System.Random.MWC.Distributions:gamma from mwc-random-0.13.3.2

Percentage Accurate: 99.9% → 99.8%

Time: 10.6s

Alternatives: 7

Speedup: 1.0×

Specification

Math

\[\begin{array}{l} \\ x \cdot 0.5 + y \cdot \left(\left(1 - z\right) + \log z\right) \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (+ (* x 0.5) (* y (+ (- 1.0 z) (log z)))))

C

double code(double x, double y, double z) {
	return (x * 0.5) + (y * ((1.0 - z) + log(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 = (x * 0.5d0) + (y * ((1.0d0 - z) + log(z)))
end function

Java

public static double code(double x, double y, double z) {
	return (x * 0.5) + (y * ((1.0 - z) + Math.log(z)));
}

Python

def code(x, y, z):
	return (x * 0.5) + (y * ((1.0 - z) + math.log(z)))

Julia

function code(x, y, z)
	return Float64(Float64(x * 0.5) + Float64(y * Float64(Float64(1.0 - z) + log(z))))
end

MATLAB

function tmp = code(x, y, z)
	tmp = (x * 0.5) + (y * ((1.0 - z) + log(z)));
end

Wolfram

code[x_, y_, z_] := N[(N[(x * 0.5), $MachinePrecision] + N[(y * N[(N[(1.0 - z), $MachinePrecision] + N[Log[z], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Initial Program: 99.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x \cdot 0.5 + y \cdot \left(\left(1 - z\right) + \log z\right) \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (+ (* x 0.5) (* y (+ (- 1.0 z) (log z)))))

C

double code(double x, double y, double z) {
	return (x * 0.5) + (y * ((1.0 - z) + log(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 = (x * 0.5d0) + (y * ((1.0d0 - z) + log(z)))
end function

Java

public static double code(double x, double y, double z) {
	return (x * 0.5) + (y * ((1.0 - z) + Math.log(z)));
}

Python

def code(x, y, z):
	return (x * 0.5) + (y * ((1.0 - z) + math.log(z)))

Julia

function code(x, y, z)
	return Float64(Float64(x * 0.5) + Float64(y * Float64(Float64(1.0 - z) + log(z))))
end

MATLAB

function tmp = code(x, y, z)
	tmp = (x * 0.5) + (y * ((1.0 - z) + log(z)));
end

Wolfram

code[x_, y_, z_] := N[(N[(x * 0.5), $MachinePrecision] + N[(y * N[(N[(1.0 - z), $MachinePrecision] + N[Log[z], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Alternative 1: 99.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x \cdot 0.5 + \left(y + \left(\log z - z\right) \cdot y\right) \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (+ (* x 0.5) (+ y (* (- (log z) z) y))))

C

double code(double x, double y, double z) {
	return (x * 0.5) + (y + ((log(z) - 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 * 0.5d0) + (y + ((log(z) - z) * y))
end function

Java

public static double code(double x, double y, double z) {
	return (x * 0.5) + (y + ((Math.log(z) - z) * y));
}

Python

def code(x, y, z):
	return (x * 0.5) + (y + ((math.log(z) - z) * y))

Julia

function code(x, y, z)
	return Float64(Float64(x * 0.5) + Float64(y + Float64(Float64(log(z) - z) * y)))
end

MATLAB

function tmp = code(x, y, z)
	tmp = (x * 0.5) + (y + ((log(z) - z) * y));
end

Wolfram

code[x_, y_, z_] := N[(N[(x * 0.5), $MachinePrecision] + N[(y + N[(N[(N[Log[z], $MachinePrecision] - z), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.9%

   \[x \cdot 0.5 + y \cdot \left(\left(1 - z\right) + \log z\right) \]
2. Step-by-step derivation

   1. +-commutative 99.9%

      \[\leadsto x \cdot 0.5 + y \cdot \color{blue}{\left(\log z + \left(1 - z\right)\right)} \]

