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

Percentage Accurate: 99.9% → 99.9%

Time: 9.7s

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: 99.9% 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: 84.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \log y\\ \mathbf{if}\;x \leq -3.8 \cdot 10^{+125}:\\ \;\;\;\;t\_0 - y\\ \mathbf{elif}\;x \leq 7 \cdot 10^{+48}:\\ \;\;\;\;\left(-y\right) - z\\ \mathbf{else}:\\ \;\;\;\;t\_0 - z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (log y))))
   (if (<= x -3.8e+125) (- t_0 y) (if (<= x 7e+48) (- (- y) z) (- t_0 z)))))

C

double code(double x, double y, double z) {
	double t_0 = x * log(y);
	double tmp;
	if (x <= -3.8e+125) {
		tmp = t_0 - y;
	} else if (x <= 7e+48) {
		tmp = -y - z;
	} 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 (x <= (-3.8d+125)) then
        tmp = t_0 - y
    else if (x <= 7d+48) then
        tmp = -y - z
    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 (x <= -3.8e+125) {
		tmp = t_0 - y;
	} else if (x <= 7e+48) {
		tmp = -y - z;
	} else {
		tmp = t_0 - z;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * math.log(y)
	tmp = 0
	if x <= -3.8e+125:
		tmp = t_0 - y
	elif x <= 7e+48:
		tmp = -y - z
	else:
		tmp = t_0 - z
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * log(y))
	tmp = 0.0
	if (x <= -3.8e+125)
		tmp = Float64(t_0 - y);
	elseif (x <= 7e+48)
		tmp = Float64(Float64(-y) - z);
	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 (x <= -3.8e+125)
		tmp = t_0 - y;
	elseif (x <= 7e+48)
		tmp = -y - z;
	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[x, -3.8e+125], N[(t$95$0 - y), $MachinePrecision], If[LessEqual[x, 7e+48], N[((-y) - z), $MachinePrecision], N[(t$95$0 - z), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if x < -3.80000000000000002e125

   1. Initial program 99.6%

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

   3. Taylor expanded in z around 0

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

      1. lower--.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-log.f64 92.1

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

   5. Applied rewrites 92.1%

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

   if -3.80000000000000002e125 < x < 6.9999999999999995e48

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0

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

      1. mul-1-neg N/A

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

      2. +-commutative N/A

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

      3. distribute-neg-in N/A

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

      4. sub-neg N/A

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

      5. lower--.f64 N/A

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

      6. lower-neg.f64 91.0

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

   5. Applied rewrites 91.0%

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

   if 6.9999999999999995e48 < x

   1. Initial program 99.7%

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

   3. Taylor expanded in y around 0

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

      1. lower--.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-log.f64 89.0

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

   5. Applied rewrites 89.0%

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

4. Final simplification 90.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.8 \cdot 10^{+125}:\\ \;\;\;\;x \cdot \log y - y\\ \mathbf{elif}\;x \leq 7 \cdot 10^{+48}:\\ \;\;\;\;\left(-y\right) - z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \log y - z\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 84.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \log y - y\\ \mathbf{if}\;x \leq -3.8 \cdot 10^{+125}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 2.95 \cdot 10^{+38}:\\ \;\;\;\;\left(-y\right) - z\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- (* x (log y)) y)))
   (if (<= x -3.8e+125) t_0 (if (<= x 2.95e+38) (- (- y) z) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = (x * log(y)) - y;
	double tmp;
	if (x <= -3.8e+125) {
		tmp = t_0;
	} else if (x <= 2.95e+38) {
		tmp = -y - z;
	} else {
		tmp = t_0;
	}
	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)) - y
    if (x <= (-3.8d+125)) then
        tmp = t_0
    else if (x <= 2.95d+38) then
        tmp = -y - z
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = (x * Math.log(y)) - y;
	double tmp;
	if (x <= -3.8e+125) {
		tmp = t_0;
	} else if (x <= 2.95e+38) {
		tmp = -y - z;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (x * math.log(y)) - y
	tmp = 0
	if x <= -3.8e+125:
		tmp = t_0
	elif x <= 2.95e+38:
		tmp = -y - z
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(x * log(y)) - y)
	tmp = 0.0
	if (x <= -3.8e+125)
		tmp = t_0;
	elseif (x <= 2.95e+38)
		tmp = Float64(Float64(-y) - z);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (x * log(y)) - y;
	tmp = 0.0;
	if (x <= -3.8e+125)
		tmp = t_0;
	elseif (x <= 2.95e+38)
		tmp = -y - z;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] - y), $MachinePrecision]}, If[LessEqual[x, -3.8e+125], t$95$0, If[LessEqual[x, 2.95e+38], N[((-y) - z), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x < -3.80000000000000002e125 or 2.94999999999999991e38 < x

