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

Percentage Accurate: 99.9% → 99.9%

Time: 9.5s

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

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

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 2: 85.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.5 \cdot 10^{+22} \lor \neg \left(z \leq 7.6 \cdot 10^{+83}\right):\\ \;\;\;\;\left(-z\right) - y\\ \mathbf{else}:\\ \;\;\;\;x \cdot \log y - y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -5.5e+22) (not (<= z 7.6e+83)))
   (- (- z) y)
   (- (* x (log y)) y)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -5.5e+22) || !(z <= 7.6e+83)) {
		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 <= (-5.5d+22)) .or. (.not. (z <= 7.6d+83))) 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 <= -5.5e+22) || !(z <= 7.6e+83)) {
		tmp = -z - y;
	} else {
		tmp = (x * Math.log(y)) - y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -5.5e+22) or not (z <= 7.6e+83):
		tmp = -z - y
	else:
		tmp = (x * math.log(y)) - y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -5.5e+22) || !(z <= 7.6e+83))
		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 <= -5.5e+22) || ~((z <= 7.6e+83)))
		tmp = -z - y;
	else
		tmp = (x * log(y)) - y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -5.5e+22], N[Not[LessEqual[z, 7.6e+83]], $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 < -5.50000000000000021e22 or 7.6000000000000004e83 < z

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 85.3%

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

      1. neg-mul-1 85.3%

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

      2. +-commutative 85.3%

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

      3. distribute-neg-in 85.3%

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

      4. sub-neg 85.3%

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

   5. Simplified 85.3%

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

   if -5.50000000000000021e22 < z < 7.6000000000000004e83

   1. Initial program 99.7%

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

   3. Taylor expanded in z around 0 93.4%

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

4. Final simplification 90.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.5 \cdot 10^{+22} \lor \neg \left(z \leq 7.6 \cdot 10^{+83}\right):\\ \;\;\;\;\left(-z\right) - y\\ \mathbf{else}:\\ \;\;\;\;x \cdot \log y - y\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 84.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \log y\\ \mathbf{if}\;x \leq -1.9 \cdot 10^{+48}:\\ \;\;\;\;t\_0 - z\\ \mathbf{elif}\;x \leq 2.8 \cdot 10^{-22}:\\ \;\;\;\;\left(-z\right) - y\\ \mathbf{else}:\\ \;\;\;\;t\_0 - y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (log y))))
   (if (<= x -1.9e+48) (- t_0 z) (if (<= x 2.8e-22) (- (- z) y) (- t_0 y)))))

C

double code(double x, double y, double z) {
	double t_0 = x * log(y);
	double tmp;
	if (x <= -1.9e+48) {
		tmp = t_0 - z;
	} else if (x <= 2.8e-22) {
		tmp = -z - y;
	} else {
		tmp = t_0 - 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) :: t_0
    real(8) :: tmp
    t_0 = x * log(y)
    if (x <= (-1.9d+48)) then
        tmp = t_0 - z
    else if (x <= 2.8d-22) then
        tmp = -z - y
    else
        tmp = t_0 - y
    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 (x <= -1.9e+48) {
		tmp = t_0 - z;
	} else if (x <= 2.8e-22) {
		tmp = -z - y;
	} else {
		tmp = t_0 - y;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * math.log(y)
	tmp = 0
	if x <= -1.9e+48:
		tmp = t_0 - z
	elif x <= 2.8e-22:
		tmp = -z - y
	else:
		tmp = t_0 - y
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * log(y))
	tmp = 0.0
	if (x <= -1.9e+48)
		tmp = Float64(t_0 - z);
	elseif (x <= 2.8e-22)
		tmp = Float64(Float64(-z) - y);
	else
		tmp = Float64(t_0 - y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * log(y);
	tmp = 0.0;
	if (x <= -1.9e+48)
		tmp = t_0 - z;
	elseif (x <= 2.8e-22)
		tmp = -z - y;
	else
		tmp = t_0 - y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.9e+48], N[(t$95$0 - z), $MachinePrecision], If[LessEqual[x, 2.8e-22], N[((-z) - y), $MachinePrecision], N[(t$95$0 - y), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.9e48