   2. sub-neg 99.9%

      \[\leadsto x \cdot 0.5 + y \cdot \left(\log z + \color{blue}{\left(1 + \left(-z\right)\right)}\right) \]

   3. +-commutative 99.9%

      \[\leadsto x \cdot 0.5 + y \cdot \left(\log z + \color{blue}{\left(\left(-z\right) + 1\right)}\right) \]

   4. associate-+l+ 99.9%

      \[\leadsto x \cdot 0.5 + y \cdot \color{blue}{\left(\left(\log z + \left(-z\right)\right) + 1\right)} \]

   5. sub-neg 99.9%

      \[\leadsto x \cdot 0.5 + y \cdot \left(\color{blue}{\left(\log z - z\right)} + 1\right) \]

   6. distribute-rgt-in 99.9%

      \[\leadsto x \cdot 0.5 + \color{blue}{\left(\left(\log z - z\right) \cdot y + 1 \cdot y\right)} \]

   7. *-un-lft-identity 99.9%

      \[\leadsto x \cdot 0.5 + \left(\left(\log z - z\right) \cdot y + \color{blue}{y}\right) \]

3. Applied egg-rr 99.9%

   \[\leadsto x \cdot 0.5 + \color{blue}{\left(\left(\log z - z\right) \cdot y + y\right)} \]

4. Final simplification 99.9%

   \[\leadsto x \cdot 0.5 + \left(y + \left(\log z - z\right) \cdot y\right) \]

Alternative 2: 86.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -130000000 \lor \neg \left(y \leq 3.3 \cdot 10^{+80}\right):\\ \;\;\;\;y + \left(\log z - z\right) \cdot y\\ \mathbf{else}:\\ \;\;\;\;x \cdot 0.5 - z \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -130000000.0) (not (<= y 3.3e+80)))
   (+ y (* (- (log z) z) y))
   (- (* x 0.5) (* z y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -130000000.0) || !(y <= 3.3e+80)) {
		tmp = y + ((log(z) - z) * y);
	} else {
		tmp = (x * 0.5) - (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 <= (-130000000.0d0)) .or. (.not. (y <= 3.3d+80))) then
        tmp = y + ((log(z) - z) * y)
    else
        tmp = (x * 0.5d0) - (z * y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -130000000.0) || !(y <= 3.3e+80)) {
		tmp = y + ((Math.log(z) - z) * y);
	} else {
		tmp = (x * 0.5) - (z * y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -130000000.0) or not (y <= 3.3e+80):
		tmp = y + ((math.log(z) - z) * y)
	else:
		tmp = (x * 0.5) - (z * y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -130000000.0) || !(y <= 3.3e+80))
		tmp = Float64(y + Float64(Float64(log(z) - z) * y));
	else
		tmp = Float64(Float64(x * 0.5) - Float64(z * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -130000000.0) || ~((y <= 3.3e+80)))
		tmp = y + ((log(z) - z) * y);
	else
		tmp = (x * 0.5) - (z * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -130000000.0], N[Not[LessEqual[y, 3.3e+80]], $MachinePrecision]], N[(y + N[(N[(N[Log[z], $MachinePrecision] - z), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision], N[(N[(x * 0.5), $MachinePrecision] - N[(z * y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.3e8 or 3.29999999999999991e80 < y

   1. Initial program 99.8%

      \[x \cdot 0.5 + y \cdot \left(\left(1 - z\right) + \log z\right) \]
   2. Step-by-step derivation

      1. +-commutative 99.8%

         \[\leadsto x \cdot 0.5 + y \cdot \color{blue}{\left(\log z + \left(1 - z\right)\right)} \]

      2. sub-neg 99.8%

         \[\leadsto x \cdot 0.5 + y \cdot \left(\log z + \color{blue}{\left(1 + \left(-z\right)\right)}\right) \]