   1. Initial program 99.6%

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

   3. Taylor expanded in z around 0

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

      1. lower--.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-log.f64 86.7

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

   5. Applied rewrites 86.7%

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

   if -3.80000000000000002e125 < x < 2.94999999999999991e38

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0

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

      1. mul-1-neg N/A

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

      2. +-commutative N/A

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

      3. distribute-neg-in N/A

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

      4. sub-neg N/A

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

      5. lower--.f64 N/A

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

      6. lower-neg.f64 90.8

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

   5. Applied rewrites 90.8%

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

4. Final simplification 89.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.8 \cdot 10^{+125}:\\ \;\;\;\;x \cdot \log y - y\\ \mathbf{elif}\;x \leq 2.95 \cdot 10^{+38}:\\ \;\;\;\;\left(-y\right) - z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \log y - y\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 79.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \log y\\ \mathbf{if}\;x \leq -4.2 \cdot 10^{+136}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 3.5 \cdot 10^{+55}:\\ \;\;\;\;\left(-y\right) - z\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (log y))))
   (if (<= x -4.2e+136) t_0 (if (<= x 3.5e+55) (- (- y) z) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = x * log(y);
	double tmp;
	if (x <= -4.2e+136) {
		tmp = t_0;
	} else if (x <= 3.5e+55) {
		tmp = -y - z;
	} else {
		tmp = t_0;
	}
	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 <= (-4.2d+136)) then
        tmp = t_0
    else if (x <= 3.5d+55) then
        tmp = -y - z
    else
        tmp = t_0
    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 <= -4.2e+136) {
		tmp = t_0;
	} else if (x <= 3.5e+55) {
		tmp = -y - z;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * math.log(y)
	tmp = 0
	if x <= -4.2e+136:
		tmp = t_0
	elif x <= 3.5e+55:
		tmp = -y - z
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * log(y))
	tmp = 0.0
	if (x <= -4.2e+136)
		tmp = t_0;
	elseif (x <= 3.5e+55)
		tmp = Float64(Float64(-y) - z);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * log(y);
	tmp = 0.0;
	if (x <= -4.2e+136)
		tmp = t_0;
	elseif (x <= 3.5e+55)
		tmp = -y - z;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -4.2e+136], t$95$0, If[LessEqual[x, 3.5e+55], N[((-y) - z), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x < -4.1999999999999998e136 or 3.5000000000000001e55 < x

   1. Initial program 99.6%

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

   3. Taylor expanded in x around inf

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

      1. lower-*.f64 N/A

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

      2. lower-log.f64 75.8

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

   5. Applied rewrites 75.8%

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

   if -4.1999999999999998e136 < x < 3.5000000000000001e55

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0

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

      1. mul-1-neg N/A

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

      2. +-commutative N/A

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

      3. distribute-neg-in N/A

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

      4. sub-neg N/A

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

      5. lower--.f64 N/A

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

      6. lower-neg.f64 90.5

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

   5. Applied rewrites 90.5%

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

4. Final simplification 85.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.2 \cdot 10^{+136}:\\ \;\;\;\;x \cdot \log y\\ \mathbf{elif}\;x \leq 3.5 \cdot 10^{+55}:\\ \;\;\;\;\left(-y\right) - z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \log y\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 52.9% accurate, 12.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 5.2 \cdot 10^{+73}:\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;-y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (if (<= y 5.2e+73) (- z) (- y)))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= 5.2e+73) {
		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 <= 5.2d+73) 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 <= 5.2e+73) {
		tmp = -z;
	} else {
		tmp = -y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= 5.2e+73:
		tmp = -z
	else:
		tmp = -y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= 5.2e+73)
		tmp = Float64(-z);
	else
		tmp = Float64(-y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= 5.2e+73)
		tmp = -z;
	else
		tmp = -y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, 5.2e+73], (-z), (-y)]

