122))
		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 <= -2e+111) || ~((z <= 9.8e+122)))
		tmp = -z - y;
	else
		tmp = (x * log(y)) - y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -2e+111], N[Not[LessEqual[z, 9.8e+122]], $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 < -1.99999999999999991e111 or 9.7999999999999995e122 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 85.9%

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

      1. neg-mul-1 85.9%

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

   5. Simplified 85.9%

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

   if -1.99999999999999991e111 < z < 9.7999999999999995e122

   1. Initial program 99.8%

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

   3. Taylor expanded in z around 0 90.7%

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

4. Final simplification 89.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{+111} \lor \neg \left(z \leq 9.8 \cdot 10^{+122}\right):\\ \;\;\;\;\left(-z\right) - y\\ \mathbf{else}:\\ \;\;\;\;x \cdot \log y - y\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 84.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \log y\\ \mathbf{if}\;z \leq -2.1 \cdot 10^{+111}:\\ \;\;\;\;\left(-z\right) - y\\ \mathbf{elif}\;z \leq 2.75 \cdot 10^{+119}:\\ \;\;\;\;t_0 - y\\ \mathbf{else}:\\ \;\;\;\;t_0 - z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (log y))))
   (if (<= z -2.1e+111)
     (- (- z) y)
     (if (<= z 2.75e+119) (- t_0 y) (- t_0 z)))))

C

double code(double x, double y, double z) {
	double t_0 = x * log(y);
	double tmp;
	if (z <= -2.1e+111) {
		tmp = -z - y;
	} else if (z <= 2.75e+119) {
		tmp = t_0 - y;
	} else {
		tmp = t_0 - 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) :: tmp
    t_0 = x * log(y)
    if (z <= (-2.1d+111)) then
        tmp = -z - y
    else if (z <= 2.75d+119) then
        tmp = t_0 - y
    else
        tmp = t_0 - z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = x * Math.log(y);
	double tmp;
	if (z <= -2.1e+111) {
		tmp = -z - y;
	} else if (z <= 2.75e+119) {
		tmp = t_0 - y;
	} else {
		tmp = t_0 - z;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * math.log(y)
	tmp = 0
	if z <= -2.1e+111:
		tmp = -z - y
	elif z <= 2.75e+119:
		tmp = t_0 - y
	else:
		tmp = t_0 - z
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * log(y))
	tmp = 0.0
	if (z <= -2.1e+111)
		tmp = Float64(Float64(-z) - y);
	elseif (z <= 2.75e+119)
		tmp = Float64(t_0 - y);
	else
		tmp = Float64(t_0 - z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * log(y);
	tmp = 0.0;
	if (z <= -2.1e+111)
		tmp = -z - y;
	elseif (z <= 2.75e+119)
		tmp = t_0 - y;
	else
		tmp = t_0 - z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.1e+111], N[((-z) - y), $MachinePrecision], If[LessEqual[z, 2.75e+119], N[(t$95$0 - y), $MachinePrecision], N[(t$95$0 - z), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.09999999999999995e111

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 83.5%

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

      1. neg-mul-1 83.5%

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

   5. Simplified 83.5%

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

   if -2.09999999999999995e111 < z < 2.7500000000000002e119

   1. Initial program 99.8%

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

   3. Taylor expanded in z around 0 90.6%

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

   if 2.7500000000000002e119 < z

   1. Initial program 100.0%

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

      1. associate--l- 100.0%

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

      2. *-commutative 100.0%

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

      3. fma-neg 100.0%

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

      4. +-commutative 100.0%

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

      5. distribute-neg-out 100.0%

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

      6. sub-neg 100.0%

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

      7. add-sqr-sqrt 0.0%

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

      8. sqrt-unprod 88.0%

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

      9. sqr-neg 88.0%

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

      10. sqrt-unprod 94.0%

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

      11. add-sqr-sqrt 94.0%

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

   4. Applied egg-rr 94.0%

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

   5. Taylor expanded in y around 0 94.4%

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

4. Final simplification 90.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.1 \cdot 10^{+111}:\\ \;\;\;\;\left(-z\right) - y\\ \mathbf{elif}\;z \leq 2.75 \cdot 10^{+119}:\\ \;\;\;\;x \cdot \log y - y\\ \mathbf{else}:\\ \;\;\;\;x \cdot \log y - z\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 80.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3 \cdot 10^{+124} \lor \neg \left(x \leq 8.2 \cdot 10^{+136}\right):\\ \;\;\;\;x \cdot \log y\\ \mathbf{else}:\\ \;\;\;\;\left(-z\right) - y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -3e+124) (not (<= x 8.2e+136))) (* x (log y)) (- (- z) y)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -3e+124) || !(x <= 8.2e+136)) {
		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 <= (-3d+124)) .or. (.not. (x <= 8.2d+136))) 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 <= -3e+124) || !(x <= 8.2e+136)) {
		tmp = x * Math.log(y);
	} else {
		tmp = -z - y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -3e+124) or not (x <= 8.2e+136):
		tmp = x * math.log(y)
	else:
		tmp = -z - y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -3e+124) || !(x <= 8.2e+136))
		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 <= -3e+124) || ~((x <= 8.2e+136)))
		tmp = x * log(y);
	else
		tmp = -z - y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -3e+124], N[Not[LessEqual[x, 8.2e+136]], $MachinePrecision]], N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision], N[((-z) - y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -3e124 or 8.1999999999999995e136 < x