      3. +-commutative 99.8%

         \[\leadsto x \cdot 0.5 + y \cdot \left(\log z + \color{blue}{\left(\left(-z\right) + 1\right)}\right) \]

      4. associate-+l+ 99.8%

         \[\leadsto x \cdot 0.5 + y \cdot \color{blue}{\left(\left(\log z + \left(-z\right)\right) + 1\right)} \]

      5. sub-neg 99.8%

         \[\leadsto x \cdot 0.5 + y \cdot \left(\color{blue}{\left(\log z - z\right)} + 1\right) \]

      6. distribute-rgt-in 99.8%

         \[\leadsto x \cdot 0.5 + \color{blue}{\left(\left(\log z - z\right) \cdot y + 1 \cdot y\right)} \]

      7. *-un-lft-identity 99.8%

         \[\leadsto x \cdot 0.5 + \left(\left(\log z - z\right) \cdot y + \color{blue}{y}\right) \]

   3. Applied egg-rr 99.8%

      \[\leadsto x \cdot 0.5 + \color{blue}{\left(\left(\log z - z\right) \cdot y + y\right)} \]

   4. Taylor expanded in x around 0 87.5%

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

   if -1.3e8 < y < 3.29999999999999991e80

   1. Initial program 99.9%

      \[x \cdot 0.5 + y \cdot \left(\left(1 - z\right) + \log z\right) \]

   2. Taylor expanded in z around inf 89.7%

      \[\leadsto x \cdot 0.5 + \color{blue}{-1 \cdot \left(y \cdot z\right)} \]
   3. Step-by-step derivation

      1. mul-1-neg 89.7%

         \[\leadsto x \cdot 0.5 + \color{blue}{\left(-y \cdot z\right)} \]

      2. distribute-rgt-neg-out 89.7%

         \[\leadsto x \cdot 0.5 + \color{blue}{y \cdot \left(-z\right)} \]

   4. Simplified 89.7%

      \[\leadsto x \cdot 0.5 + \color{blue}{y \cdot \left(-z\right)} \]
   5. Step-by-step derivation

      1. distribute-rgt-neg-out 89.7%

         \[\leadsto x \cdot 0.5 + \color{blue}{\left(-y \cdot z\right)} \]

      2. unsub-neg 89.7%

         \[\leadsto \color{blue}{x \cdot 0.5 - y \cdot z} \]

   6. Applied egg-rr 89.7%

      \[\leadsto \color{blue}{x \cdot 0.5 - y \cdot z} \]
3. Recombined 2 regimes into one program.

4. Final simplification 88.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -130000000 \lor \neg \left(y \leq 3.3 \cdot 10^{+80}\right):\\ \;\;\;\;y + \left(\log z - z\right) \cdot y\\ \mathbf{else}:\\ \;\;\;\;x \cdot 0.5 - z \cdot y\\ \end{array} \]

Alternative 3: 98.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq 0.56:\\ \;\;\;\;x \cdot 0.5 + y \cdot \left(\log z + 1\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 0.5 + y \cdot \left(1 - z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z 0.56)
   (+ (* x 0.5) (* y (+ (log z) 1.0)))
   (+ (* x 0.5) (* y (- 1.0 z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= 0.56) {
		tmp = (x * 0.5) + (y * (log(z) + 1.0));
	} else {
		tmp = (x * 0.5) + (y * (1.0 - z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z <= 0.56d0) then
        tmp = (x * 0.5d0) + (y * (log(z) + 1.0d0))
    else
        tmp = (x * 0.5d0) + (y * (1.0d0 - z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= 0.56) {
		tmp = (x * 0.5) + (y * (Math.log(z) + 1.0));
	} else {
		tmp = (x * 0.5) + (y * (1.0 - z));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= 0.56:
		tmp = (x * 0.5) + (y * (math.log(z) + 1.0))
	else:
		tmp = (x * 0.5) + (y * (1.0 - z))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= 0.56)
		tmp = Float64(Float64(x * 0.5) + Float64(y * Float64(log(z) + 1.0)));
	else
		tmp = Float64(Float64(x * 0.5) + Float64(y * Float64(1.0 - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= 0.56)
		tmp = (x * 0.5) + (y * (log(z) + 1.0));
	else
		tmp = (x * 0.5) + (y * (1.0 - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, 0.56], N[(N[(x * 0.5), $MachinePrecision] + N[(y * N[(N[Log[z], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * 0.5), $MachinePrecision] + N[(y * N[(1.0 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 0.56000000000000005