   1. Initial program 99.7%

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

   3. Taylor expanded in y around 0 94.9%

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

   if -1.9e48 < x < 2.79999999999999995e-22

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 94.4%

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

      1. neg-mul-1 94.4%

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

      2. +-commutative 94.4%

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

      3. distribute-neg-in 94.4%

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

      4. sub-neg 94.4%

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

   5. Simplified 94.4%

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

   if 2.79999999999999995e-22 < x

   1. Initial program 99.6%

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

   3. Taylor expanded in z around 0 83.3%

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

Alternative 4: 79.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4 \cdot 10^{+129} \lor \neg \left(x \leq 3 \cdot 10^{+101}\right):\\ \;\;\;\;x \cdot \log y\\ \mathbf{else}:\\ \;\;\;\;\left(-z\right) - y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -4e+129) (not (<= x 3e+101))) (* x (log y)) (- (- z) y)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -4e+129) || !(x <= 3e+101)) {
		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 <= (-4d+129)) .or. (.not. (x <= 3d+101))) 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 <= -4e+129) || !(x <= 3e+101)) {
		tmp = x * Math.log(y);
	} else {
		tmp = -z - y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -4e+129) or not (x <= 3e+101):
		tmp = x * math.log(y)
	else:
		tmp = -z - y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -4e+129) || !(x <= 3e+101))
		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 <= -4e+129) || ~((x <= 3e+101)))
		tmp = x * log(y);
	else
		tmp = -z - y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -4e+129], N[Not[LessEqual[x, 3e+101]], $MachinePrecision]], N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision], N[((-z) - y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -4e129 or 2.99999999999999993e101 < x

   1. Initial program 99.5%

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

   3. Taylor expanded in x around inf 87.5%

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

   if -4e129 < x < 2.99999999999999993e101

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 83.5%

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

      1. neg-mul-1 83.5%

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

      2. +-commutative 83.5%

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

      3. distribute-neg-in 83.5%

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

      4. sub-neg 83.5%

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

   5. Simplified 83.5%

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

4. Final simplification 84.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4 \cdot 10^{+129} \lor \neg \left(x \leq 3 \cdot 10^{+101}\right):\\ \;\;\;\;x \cdot \log y\\ \mathbf{else}:\\ \;\;\;\;\left(-z\right) - y\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 51.8% accurate, 15.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 1.26 \cdot 10^{+57}:\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;-y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (if (<= y 1.26e+57) (- z) (- y)))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= 1.26e+57) {
		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 <= 1.26d+57) 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 <= 1.26e+57) {
		tmp = -z;
	} else {
		tmp = -y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= 1.26e+57:
		tmp = -z
	else:
		tmp = -y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= 1.26e+57)
		tmp = Float64(-z);
	else
		tmp = Float64(-y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= 1.26e+57)
		tmp = -z;
	else
		tmp = -y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, 1.26e+57], (-z), (-y)]

Derivation

1. Split input into 2 regimes

2. if y < 1.26e57

   1. Initial program 99.7%

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

   3. Taylor expanded in z around inf 43.5%

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

      1. neg-mul-1 43.5%

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

   5. Simplified 43.5%

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

   if 1.26e57 < y

   1. Initial program 99.8%

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

   3. Taylor expanded in y around inf 57.9%

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

      1. neg-mul-1 57.9%

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

   5. Simplified 57.9%

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

Alternative 6: 65.5% 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 99.8%

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

3. Taylor expanded in x around 0 62.5%

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

   1. neg-mul-1 62.5%

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

   2. +-commutative 62.5%

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

   3. distribute-neg-in 62.5%

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

   4. sub-neg 62.5%

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

5. Simplified 62.5%

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

Alternative 7: 33.5% 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 30.6%

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

   1. neg-mul-1 30.6%

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

5. Simplified 30.6%

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

Alternative 8: 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 y around 0 70.4%

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

   1. add-sqr-sqrt 25.4%

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

   2. associate-*r* 25.4%

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

   3. fmm-def 25.4%

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

5. Applied egg-rr 25.4%

   \[\leadsto \color{blue}{\mathsf{fma}\left(x \cdot \sqrt{\log y}, \sqrt{\log y}, -z\right)} \]
6. Step-by-step derivation

   1. add-cube-cbrt 25.1%

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

   2. pow3 25.1%

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

   3. fma-undefine 25.1%

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

   4. associate-*r* 25.1%

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

   5. add-sqr-sqrt 69.3%

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

   6. add-sqr-sqrt 27.7%

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

   7. sqrt-unprod 40.8%

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

   8. sqr-neg 40.8%

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

   9. sqrt-unprod 23.3%

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

   10. add-sqr-sqrt 38.5%

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

7. Applied egg-rr 38.5%

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

8. Taylor expanded in x around 0 2.3%

   \[\leadsto \color{blue}{z} \]
9. 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 99.8%

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

3. Taylor expanded in y around inf 30.6%

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

   1. neg-mul-1 30.6%

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

5. Simplified 30.6%

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

   1. neg-sub0 30.6%

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

   2. sub-neg 30.6%

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

   3. add-sqr-sqrt 0.0%

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

   4. sqrt-unprod 2.0%

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

   5. sqr-neg 2.0%

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

   6. sqrt-unprod 2.1%

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

   7. add-sqr-sqrt 2.1%

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

7. Applied egg-rr 2.1%

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

   1. +-lft-identity 2.1%

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

9. Simplified 2.1%

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

Reproduce

herbie shell --seed 2024163 
(FPCore (x y z)
  :name "Statistics.Distribution.Poisson:$clogProbability from math-functions-0.1.5.2"
  :precision binary64
  (- (- (* x (log y)) z) y))