Derivation

1. Split input into 2 regimes

2. if y < 5.2000000000000001e73

   1. Initial program 99.8%

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

   3. Taylor expanded in z around inf

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 47.3

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

   5. Applied rewrites 47.3%

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

   if 5.2000000000000001e73 < y

   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 69.2

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

   5. Applied rewrites 69.2%

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

Alternative 6: 66.8% accurate, 18.7× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z) {
	return -y - 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 = -y - z
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

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

   1. mul-1-neg N/A

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

   2. +-commutative N/A

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

   3. distribute-neg-in N/A

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

   4. sub-neg N/A

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

   5. lower--.f64 N/A

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

   6. lower-neg.f64 67.3

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

5. Applied rewrites 67.3%

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

6. Final simplification 67.3%

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

Alternative 7: 34.0% 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 99.8%

   \[\left(x \cdot \log y - z\right) - y \]
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 34.9

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

5. Applied rewrites 34.9%

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

Alternative 8: 2.2% accurate, 112.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := z

Derivation

1. Initial program 99.8%

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

3. Taylor expanded in z around inf

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

   1. mul-1-neg N/A

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

   2. lower-neg.f64 33.9

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

5. Applied rewrites 33.9%

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

   1. neg-mul-1 N/A

      \[\leadsto \color{blue}{-1 \cdot z} \]

   2. metadata-eval N/A

      \[\leadsto \color{blue}{{-1}^{1}} \cdot z \]

   3. unpow1 N/A

      \[\leadsto {-1}^{1} \cdot \color{blue}{{z}^{1}} \]

   4. remove-double-neg N/A

      \[\leadsto {-1}^{1} \cdot {\color{blue}{\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(z\right)\right)\right)\right)}}^{1} \]

   5. lift-neg.f64 N/A

      \[\leadsto {-1}^{1} \cdot {\left(\mathsf{neg}\left(\color{blue}{\left(\mathsf{neg}\left(z\right)\right)}\right)\right)}^{1} \]

   6. neg-mul-1 N/A

      \[\leadsto {-1}^{1} \cdot {\color{blue}{\left(-1 \cdot \left(\mathsf{neg}\left(z\right)\right)\right)}}^{1} \]

   7. unpow-prod-down N/A

      \[\leadsto {-1}^{1} \cdot \color{blue}{\left({-1}^{1} \cdot {\left(\mathsf{neg}\left(z\right)\right)}^{1}\right)} \]

   8. metadata-eval N/A

      \[\leadsto {-1}^{1} \cdot \left(\color{blue}{-1} \cdot {\left(\mathsf{neg}\left(z\right)\right)}^{1}\right) \]

   9. metadata-eval N/A

      \[\leadsto {-1}^{1} \cdot \left(\color{blue}{\frac{-1}{1}} \cdot {\left(\mathsf{neg}\left(z\right)\right)}^{1}\right) \]

   10. metadata-eval N/A

       \[\leadsto {-1}^{1} \cdot \left(\frac{-1}{1} \cdot {\left(\mathsf{neg}\left(z\right)\right)}^{\color{blue}{\left(3 - 2\right)}}\right) \]

   11. pow-div N/A

       \[\leadsto {-1}^{1} \cdot \left(\frac{-1}{1} \cdot \color{blue}{\frac{{\left(\mathsf{neg}\left(z\right)\right)}^{3}}{{\left(\mathsf{neg}\left(z\right)\right)}^{2}}}\right) \]

   12. sqr-pow N/A

       \[\leadsto {-1}^{1} \cdot \left(\frac{-1}{1} \cdot \frac{\color{blue}{{\left(\mathsf{neg}\left(z\right)\right)}^{\left(\frac{3}{2}\right)} \cdot {\left(\mathsf{neg}\left(z\right)\right)}^{\left(\frac{3}{2}\right)}}}{{\left(\mathsf{neg}\left(z\right)\right)}^{2}}\right) \]

