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

Percentage Accurate: 99.9% → 99.9%

Time: 6.7s

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: 81.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(x \cdot \log y - z\right) - y\\ \mathbf{if}\;t\_0 \leq -1 \cdot 10^{+168}:\\ \;\;\;\;\left(-z\right) - y\\ \mathbf{elif}\;t\_0 \leq -1 \cdot 10^{-74}:\\ \;\;\;\;\log y \cdot x - y\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\log y, x, -z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- (- (* x (log y)) z) y)))
   (if (<= t_0 -1e+168)
     (- (- z) y)
     (if (<= t_0 -1e-74) (- (* (log y) x) y) (fma (log y) x (- z))))))

C

double code(double x, double y, double z) {
	double t_0 = ((x * log(y)) - z) - y;
	double tmp;
	if (t_0 <= -1e+168) {
		tmp = -z - y;
	} else if (t_0 <= -1e-74) {
		tmp = (log(y) * x) - y;
	} else {
		tmp = fma(log(y), x, -z);
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = Float64(Float64(Float64(x * log(y)) - z) - y)
	tmp = 0.0
	if (t_0 <= -1e+168)
		tmp = Float64(Float64(-z) - y);
	elseif (t_0 <= -1e-74)
		tmp = Float64(Float64(log(y) * x) - y);
	else
		tmp = fma(log(y), x, Float64(-z));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision] - y), $MachinePrecision]}, If[LessEqual[t$95$0, -1e+168], N[((-z) - y), $MachinePrecision], If[LessEqual[t$95$0, -1e-74], N[(N[(N[Log[y], $MachinePrecision] * x), $MachinePrecision] - y), $MachinePrecision], N[(N[Log[y], $MachinePrecision] * x + (-z)), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (-.f64 (-.f64 (*.f64 x (log.f64 y)) z) y) < -9.9999999999999993e167

   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 85.2

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

   5. Applied rewrites 85.2%

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

   if -9.9999999999999993e167 < (-.f64 (-.f64 (*.f64 x (log.f64 y)) z) y) < -9.99999999999999958e-75

   1. Initial program 99.9%

      \[\left(x \cdot \log y - z\right) - y \]
   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 82.9

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

   5. Applied rewrites 82.9%

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

   7. Applied rewrites 82.9%

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

   if -9.99999999999999958e-75 < (-.f64 (-.f64 (*.f64 x (log.f64 y)) z) y)

   1. Initial program 99.7%

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

   3. Taylor expanded in y around inf

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

   5. Applied rewrites 73.5%

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

   6. Taylor expanded in z around -inf

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

   8. Applied rewrites 62.5%

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

   9. Taylor expanded in y around inf

      \[\leadsto \left(-1 \cdot \frac{y}{z}\right) \cdot z \]
   10. Step-by-step derivation

   11. Applied rewrites 2.6%

       \[\leadsto \frac{y}{-z} \cdot z \]

   12. Taylor expanded in y around 0

       \[\leadsto \color{blue}{x \cdot \log y - z} \]
   13. 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 97.8

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

   14. Applied rewrites 97.8%

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

4. Final simplification 89.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(x \cdot \log y - z\right) - y \leq -1 \cdot 10^{+168}:\\ \;\;\;\;\left(-z\right) - y\\ \mathbf{elif}\;\left(x \cdot \log y - z\right) - y \leq -1 \cdot 10^{-74}:\\ \;\;\;\;\log y \cdot x - y\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\log y, x, -z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 81.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(x \cdot \log y - z\right) - y\\ \mathbf{if}\;t\_0 \leq -1 \cdot 10^{+168}:\\ \;\;\;\;\left(-z\right) - y\\ \mathbf{elif}\;t\_0 \leq -1 \cdot 10^{-74}:\\ \;\;\;\;\mathsf{fma}\left(\log y, x, -y\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\log y, x, -z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- (- (* x (log y)) z) y)))
   (if (<= t_0 -1e+168)
     (- (- z) y)
     (if (<= t_0 -1e-74) (fma (log y) x (- y)) (fma (log y) x (- z))))))

