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

Percentage Accurate: 99.9% → 99.9%

Time: 15.0s

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, 0.5× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 99.8%

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

   1. sub-neg 99.8%

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

   2. associate--l+ 99.8%

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

   3. *-commutative 99.8%

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

   4. fma-define 99.8%

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

4. Applied egg-rr 99.8%

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

Alternative 2: 78.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -7.8 \cdot 10^{+220} \lor \neg \left(x \leq -2.2 \cdot 10^{+194} \lor \neg \left(x \leq -1.12 \cdot 10^{+64}\right) \land x \leq 3.8 \cdot 10^{+151}\right):\\ \;\;\;\;\log y \cdot x\\ \mathbf{else}:\\ \;\;\;\;\left(-z\right) - y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -7.8e+220)
         (not
          (or (<= x -2.2e+194) (and (not (<= x -1.12e+64)) (<= x 3.8e+151)))))
   (* (log y) x)
   (- (- z) y)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -7.8e+220) || !((x <= -2.2e+194) || (!(x <= -1.12e+64) && (x <= 3.8e+151)))) {
		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 <= (-7.8d+220)) .or. (.not. (x <= (-2.2d+194)) .or. (.not. (x <= (-1.12d+64))) .and. (x <= 3.8d+151))) 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 <= -7.8e+220) || !((x <= -2.2e+194) || (!(x <= -1.12e+64) && (x <= 3.8e+151)))) {
		tmp = Math.log(y) * x;
	} else {
		tmp = -z - y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -7.8e+220) or not ((x <= -2.2e+194) or (not (x <= -1.12e+64) and (x <= 3.8e+151))):
		tmp = math.log(y) * x
	else:
		tmp = -z - y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -7.8e+220) || !((x <= -2.2e+194) || (!(x <= -1.12e+64) && (x <= 3.8e+151))))
		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 <= -7.8e+220) || ~(((x <= -2.2e+194) || (~((x <= -1.12e+64)) && (x <= 3.8e+151)))))
		tmp = log(y) * x;
	else
		tmp = -z - y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -7.8e+220], N[Not[Or[LessEqual[x, -2.2e+194], And[N[Not[LessEqual[x, -1.12e+64]], $MachinePrecision], LessEqual[x, 3.8e+151]]]], $MachinePrecision]], N[(N[Log[y], $MachinePrecision] * x), $MachinePrecision], N[((-z) - y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -7.80000000000000032e220 or -2.2000000000000001e194 < x < -1.11999999999999995e64 or 3.8e151 < x

   1. Initial program 99.6%

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

   3. Taylor expanded in y around inf 67.3%

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

      1. sub-neg 67.3%

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

      2. mul-1-neg 67.3%

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

      3. *-commutative 67.3%

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

      4. associate-/l* 67.4%

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

      5. distribute-lft-neg-in 67.4%

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

      6. log-rec 67.4%

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

      7. remove-double-neg 67.4%

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

      8. distribute-neg-in 67.4%

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

      9. metadata-eval 67.4%

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

      10. unsub-neg 67.4%

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

   5. Simplified 67.4%

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

   6. Taylor expanded in x around inf 75.7%

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

   if -7.80000000000000032e220 < x < -2.2000000000000001e194 or -1.11999999999999995e64 < x < 3.8e151

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 85.4%

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

      1. neg-mul-1 85.4%

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

   5. Simplified 85.4%

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

4. Final simplification 82.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7.8 \cdot 10^{+220} \lor \neg \left(x \leq -2.2 \cdot 10^{+194} \lor \neg \left(x \leq -1.12 \cdot 10^{+64}\right) \land x \leq 3.8 \cdot 10^{+151}\right):\\ \;\;\;\;\log y \cdot x\\ \mathbf{else}:\\ \;\;\;\;\left(-z\right) - y\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 85.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -7.6 \cdot 10^{+63} \lor \neg \left(x \leq 1.75 \cdot 10^{-13}\right):\\ \;\;\;\;\log y \cdot x - y\\ \mathbf{else}:\\ \;\;\;\;\left(-z\right) - y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -7.6e+63) (not (<= x 1.75e-13)))
   (- (* (log y) x) y)
   (- (- z) y)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -7.6e+63) || !(x <= 1.75e-13)) {
		tmp = (log(y) * x) - y;
	} else {
		tmp = -z - y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((x <= (-7.6d+63)) .or. (.not. (x <= 1.75d-13))) then
        tmp = (log(y) * x) - y
    else
        tmp = -z - y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -7.6e+63) || !(x <= 1.75e-13)) {
		tmp = (Math.log(y) * x) - y;
	} else {
		tmp = -z - y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -7.6e+63) or not (x <= 1.75e-13):
		tmp = (math.log(y) * x) - y
	else:
		tmp = -z - y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -7.6e+63) || !(x <= 1.75e-13))
		tmp = Float64(Float64(log(y) * x) - y);
	else
		tmp = Float64(Float64(-z) - y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -7.6e+63) || ~((x <= 1.75e-13)))
		tmp = (log(y) * x) - y;
	else
		tmp = -z - y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -7.6e+63], N[Not[LessEqual[x, 1.75e-13]], $MachinePrecision]], N[(N[(N[Log[y], $MachinePrecision] * x), $MachinePrecision] - y), $MachinePrecision], N[((-z) - y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -7.6000000000000002e63 or 1.7500000000000001e-13 < x