   1. Initial program 99.7%

      \[x \cdot 0.5 + y \cdot \left(\left(1 - z\right) + \log z\right) \]

   2. Taylor expanded in z around 0 98.1%

      \[\leadsto x \cdot 0.5 + \color{blue}{y \cdot \left(1 + \log z\right)} \]

   if 0.56000000000000005 < z

   1. Initial program 100.0%

      \[x \cdot 0.5 + y \cdot \left(\left(1 - z\right) + \log z\right) \]
   2. Step-by-step derivation

      1. +-commutative 100.0%

         \[\leadsto x \cdot 0.5 + y \cdot \color{blue}{\left(\log z + \left(1 - z\right)\right)} \]

      2. sub-neg 100.0%

         \[\leadsto x \cdot 0.5 + y \cdot \left(\log z + \color{blue}{\left(1 + \left(-z\right)\right)}\right) \]

      3. +-commutative 100.0%

         \[\leadsto x \cdot 0.5 + y \cdot \left(\log z + \color{blue}{\left(\left(-z\right) + 1\right)}\right) \]

      4. associate-+l+ 100.0%

         \[\leadsto x \cdot 0.5 + y \cdot \color{blue}{\left(\left(\log z + \left(-z\right)\right) + 1\right)} \]

      5. sub-neg 100.0%

         \[\leadsto x \cdot 0.5 + y \cdot \left(\color{blue}{\left(\log z - z\right)} + 1\right) \]

      6. distribute-rgt-in 100.0%

         \[\leadsto x \cdot 0.5 + \color{blue}{\left(\left(\log z - z\right) \cdot y + 1 \cdot y\right)} \]

      7. *-un-lft-identity 100.0%

         \[\leadsto x \cdot 0.5 + \left(\left(\log z - z\right) \cdot y + \color{blue}{y}\right) \]

   3. Applied egg-rr 100.0%

      \[\leadsto x \cdot 0.5 + \color{blue}{\left(\left(\log z - z\right) \cdot y + y\right)} \]
   4. Step-by-step derivation

      1. flip-- 47.3%

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

      2. clear-num 47.3%

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

      3. *-un-lft-identity 47.3%

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

      4. associate-/l* 47.3%

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

      5. flip-- 71.1%

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

   5. Applied egg-rr 99.9%

      \[\leadsto x \cdot 0.5 + \left(\color{blue}{\frac{1}{\frac{1}{\log z - z}}} \cdot y + y\right) \]

   6. Taylor expanded in z around inf 99.4%

      \[\leadsto x \cdot 0.5 + \left(\color{blue}{\left(-1 \cdot z\right)} \cdot y + y\right) \]
   7. Step-by-step derivation

      1. mul-1-neg 70.6%

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

   8. Simplified 99.4%

      \[\leadsto x \cdot 0.5 + \left(\color{blue}{\left(-z\right)} \cdot y + y\right) \]

   9. Taylor expanded in z around 0 99.4%

      \[\leadsto x \cdot 0.5 + \color{blue}{\left(y + -1 \cdot \left(y \cdot z\right)\right)} \]
   10. Step-by-step derivation

       1. remove-double-neg 99.4%

          \[\leadsto x \cdot 0.5 + \left(\color{blue}{\left(-\left(-y\right)\right)} + -1 \cdot \left(y \cdot z\right)\right) \]