   1. Initial program 99.7%

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

   3. Taylor expanded in z around 0 89.9%

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

   4. Taylor expanded in x around inf 81.2%

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

   if -3e124 < x < 8.1999999999999995e136

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 85.6%

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

      1. neg-mul-1 85.6%

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

   5. Simplified 85.6%

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

4. Final simplification 84.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3 \cdot 10^{+124} \lor \neg \left(x \leq 8.2 \cdot 10^{+136}\right):\\ \;\;\;\;x \cdot \log y\\ \mathbf{else}:\\ \;\;\;\;\left(-z\right) - y\\ \end{array} \]
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 99.9%

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

3. Final simplification 99.9%

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

Alternative 6: 52.0% accurate, 17.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.9 \cdot 10^{+106} \lor \neg \left(z \leq 3.9 \cdot 10^{+122}\right):\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;-y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -2.9e+106) (not (<= z 3.9e+122))) (- z) (- y)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -2.9e+106) || !(z <= 3.9e+122)) {
		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 <= (-2.9d+106)) .or. (.not. (z <= 3.9d+122))) 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 <= -2.9e+106) || !(z <= 3.9e+122)) {
		tmp = -z;
	} else {
		tmp = -y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -2.9e+106) or not (z <= 3.9e+122):
		tmp = -z
	else:
		tmp = -y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -2.9e+106) || !(z <= 3.9e+122))
		tmp = Float64(-z);
	else
		tmp = Float64(-y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -2.9e+106) || ~((z <= 3.9e+122)))
		tmp = -z;
	else
		tmp = -y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -2.9e+106], N[Not[LessEqual[z, 3.9e+122]], $MachinePrecision]], (-z), (-y)]

Derivation

1. Split input into 2 regimes

2. if z < -2.9000000000000002e106 or 3.8999999999999999e122 < z

   1. Initial program 100.0%

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

      1. associate--l- 100.0%

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

      2. *-commutative 100.0%

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

      3. fma-neg 100.0%

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

      4. +-commutative 100.0%

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

      5. distribute-neg-out 100.0%

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

      6. sub-neg 100.0%

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

      7. add-sqr-sqrt 0.0%

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

      8. sqrt-unprod 77.9%

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

      9. sqr-neg 77.9%

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

      10. sqrt-unprod 88.6%

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

      11. add-sqr-sqrt 88.6%

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

   4. Applied egg-rr 88.6%

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

   5. Taylor expanded in z around inf 72.0%

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

      1. neg-mul-1 72.0%

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

   7. Simplified 72.0%

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

   if -2.9000000000000002e106 < z < 3.8999999999999999e122

   1. Initial program 99.9%

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

   3. Taylor expanded in y around inf 46.1%

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

      1. mul-1-neg 46.1%

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

   5. Simplified 46.1%

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

4. Final simplification 55.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.9 \cdot 10^{+106} \lor \neg \left(z \leq 3.9 \cdot 10^{+122}\right):\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;-y\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 66.5% 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 64.9%

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

   1. neg-mul-1 64.9%

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

5. Simplified 64.9%

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

6. Final simplification 64.9%

   \[\leadsto \left(-z\right) - y \]
7. Add Preprocessing

Alternative 8: 34.1% 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 34.5%

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

   1. mul-1-neg 34.5%

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

5. Simplified 34.5%

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

6. Final simplification 34.5%

   \[\leadsto -y \]
7. Add Preprocessing

Alternative 9: 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. Step-by-step derivation

   1. associate--l- 99.9%

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

   2. *-commutative 99.9%

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

   3. fma-neg 99.9%

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

   4. +-commutative 99.9%

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

   5. distribute-neg-out 99.9%

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

   6. sub-neg 99.9%

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

   7. add-sqr-sqrt 0.0%

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

   8. sqrt-unprod 59.9%

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

   9. sqr-neg 59.9%

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

   10. sqrt-unprod 66.6%

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

   11. add-sqr-sqrt 66.6%

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

4. Applied egg-rr 66.6%

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

5. Taylor expanded in y around inf 2.1%

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

6. Final simplification 2.1%

   \[\leadsto y \]
7. Add Preprocessing

Reproduce

herbie shell --seed 2024013 
(FPCore (x y z)
  :name "Statistics.Distribution.Poisson:$clogProbability from math-functions-0.1.5.2"
  :precision binary64
  (- (- (* x (log y)) z) y))