   13. unpow-prod-down N/A

       \[\leadsto {-1}^{1} \cdot \left(\frac{-1}{1} \cdot \frac{\color{blue}{{\left(\left(\mathsf{neg}\left(z\right)\right) \cdot \left(\mathsf{neg}\left(z\right)\right)\right)}^{\left(\frac{3}{2}\right)}}}{{\left(\mathsf{neg}\left(z\right)\right)}^{2}}\right) \]

   14. lift-neg.f64 N/A

       \[\leadsto {-1}^{1} \cdot \left(\frac{-1}{1} \cdot \frac{{\left(\color{blue}{\left(\mathsf{neg}\left(z\right)\right)} \cdot \left(\mathsf{neg}\left(z\right)\right)\right)}^{\left(\frac{3}{2}\right)}}{{\left(\mathsf{neg}\left(z\right)\right)}^{2}}\right) \]

   15. lift-neg.f64 N/A

       \[\leadsto {-1}^{1} \cdot \left(\frac{-1}{1} \cdot \frac{{\left(\left(\mathsf{neg}\left(z\right)\right) \cdot \color{blue}{\left(\mathsf{neg}\left(z\right)\right)}\right)}^{\left(\frac{3}{2}\right)}}{{\left(\mathsf{neg}\left(z\right)\right)}^{2}}\right) \]

   16. sqr-neg N/A

       \[\leadsto {-1}^{1} \cdot \left(\frac{-1}{1} \cdot \frac{{\color{blue}{\left(z \cdot z\right)}}^{\left(\frac{3}{2}\right)}}{{\left(\mathsf{neg}\left(z\right)\right)}^{2}}\right) \]

   17. unpow-prod-down N/A

       \[\leadsto {-1}^{1} \cdot \left(\frac{-1}{1} \cdot \frac{\color{blue}{{z}^{\left(\frac{3}{2}\right)} \cdot {z}^{\left(\frac{3}{2}\right)}}}{{\left(\mathsf{neg}\left(z\right)\right)}^{2}}\right) \]

   18. sqr-pow N/A

       \[\leadsto {-1}^{1} \cdot \left(\frac{-1}{1} \cdot \frac{\color{blue}{{z}^{3}}}{{\left(\mathsf{neg}\left(z\right)\right)}^{2}}\right) \]

   19. pow2 N/A

       \[\leadsto {-1}^{1} \cdot \left(\frac{-1}{1} \cdot \frac{{z}^{3}}{\color{blue}{\left(\mathsf{neg}\left(z\right)\right) \cdot \left(\mathsf{neg}\left(z\right)\right)}}\right) \]

   20. lift-neg.f64 N/A

       \[\leadsto {-1}^{1} \cdot \left(\frac{-1}{1} \cdot \frac{{z}^{3}}{\color{blue}{\left(\mathsf{neg}\left(z\right)\right)} \cdot \left(\mathsf{neg}\left(z\right)\right)}\right) \]

   21. lift-neg.f64 N/A

       \[\leadsto {-1}^{1} \cdot \left(\frac{-1}{1} \cdot \frac{{z}^{3}}{\left(\mathsf{neg}\left(z\right)\right) \cdot \color{blue}{\left(\mathsf{neg}\left(z\right)\right)}}\right) \]

   22. sqr-neg N/A

       \[\leadsto {-1}^{1} \cdot \left(\frac{-1}{1} \cdot \frac{{z}^{3}}{\color{blue}{z \cdot z}}\right) \]

   23. lift-*.f64 N/A

       \[\leadsto {-1}^{1} \cdot \left(\frac{-1}{1} \cdot \frac{{z}^{3}}{\color{blue}{z \cdot z}}\right) \]

   24. times-frac N/A

       \[\leadsto {-1}^{1} \cdot \color{blue}{\frac{-1 \cdot {z}^{3}}{1 \cdot \left(z \cdot z\right)}} \]

7. Applied rewrites 2.3%

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

Reproduce

herbie shell --seed 2024219 
(FPCore (x y z)
  :name "Statistics.Distribution.Poisson:$clogProbability from math-functions-0.1.5.2"
  :precision binary64
  (- (- (* x (log y)) z) y))