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

Percentage Accurate: 99.9% → 99.9%

Time: 7.4s

Alternatives: 7

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

Alternative 2: 84.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -7 \cdot 10^{+98}:\\ \;\;\;\;x \cdot \log y - z\\ \mathbf{elif}\;x \leq 3.3 \cdot 10^{-48}:\\ \;\;\;\;\left(-z\right) - y\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\log y, x, -y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -7e+98)
   (- (* x (log y)) z)
   (if (<= x 3.3e-48) (- (- z) y) (fma (log y) x (- y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -7e+98) {
		tmp = (x * log(y)) - z;
	} else if (x <= 3.3e-48) {
		tmp = -z - y;
	} else {
		tmp = fma(log(y), x, -y);
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -7e+98)
		tmp = Float64(Float64(x * log(y)) - z);
	elseif (x <= 3.3e-48)
		tmp = Float64(Float64(-z) - y);
	else
		tmp = fma(log(y), x, Float64(-y));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -7e+98], N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision], If[LessEqual[x, 3.3e-48], N[((-z) - y), $MachinePrecision], N[(N[Log[y], $MachinePrecision] * x + (-y)), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -7e98

   1. Initial program 99.7%

      \[\left(x \cdot \log y - z\right) - y \]
   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 12.4

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

   5. Applied rewrites 12.4%

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

   6. Taylor expanded in y around 0

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

      1. *-lft-identity N/A

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

      2. metadata-eval N/A

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

      3. fp-cancel-sign-sub-inv N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. lower-log.f64 N/A

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

      7. mul-1-neg N/A

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

      8. lower-neg.f64 89.0

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

   8. Applied rewrites 89.0%

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

   10. Applied rewrites 89.0%

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

   if -7e98 < x < 3.3e-48

   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 91.8

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

   5. Applied rewrites 91.8%

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

   if 3.3e-48 < x

   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. *-lft-identity N/A

         \[\leadsto x \cdot \log y - \color{blue}{1 \cdot y} \]

      2. metadata-eval N/A

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

      3. fp-cancel-sign-sub-inv N/A

         \[\leadsto \color{blue}{x \cdot \log y + -1 \cdot y} \]

      4. *-commutative N/A

         \[\leadsto \color{blue}{\log y \cdot x} + -1 \cdot y \]

      5. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(\log y, x, -1 \cdot y\right)} \]

      6. lower-log.f64 N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{\log y}, x, -1 \cdot y\right) \]

      7. mul-1-neg N/A

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

      8. lower-neg.f64 86.8

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

   5. Applied rewrites 86.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\log y, x, -y\right)} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 3: 49.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\left(x \cdot \log y - z\right) - y \leq -5 \cdot 10^{-107}:\\ \;\;\;\;-y\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= (- (- (* x (log y)) z) y) -5e-107) (- y) (- z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((((x * log(y)) - z) - y) <= -5e-107) {
		tmp = -y;
	} else {
		tmp = -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) :: tmp
    if ((((x * log(y)) - z) - y) <= (-5d-107)) then
        tmp = -y
    else
        tmp = -z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((((x * Math.log(y)) - z) - y) <= -5e-107) {
		tmp = -y;
	} else {
		tmp = -z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (((x * math.log(y)) - z) - y) <= -5e-107:
		tmp = -y
	else:
		tmp = -z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (Float64(Float64(Float64(x * log(y)) - z) - y) <= -5e-107)
		tmp = Float64(-y);
	else
		tmp = Float64(-z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((((x * log(y)) - z) - y) <= -5e-107)
		tmp = -y;
	else
		tmp = -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[N[(N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision] - y), $MachinePrecision], -5e-107], (-y), (-z)]

Derivation

1. Split input into 2 regimes

2. if (-.f64 (-.f64 (*.f64 x (log.f64 y)) z) y) < -4.99999999999999971e-107

   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 53.0

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

   5. Applied rewrites 53.0%

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

   if -4.99999999999999971e-107 < (-.f64 (-.f64 (*.f64 x (log.f64 y)) z) y)

   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 3.9

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

   5. Applied rewrites 3.9%

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

   6. Taylor expanded in y around 0

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

      1. *-lft-identity N/A

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

      2. metadata-eval N/A

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

      3. fp-cancel-sign-sub-inv N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. lower-log.f64 N/A