   1. Initial program 99.7%

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

   3. Taylor expanded in z around 0 84.4%

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

   if -7.6000000000000002e63 < x < 1.7500000000000001e-13

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 90.4%

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

      1. neg-mul-1 90.4%

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

   5. Simplified 90.4%

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

4. Final simplification 87.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7.6 \cdot 10^{+63} \lor \neg \left(x \leq 1.75 \cdot 10^{-13}\right):\\ \;\;\;\;\log y \cdot x - y\\ \mathbf{else}:\\ \;\;\;\;\left(-z\right) - y\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 85.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \log y \cdot x\\ \mathbf{if}\;y \leq 0.65:\\ \;\;\;\;t\_0 - z\\ \mathbf{else}:\\ \;\;\;\;t\_0 - y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (log y) x))) (if (<= y 0.65) (- t_0 z) (- t_0 y))))

C

double code(double x, double y, double z) {
	double t_0 = log(y) * x;
	double tmp;
	if (y <= 0.65) {
		tmp = t_0 - z;
	} else {
		tmp = t_0 - y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = log(y) * x
    if (y <= 0.65d0) then
        tmp = t_0 - z
    else
        tmp = t_0 - y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = Math.log(y) * x;
	double tmp;
	if (y <= 0.65) {
		tmp = t_0 - z;
	} else {
		tmp = t_0 - y;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = math.log(y) * x
	tmp = 0
	if y <= 0.65:
		tmp = t_0 - z
	else:
		tmp = t_0 - y
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(log(y) * x)
	tmp = 0.0
	if (y <= 0.65)
		tmp = Float64(t_0 - z);
	else
		tmp = Float64(t_0 - y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = log(y) * x;
	tmp = 0.0;
	if (y <= 0.65)
		tmp = t_0 - z;
	else
		tmp = t_0 - y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[Log[y], $MachinePrecision] * x), $MachinePrecision]}, If[LessEqual[y, 0.65], N[(t$95$0 - z), $MachinePrecision], N[(t$95$0 - y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < 0.650000000000000022

   1. Initial program 99.7%

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

   3. Taylor expanded in y around inf 60.4%

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

      1. sub-neg 60.4%

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

      2. mul-1-neg 60.4%

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

      3. *-commutative 60.4%

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

      4. associate-/l* 60.4%

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

      5. distribute-lft-neg-in 60.4%

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

      6. log-rec 60.4%

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

      7. remove-double-neg 60.4%

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

      8. distribute-neg-in 60.4%

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

      9. metadata-eval 60.4%

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

      10. unsub-neg 60.4%

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

   5. Simplified 60.4%

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

   6. Taylor expanded in y around 0 95.3%

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

   if 0.650000000000000022 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0 86.9%

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

4. Final simplification 90.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 0.65:\\ \;\;\;\;\log y \cdot x - z\\ \mathbf{else}:\\ \;\;\;\;\log y \cdot x - y\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.8%

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

3. Final simplification 99.8%

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

Alternative 6: 52.6% accurate, 15.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 7 \cdot 10^{+41}:\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;-y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (if (<= y 7e+41) (- z) (- y)))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= 7e+41) {
		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 <= 7d+41) 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 <= 7e+41) {
		tmp = -z;
	} else {
		tmp = -y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= 7e+41:
		tmp = -z
	else:
		tmp = -y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= 7e+41)
		tmp = Float64(-z);
	else
		tmp = Float64(-y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= 7e+41)
		tmp = -z;
	else
		tmp = -y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, 7e+41], (-z), (-y)]

Derivation

1. Split input into 2 regimes

2. if y < 6.9999999999999998e41

   1. Initial program 99.8%

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

   3. Taylor expanded in y around inf 64.4%

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

      1. sub-neg 64.4%

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

      2. mul-1-neg 64.4%

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

      3. *-commutative 64.4%

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

      4. associate-/l* 64.4%

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

      5. distribute-lft-neg-in 64.4%

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

      6. log-rec 64.4%

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

      7. remove-double-neg 64.4%

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

      8. distribute-neg-in 64.4%

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

      9. metadata-eval 64.4%

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

      10. unsub-neg 64.4%

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

   5. Simplified 64.4%

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

   6. Taylor expanded in z around inf 46.9%

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

      1. neg-mul-1 46.9%

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

   8. Simplified 46.9%

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

   if 6.9999999999999998e41 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in y around inf 67.3%

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

      1. neg-mul-1 67.3%

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

   5. Simplified 67.3%

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

Alternative 7: 66.0% accurate, 26.8× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.8%

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

3. Taylor expanded in x around 0 65.3%

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

   1. neg-mul-1 65.3%

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

5. Simplified 65.3%

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

Alternative 8: 34.7% accurate, 53.5× speedup

Math

\[\begin{array}{l} \\ -y \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.8%

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

3. Taylor expanded in y around inf 35.9%

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

   1. neg-mul-1 35.9%

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

5. Simplified 35.9%

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

Reproduce

herbie shell --seed 2024111 
(FPCore (x y z)
  :name "Statistics.Distribution.Poisson:$clogProbability from math-functions-0.1.5.2"
  :precision binary64
  (- (- (* x (log y)) z) y))