       2. neg-mul-1 99.4%

          \[\leadsto x \cdot 0.5 + \left(\color{blue}{-1 \cdot \left(-y\right)} + -1 \cdot \left(y \cdot z\right)\right) \]

       3. neg-mul-1 99.4%

          \[\leadsto x \cdot 0.5 + \left(-1 \cdot \color{blue}{\left(-1 \cdot y\right)} + -1 \cdot \left(y \cdot z\right)\right) \]

       4. associate-*r* 99.4%

          \[\leadsto x \cdot 0.5 + \left(\color{blue}{\left(-1 \cdot -1\right) \cdot y} + -1 \cdot \left(y \cdot z\right)\right) \]

       5. metadata-eval 99.4%

          \[\leadsto x \cdot 0.5 + \left(\color{blue}{1} \cdot y + -1 \cdot \left(y \cdot z\right)\right) \]

       6. *-commutative 99.4%

          \[\leadsto x \cdot 0.5 + \left(1 \cdot y + -1 \cdot \color{blue}{\left(z \cdot y\right)}\right) \]

       7. associate-*r* 99.4%

          \[\leadsto x \cdot 0.5 + \left(1 \cdot y + \color{blue}{\left(-1 \cdot z\right) \cdot y}\right) \]

       8. distribute-rgt-in 99.4%

          \[\leadsto x \cdot 0.5 + \color{blue}{y \cdot \left(1 + -1 \cdot z\right)} \]

       9. mul-1-neg 99.4%

          \[\leadsto x \cdot 0.5 + y \cdot \left(1 + \color{blue}{\left(-z\right)}\right) \]

       10. sub-neg 99.4%

           \[\leadsto x \cdot 0.5 + y \cdot \color{blue}{\left(1 - z\right)} \]

   11. Simplified 99.4%

       \[\leadsto x \cdot 0.5 + \color{blue}{y \cdot \left(1 - z\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 98.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 0.56:\\ \;\;\;\;x \cdot 0.5 + y \cdot \left(\log z + 1\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 0.5 + y \cdot \left(1 - z\right)\\ \end{array} \]

Alternative 4: 99.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x \cdot 0.5 + y \cdot \left(\log z + \left(1 - z\right)\right) \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (+ (* x 0.5) (* y (+ (log z) (- 1.0 z)))))

C

double code(double x, double y, double z) {
	return (x * 0.5) + (y * (log(z) + (1.0 - 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 = (x * 0.5d0) + (y * (log(z) + (1.0d0 - z)))
end function

Java

public static double code(double x, double y, double z) {
	return (x * 0.5) + (y * (Math.log(z) + (1.0 - z)));
}

Python

def code(x, y, z):
	return (x * 0.5) + (y * (math.log(z) + (1.0 - z)))

Julia

function code(x, y, z)
	return Float64(Float64(x * 0.5) + Float64(y * Float64(log(z) + Float64(1.0 - z))))
end

MATLAB

function tmp = code(x, y, z)
	tmp = (x * 0.5) + (y * (log(z) + (1.0 - z)));
end

Wolfram

code[x_, y_, z_] := N[(N[(x * 0.5), $MachinePrecision] + N[(y * N[(N[Log[z], $MachinePrecision] + N[(1.0 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.9%

   \[x \cdot 0.5 + y \cdot \left(\left(1 - z\right) + \log z\right) \]

2. Final simplification 99.9%

   \[\leadsto x \cdot 0.5 + y \cdot \left(\log z + \left(1 - z\right)\right) \]