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

      7. mul-1-neg N/A

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

      8. lower-neg.f64 94.3

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

   8. Applied rewrites 94.3%

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

   9. Taylor expanded in x around 0

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

   11. Applied rewrites 56.6%

       \[\leadsto -z \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 4: 80.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.2 \cdot 10^{+159} \lor \neg \left(x \leq 1.9 \cdot 10^{+103}\right):\\ \;\;\;\;\log y \cdot x\\ \mathbf{else}:\\ \;\;\;\;\left(-z\right) - y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -4.2e+159) (not (<= x 1.9e+103))) (* (log y) x) (- (- z) y)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -4.2e+159) || !(x <= 1.9e+103)) {
		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 <= (-4.2d+159)) .or. (.not. (x <= 1.9d+103))) 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 <= -4.2e+159) || !(x <= 1.9e+103)) {
		tmp = Math.log(y) * x;
	} else {
		tmp = -z - y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -4.2e+159) or not (x <= 1.9e+103):
		tmp = math.log(y) * x
	else:
		tmp = -z - y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -4.2e+159) || !(x <= 1.9e+103))
		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 <= -4.2e+159) || ~((x <= 1.9e+103)))
		tmp = log(y) * x;
	else
		tmp = -z - y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -4.2e+159], N[Not[LessEqual[x, 1.9e+103]], $MachinePrecision]], N[(N[Log[y], $MachinePrecision] * x), $MachinePrecision], N[((-z) - y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -4.19999999999999978e159 or 1.8999999999999998e103 < x

   1. Initial program 99.7%

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

   3. Taylor expanded in z around 0

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

      1. *-lft-identity N/A

         \[\leadsto x \cdot \log y - \color{blue}{1 \cdot y} \]

      2. metadata-eval N/A

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

      3. fp-cancel-sign-sub-inv N/A

         \[\leadsto \color{blue}{x \cdot \log y + -1 \cdot y} \]

      4. *-commutative N/A

         \[\leadsto \color{blue}{\log y \cdot x} + -1 \cdot y \]

      5. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(\log y, x, -1 \cdot y\right)} \]

      6. lower-log.f64 N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{\log y}, x, -1 \cdot y\right) \]

      7. mul-1-neg N/A

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

      8. lower-neg.f64 90.9

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

   5. Applied rewrites 90.9%

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

   7. Applied rewrites 46.2%

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

   8. Taylor expanded in x around -inf

      \[\leadsto -1 \cdot \color{blue}{\left(x \cdot \left(\log y \cdot {\left(\sqrt{-1}\right)}^{2}\right)\right)} \]
   9. Step-by-step derivation

   10. Applied rewrites 69.9%

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

   if -4.19999999999999978e159 < x < 1.8999999999999998e103

   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 84.9

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

   5. Applied rewrites 84.9%

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

4. Final simplification 80.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.2 \cdot 10^{+159} \lor \neg \left(x \leq 1.9 \cdot 10^{+103}\right):\\ \;\;\;\;\log y \cdot x\\ \mathbf{else}:\\ \;\;\;\;\left(-z\right) - y\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 84.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 1.4 \cdot 10^{+107}:\\ \;\;\;\;x \cdot \log y - z\\ \mathbf{else}:\\ \;\;\;\;\left(-z\right) - y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y 1.4e+107) (- (* x (log y)) z) (- (- z) y)))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= 1.4e+107) {
		tmp = (x * log(y)) - z;
	} else {
		tmp = -z - y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= 1.4d+107) then
        tmp = (x * log(y)) - z
    else
        tmp = -z - y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= 1.4e+107) {
		tmp = (x * Math.log(y)) - z;
	} else {
		tmp = -z - y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= 1.4e+107:
		tmp = (x * math.log(y)) - z
	else:
		tmp = -z - y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= 1.4e+107)
		tmp = Float64(Float64(x * log(y)) - z);
	else
		tmp = Float64(Float64(-z) - y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= 1.4e+107)
		tmp = (x * log(y)) - z;
	else
		tmp = -z - y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, 1.4e+107], N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision], N[((-z) - y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 1.39999999999999992e107

   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 16.4

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

   5. Applied rewrites 16.4%

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

   6. Taylor expanded in y around 0

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

      1. *-lft-identity N/A

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

      2. metadata-eval N/A

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

      3. fp-cancel-sign-sub-inv N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. lower-log.f64 N/A

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

      7. mul-1-neg N/A

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

      8. lower-neg.f64 85.7

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

   8. Applied rewrites 85.7%

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

   10. Applied rewrites 85.8%

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

   if 1.39999999999999992e107 < y

   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 90.9

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

   5. Applied rewrites 90.9%

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

Alternative 6: 67.0% 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 68.8

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

5. Applied rewrites 68.8%

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

Alternative 7: 34.6% accurate, 37.3× 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 Float64(-z)
end

MATLAB

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

Wolfram

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

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 36.7

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

5. Applied rewrites 36.7%

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

6. Taylor expanded in y around 0

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

   1. *-lft-identity N/A

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

   2. metadata-eval N/A

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

   3. fp-cancel-sign-sub-inv N/A

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

   4. *-commutative N/A

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

   5. lower-fma.f64 N/A

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

   6. lower-log.f64 N/A

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

   7. mul-1-neg N/A

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

   8. lower-neg.f64 63.9

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

8. Applied rewrites 63.9%

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

9. Taylor expanded in x around 0

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

11. Applied rewrites 34.1%

    \[\leadsto -z \]
12. Add Preprocessing

Reproduce

herbie shell --seed 2024337 
(FPCore (x y z)
  :name "Statistics.Distribution.Poisson:$clogProbability from math-functions-0.1.5.2"
  :precision binary64
  (- (- (* x (log y)) z) y))