C

double code(double x, double y, double z) {
	double t_0 = ((x * log(y)) - z) - y;
	double tmp;
	if (t_0 <= -1e+168) {
		tmp = -z - y;
	} else if (t_0 <= -1e-74) {
		tmp = fma(log(y), x, -y);
	} else {
		tmp = fma(log(y), x, -z);
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = Float64(Float64(Float64(x * log(y)) - z) - y)
	tmp = 0.0
	if (t_0 <= -1e+168)
		tmp = Float64(Float64(-z) - y);
	elseif (t_0 <= -1e-74)
		tmp = fma(log(y), x, Float64(-y));
	else
		tmp = fma(log(y), x, Float64(-z));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision] - y), $MachinePrecision]}, If[LessEqual[t$95$0, -1e+168], N[((-z) - y), $MachinePrecision], If[LessEqual[t$95$0, -1e-74], N[(N[Log[y], $MachinePrecision] * x + (-y)), $MachinePrecision], N[(N[Log[y], $MachinePrecision] * x + (-z)), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (-.f64 (-.f64 (*.f64 x (log.f64 y)) z) y) < -9.9999999999999993e167

   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 85.2

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

   5. Applied rewrites 85.2%

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

   if -9.9999999999999993e167 < (-.f64 (-.f64 (*.f64 x (log.f64 y)) z) y) < -9.99999999999999958e-75

   1. Initial program 99.9%

      \[\left(x \cdot \log y - z\right) - y \]
   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 82.9

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

   5. Applied rewrites 82.9%

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

   if -9.99999999999999958e-75 < (-.f64 (-.f64 (*.f64 x (log.f64 y)) z) y)

   1. Initial program 99.7%

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

   3. Taylor expanded in y around inf

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

   5. Applied rewrites 73.5%

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

   6. Taylor expanded in z around -inf

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

   8. Applied rewrites 62.5%

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

   9. Taylor expanded in y around inf

      \[\leadsto \left(-1 \cdot \frac{y}{z}\right) \cdot z \]
   10. Step-by-step derivation

   11. Applied rewrites 2.6%

       \[\leadsto \frac{y}{-z} \cdot z \]

   12. Taylor expanded in y around 0

       \[\leadsto \color{blue}{x \cdot \log y - z} \]
   13. 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 97.8

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

   14. Applied rewrites 97.8%

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

Alternative 4: 84.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4600000 \lor \neg \left(z \leq 1.8 \cdot 10^{+121}\right):\\ \;\;\;\;\left(-z\right) - y\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\log y, x, -y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -4600000.0) (not (<= z 1.8e+121)))
   (- (- z) y)
   (fma (log y) x (- y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -4600000.0) || !(z <= 1.8e+121)) {
		tmp = -z - y;
	} else {
		tmp = fma(log(y), x, -y);
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -4600000.0) || !(z <= 1.8e+121))
		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, -4600000.0], N[Not[LessEqual[z, 1.8e+121]], $MachinePrecision]], N[((-z) - y), $MachinePrecision], N[(N[Log[y], $MachinePrecision] * x + (-y)), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4.6e6 or 1.79999999999999991e121 < 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 79.8

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

   5. Applied rewrites 79.8%

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

   if -4.6e6 < z < 1.79999999999999991e121

   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 89.6

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

   5. Applied rewrites 89.6%

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

4. Final simplification 85.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4600000 \lor \neg \left(z \leq 1.8 \cdot 10^{+121}\right):\\ \;\;\;\;\left(-z\right) - y\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\log y, x, -y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 79.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.8 \cdot 10^{+79} \lor \neg \left(x \leq 2.9 \cdot 10^{+105}\right):\\ \;\;\;\;\log y \cdot x\\ \mathbf{else}:\\ \;\;\;\;\left(-z\right) - y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -2.8e+79) (not (<= x 2.9e+105))) (* (log y) x) (- (- z) y)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -2.8e+79) || !(x <= 2.9e+105)) {
		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 <= (-2.8d+79)) .or. (.not. (x <= 2.9d+105))) 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 <= -2.8e+79) || !(x <= 2.9e+105)) {
		tmp = Math.log(y) * x;
	} else {
		tmp = -z - y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -2.8e+79) or not (x <= 2.9e+105):
		tmp = math.log(y) * x
	else:
		tmp = -z - y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -2.8e+79) || !(x <= 2.9e+105))
		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 <= -2.8e+79) || ~((x <= 2.9e+105)))
		tmp = log(y) * x;
	else
		tmp = -z - y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -2.8e+79], N[Not[LessEqual[x, 2.9e+105]], $MachinePrecision]], N[(N[Log[y], $MachinePrecision] * x), $MachinePrecision], N[((-z) - y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -2.8000000000000001e79 or 2.9000000000000001e105 < 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 82.5