Alternative 5: 58.4% accurate, 15.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq 5 \cdot 10^{+89}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;y - z \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (if (<= z 5e+89) (* x 0.5) (- y (* z y))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= 5e+89) {
		tmp = x * 0.5;
	} else {
		tmp = y - (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 (z <= 5d+89) then
        tmp = x * 0.5d0
    else
        tmp = y - (z * y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= 5e+89) {
		tmp = x * 0.5;
	} else {
		tmp = y - (z * y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= 5e+89:
		tmp = x * 0.5
	else:
		tmp = y - (z * y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= 5e+89)
		tmp = Float64(x * 0.5);
	else
		tmp = Float64(y - Float64(z * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= 5e+89)
		tmp = x * 0.5;
	else
		tmp = y - (z * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, 5e+89], N[(x * 0.5), $MachinePrecision], N[(y - N[(z * y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 4.99999999999999983e89

   1. Initial program 99.8%

      \[x \cdot 0.5 + y \cdot \left(\left(1 - z\right) + \log z\right) \]

   2. Taylor expanded in x around inf 53.9%

      \[\leadsto \color{blue}{0.5 \cdot x} \]

   if 4.99999999999999983e89 < z

   1. Initial program 100.0%

      \[x \cdot 0.5 + y \cdot \left(\left(1 - z\right) + \log z\right) \]
   2. Step-by-step derivation

      1. +-commutative 100.0%

         \[\leadsto x \cdot 0.5 + y \cdot \color{blue}{\left(\log z + \left(1 - z\right)\right)} \]

      2. sub-neg 100.0%

         \[\leadsto x \cdot 0.5 + y \cdot \left(\log z + \color{blue}{\left(1 + \left(-z\right)\right)}\right) \]

      3. +-commutative 100.0%

         \[\leadsto x \cdot 0.5 + y \cdot \left(\log z + \color{blue}{\left(\left(-z\right) + 1\right)}\right) \]

      4. associate-+l+ 100.0%

         \[\leadsto x \cdot 0.5 + y \cdot \color{blue}{\left(\left(\log z + \left(-z\right)\right) + 1\right)} \]

      5. sub-neg 100.0%

         \[\leadsto x \cdot 0.5 + y \cdot \left(\color{blue}{\left(\log z - z\right)} + 1\right) \]

      6. distribute-rgt-in 100.0%

         \[\leadsto x \cdot 0.5 + \color{blue}{\left(\left(\log z - z\right) \cdot y + 1 \cdot y\right)} \]

      7. *-un-lft-identity 100.0%

         \[\leadsto x \cdot 0.5 + \left(\left(\log z - z\right) \cdot y + \color{blue}{y}\right) \]

   3. Applied egg-rr 100.0%

      \[\leadsto x \cdot 0.5 + \color{blue}{\left(\left(\log z - z\right) \cdot y + y\right)} \]

   4. Taylor expanded in x around 0 81.4%

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

      1. flip-- 51.0%

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

      2. clear-num 50.9%

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

      3. *-un-lft-identity 50.9%

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

      4. associate-/l* 50.9%

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

      5. flip-- 81.3%

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

   6. Applied egg-rr 81.3%

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

   7. Taylor expanded in z around inf 81.4%

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

      1. mul-1-neg 81.4%

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

   9. Simplified 81.4%

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

4. Final simplification 64.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 5 \cdot 10^{+89}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;y - z \cdot y\\ \end{array} \]

Alternative 6: 75.1% accurate, 15.9× speedup

Math

\[\begin{array}{l} \\ x \cdot 0.5 - z \cdot y \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (- (* x 0.5) (* z y)))

C

double code(double x, double y, double z) {
	return (x * 0.5) - (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 * 0.5d0) - (z * y)
end function

Java

public static double code(double x, double y, double z) {
	return (x * 0.5) - (z * y);
}

Python

def code(x, y, z):
	return (x * 0.5) - (z * y)

Julia

function code(x, y, z)
	return Float64(Float64(x * 0.5) - Float64(z * y))
end

MATLAB

function tmp = code(x, y, z)
	tmp = (x * 0.5) - (z * y);
end

Wolfram

code[x_, y_, z_] := N[(N[(x * 0.5), $MachinePrecision] - N[(z * y), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.9%

   \[x \cdot 0.5 + y \cdot \left(\left(1 - z\right) + \log z\right) \]

