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

Percentage Accurate: 99.9% → 99.9%

Time: 7.1s

Alternatives: 6

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: 83.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.55 \cdot 10^{-75} \lor \neg \left(z \leq 160000000000\right):\\ \;\;\;\;\left(-z\right) - y\\ \mathbf{else}:\\ \;\;\;\;\log y \cdot x - y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -1.55e-75) (not (<= z 160000000000.0)))
   (- (- z) y)
   (- (* (log y) x) y)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.55e-75) || !(z <= 160000000000.0)) {
		tmp = -z - y;
	} else {
		tmp = (log(y) * x) - 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 <= (-1.55d-75)) .or. (.not. (z <= 160000000000.0d0))) then
        tmp = -z - y
    else
        tmp = (log(y) * x) - y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.55e-75) || !(z <= 160000000000.0)) {
		tmp = -z - y;
	} else {
		tmp = (Math.log(y) * x) - y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -1.55e-75) or not (z <= 160000000000.0):
		tmp = -z - y
	else:
		tmp = (math.log(y) * x) - y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -1.55e-75) || !(z <= 160000000000.0))
		tmp = Float64(Float64(-z) - y);
	else
		tmp = Float64(Float64(log(y) * x) - y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -1.55e-75) || ~((z <= 160000000000.0)))
		tmp = -z - y;
	else
		tmp = (log(y) * x) - y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -1.55e-75], N[Not[LessEqual[z, 160000000000.0]], $MachinePrecision]], N[((-z) - y), $MachinePrecision], N[(N[(N[Log[y], $MachinePrecision] * x), $MachinePrecision] - y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.55000000000000003e-75 or 1.6e11 < z

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 83.4

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

   5. Applied rewrites 83.4%

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

   if -1.55000000000000003e-75 < z < 1.6e11

   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 92.0

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

   5. Applied rewrites 92.0%

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

   7. Applied rewrites 92.0%

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

4. Final simplification 87.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.55 \cdot 10^{-75} \lor \neg \left(z \leq 160000000000\right):\\ \;\;\;\;\left(-z\right) - y\\ \mathbf{else}:\\ \;\;\;\;\log y \cdot x - y\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 83.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.55 \cdot 10^{-75} \lor \neg \left(z \leq 160000000000\right):\\ \;\;\;\;\left(-z\right) - y\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\log y, x, -y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -1.55e-75) (not (<= z 160000000000.0)))
   (- (- z) y)
   (fma (log y) x (- y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.55e-75) || !(z <= 160000000000.0)) {
		tmp = -z - y;
	} else {
		tmp = fma(log(y), x, -y);
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -1.55e-75) || !(z <= 160000000000.0))
		tmp = Float64(Float64(-z) - y);
	else
		tmp = fma(log(y), x, Float64(-y));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -1.55e-75], N[Not[LessEqual[z, 160000000000.0]], $MachinePrecision]], N[((-z) - y), $MachinePrecision], N[(N[Log[y], $MachinePrecision] * x + (-y)), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.55000000000000003e-75 or 1.6e11 < z

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 83.4

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

   5. Applied rewrites 83.4%

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

   if -1.55000000000000003e-75 < z < 1.6e11

   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 92.0

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

   5. Applied rewrites 92.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\log y, x, -y\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 87.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.55 \cdot 10^{-75} \lor \neg \left(z \leq 160000000000\right):\\ \;\;\;\;\left(-z\right) - y\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\log y, x, -y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 80.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.7 \cdot 10^{+133} \lor \neg \left(x \leq 1.25 \cdot 10^{+125}\right):\\ \;\;\;\;\log y \cdot x\\ \mathbf{else}:\\ \;\;\;\;\left(-z\right) - y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -1.7e+133) (not (<= x 1.25e+125))) (* (log y) x) (- (- z) y)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.7e+133) || !(x <= 1.25e+125)) {
		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 <= (-1.7d+133)) .or. (.not. (x <= 1.25d+125))) 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 <= -1.7e+133) || !(x <= 1.25e+125)) {
		tmp = Math.log(y) * x;
	} else {
		tmp = -z - y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -1.7e+133) or not (x <= 1.25e+125):
		tmp = math.log(y) * x
	else:
		tmp = -z - y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -1.7e+133) || !(x <= 1.25e+125))
		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 <= -1.7e+133) || ~((x <= 1.25e+125)))
		tmp = log(y) * x;
	else
		tmp = -z - y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -1.7e+133], N[Not[LessEqual[x, 1.25e+125]], $MachinePrecision]], N[(N[Log[y], $MachinePrecision] * x), $MachinePrecision], N[((-z) - y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.69999999999999994e133 or 1.24999999999999991e125 < x

   1. Initial program 99.6%

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

      1. lift--.f64 N/A

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

      2. lift--.f64 N/A

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

      3. associate--l- N/A

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

      4. flip-- N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 N/A

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

      7. pow2 N/A

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

      8. lower-pow.f64 N/A

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

      9. lift-*.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 N/A

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

      12. pow2 N/A

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

      13. lower-pow.f64 N/A

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

      14. lower-+.f64 N/A

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

      15. lift-*.f64 N/A

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

      16. *-commutative N/A

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

      17. lower-fma.f64 N/A

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

      18. lower-+.f64 11.8

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

   4. Applied rewrites 11.8%

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

   6. Applied rewrites 98.1%

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

      1. lift-fma.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-*l* N/A

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

      4. lift-neg.f64 N/A

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

      5. lift-neg.f64 N/A

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

      6. sqr-neg-rev N/A

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

      7. associate-*r* N/A

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

      8. lower-fma.f64 N/A

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

   8. Applied rewrites 97.1%

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

   9. Taylor expanded in x around inf

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

       1. *-commutative N/A

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

       2. lower-*.f64 N/A

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

       3. lower-log.f64 76.0

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

   11. Applied rewrites 76.0%

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

   if -1.69999999999999994e133 < x < 1.24999999999999991e125

   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 85.0

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

   5. Applied rewrites 85.0%

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

4. Final simplification 82.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.7 \cdot 10^{+133} \lor \neg \left(x \leq 1.25 \cdot 10^{+125}\right):\\ \;\;\;\;\log y \cdot x\\ \mathbf{else}:\\ \;\;\;\;\left(-z\right) - y\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 66.3% 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 99.8%

   \[\left(x \cdot \log y - z\right) - y \]
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 67.2

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

5. Applied rewrites 67.2%

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

Alternative 6: 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 33.8

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

5. Applied rewrites 33.8%

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

Reproduce

herbie shell --seed 2024329 
(FPCore (x y z)
  :name "Statistics.Distribution.Poisson:$clogProbability from math-functions-0.1.5.2"
  :precision binary64
  (- (- (* x (log y)) z) y))