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

   5. Applied rewrites 82.5%

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

   7. Applied rewrites 53.1%

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

   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 70.4%

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

   if -2.8000000000000001e79 < x < 2.9000000000000001e105

   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 85.9

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

   5. Applied rewrites 85.9%

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

4. Final simplification 80.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.8 \cdot 10^{+79} \lor \neg \left(x \leq 2.9 \cdot 10^{+105}\right):\\ \;\;\;\;\log y \cdot x\\ \mathbf{else}:\\ \;\;\;\;\left(-z\right) - y\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 52.4% accurate, 6.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8000000 \lor \neg \left(z \leq 2.3 \cdot 10^{+77}\right):\\ \;\;\;\;-1 \cdot z\\ \mathbf{else}:\\ \;\;\;\;-y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -8000000.0) (not (<= z 2.3e+77))) (* -1.0 z) (- y)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -8000000.0) || !(z <= 2.3e+77)) {
		tmp = -1.0 * z;
	} else {
		tmp = -y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((z <= (-8000000.0d0)) .or. (.not. (z <= 2.3d+77))) then
        tmp = (-1.0d0) * z
    else
        tmp = -y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -8000000.0) || !(z <= 2.3e+77)) {
		tmp = -1.0 * z;
	} else {
		tmp = -y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -8000000.0) or not (z <= 2.3e+77):
		tmp = -1.0 * z
	else:
		tmp = -y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -8000000.0) || !(z <= 2.3e+77))
		tmp = Float64(-1.0 * z);
	else
		tmp = Float64(-y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -8000000.0) || ~((z <= 2.3e+77)))
		tmp = -1.0 * z;
	else
		tmp = -y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -8000000.0], N[Not[LessEqual[z, 2.3e+77]], $MachinePrecision]], N[(-1.0 * z), $MachinePrecision], (-y)]

Derivation

1. Split input into 2 regimes

2. if z < -8e6 or 2.29999999999999995e77 < z

   1. Initial program 99.9%

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

   3. Taylor expanded in y around inf

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

   5. Applied rewrites 74.5%

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

   6. Taylor expanded in z around -inf

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

   8. Applied rewrites 89.1%

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

   9. Taylor expanded in y around inf

      \[\leadsto \left(-1 \cdot \frac{y}{z}\right) \cdot z \]
   10. Step-by-step derivation

   11. Applied rewrites 15.9%

       \[\leadsto \frac{y}{-z} \cdot z \]

   12. Taylor expanded in z around inf

       \[\leadsto -1 \cdot z \]
   13. Step-by-step derivation

   14. Applied rewrites 62.9%

       \[\leadsto -1 \cdot z \]

   if -8e6 < z < 2.29999999999999995e77

   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 49.7

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

   5. Applied rewrites 49.7%

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

4. Final simplification 55.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8000000 \lor \neg \left(z \leq 2.3 \cdot 10^{+77}\right):\\ \;\;\;\;-1 \cdot z\\ \mathbf{else}:\\ \;\;\;\;-y\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 66.4% 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 65.5

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

5. Applied rewrites 65.5%

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

Alternative 8: 34.1% 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 34.6

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

5. Applied rewrites 34.6%

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

Reproduce

herbie shell --seed 2024326 
(FPCore (x y z)
  :name "Statistics.Distribution.Poisson:$clogProbability from math-functions-0.1.5.2"
  :precision binary64
  (- (- (* x (log y)) z) y))