2. Taylor expanded in z around inf 76.3%

   \[\leadsto x \cdot 0.5 + \color{blue}{-1 \cdot \left(y \cdot z\right)} \]
3. Step-by-step derivation

   1. mul-1-neg 76.3%

      \[\leadsto x \cdot 0.5 + \color{blue}{\left(-y \cdot z\right)} \]

   2. distribute-rgt-neg-out 76.3%

      \[\leadsto x \cdot 0.5 + \color{blue}{y \cdot \left(-z\right)} \]

4. Simplified 76.3%

   \[\leadsto x \cdot 0.5 + \color{blue}{y \cdot \left(-z\right)} \]
5. Step-by-step derivation

   1. distribute-rgt-neg-out 76.3%

      \[\leadsto x \cdot 0.5 + \color{blue}{\left(-y \cdot z\right)} \]

   2. unsub-neg 76.3%

      \[\leadsto \color{blue}{x \cdot 0.5 - y \cdot z} \]

6. Applied egg-rr 76.3%

   \[\leadsto \color{blue}{x \cdot 0.5 - y \cdot z} \]

7. Final simplification 76.3%

   \[\leadsto x \cdot 0.5 - z \cdot y \]

Alternative 7: 39.7% accurate, 37.0× speedup

Math

\[\begin{array}{l} \\ x \cdot 0.5 \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (* x 0.5))

C

double code(double x, double y, double z) {
	return x * 0.5;
}

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 * 0.5d0
end function

Java

public static double code(double x, double y, double z) {
	return x * 0.5;
}

Python

def code(x, y, z):
	return x * 0.5

Julia

function code(x, y, z)
	return Float64(x * 0.5)
end

MATLAB

function tmp = code(x, y, z)
	tmp = x * 0.5;
end

Wolfram

code[x_, y_, z_] := N[(x * 0.5), $MachinePrecision]

Derivation

1. Initial program 99.9%

   \[x \cdot 0.5 + y \cdot \left(\left(1 - z\right) + \log z\right) \]

2. Taylor expanded in x around inf 40.0%

   \[\leadsto \color{blue}{0.5 \cdot x} \]

3. Final simplification 40.0%

   \[\leadsto x \cdot 0.5 \]

Developer target: 99.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \left(y + 0.5 \cdot x\right) - y \cdot \left(z - \log z\right) \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (- (+ y (* 0.5 x)) (* y (- z (log z)))))

C

double code(double x, double y, double z) {
	return (y + (0.5 * x)) - (y * (z - log(z)));
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = (y + (0.5d0 * x)) - (y * (z - log(z)))
end function

Java

public static double code(double x, double y, double z) {
	return (y + (0.5 * x)) - (y * (z - Math.log(z)));
}

Python

def code(x, y, z):
	return (y + (0.5 * x)) - (y * (z - math.log(z)))

Julia

function code(x, y, z)
	return Float64(Float64(y + Float64(0.5 * x)) - Float64(y * Float64(z - log(z))))
end

MATLAB

function tmp = code(x, y, z)
	tmp = (y + (0.5 * x)) - (y * (z - log(z)));
end

Wolfram

code[x_, y_, z_] := N[(N[(y + N[(0.5 * x), $MachinePrecision]), $MachinePrecision] - N[(y * N[(z - N[Log[z], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Reproduce

herbie shell --seed 2023301 
(FPCore (x y z)
  :name "System.Random.MWC.Distributions:gamma from mwc-random-0.13.3.2"
  :precision binary64

  :herbie-target
  (- (+ y (* 0.5 x)) (* y (- z (log z))))

  (+ (* x 0.5) (* y (+ (- 1.0 z) (log z)))))