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

Percentage Accurate: 99.9% → 99.6%

Time: 9.1s

Alternatives: 8

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: 99.6% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

3. Taylor expanded in z around 0 99.9%

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

   1. mul-1-neg 99.9%

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

5. Applied egg-rr 99.9%

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

6. Final simplification 99.9%

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

Alternative 2: 73.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y + y \cdot \log z\\ \mathbf{if}\;z \leq 9.5 \cdot 10^{-235}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{-138}:\\ \;\;\;\;x \cdot \left(0.5 - z \cdot \frac{y}{x}\right)\\ \mathbf{elif}\;z \leq 0.047:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;x \cdot 0.5 + y \cdot \left(1 - z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ y (* y (log z)))))
   (if (<= z 9.5e-235)
     t_0
     (if (<= z 2.5e-138)
       (* x (- 0.5 (* z (/ y x))))
       (if (<= z 0.047) t_0 (+ (* x 0.5) (* y (- 1.0 z))))))))

C

double code(double x, double y, double z) {
	double t_0 = y + (y * log(z));
	double tmp;
	if (z <= 9.5e-235) {
		tmp = t_0;
	} else if (z <= 2.5e-138) {
		tmp = x * (0.5 - (z * (y / x)));
	} else if (z <= 0.047) {
		tmp = t_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) :: t_0
    real(8) :: tmp
    t_0 = y + (y * log(z))
    if (z <= 9.5d-235) then
        tmp = t_0
    else if (z <= 2.5d-138) then
        tmp = x * (0.5d0 - (z * (y / x)))
    else if (z <= 0.047d0) then
        tmp = t_0
    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 t_0 = y + (y * Math.log(z));
	double tmp;
	if (z <= 9.5e-235) {
		tmp = t_0;
	} else if (z <= 2.5e-138) {
		tmp = x * (0.5 - (z * (y / x)));
	} else if (z <= 0.047) {
		tmp = t_0;
	} else {
		tmp = (x * 0.5) + (y * (1.0 - z));
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = y + (y * math.log(z))
	tmp = 0
	if z <= 9.5e-235:
		tmp = t_0
	elif z <= 2.5e-138:
		tmp = x * (0.5 - (z * (y / x)))
	elif z <= 0.047:
		tmp = t_0
	else:
		tmp = (x * 0.5) + (y * (1.0 - z))
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(y + Float64(y * log(z)))
	tmp = 0.0
	if (z <= 9.5e-235)
		tmp = t_0;
	elseif (z <= 2.5e-138)
		tmp = Float64(x * Float64(0.5 - Float64(z * Float64(y / x))));
	elseif (z <= 0.047)
		tmp = t_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)
	t_0 = y + (y * log(z));
	tmp = 0.0;
	if (z <= 9.5e-235)
		tmp = t_0;
	elseif (z <= 2.5e-138)
		tmp = x * (0.5 - (z * (y / x)));
	elseif (z <= 0.047)
		tmp = t_0;
	else
		tmp = (x * 0.5) + (y * (1.0 - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(y + N[(y * N[Log[z], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, 9.5e-235], t$95$0, If[LessEqual[z, 2.5e-138], N[(x * N[(0.5 - N[(z * N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 0.047], t$95$0, N[(N[(x * 0.5), $MachinePrecision] + N[(y * N[(1.0 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if z < 9.4999999999999996e-235 or 2.49999999999999994e-138 < z < 0.047

   1. Initial program 99.7%

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

      1. distribute-rgt-in 99.6%

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

   4. Applied egg-rr 99.6%

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

   5. Taylor expanded in z around 0 96.7%

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

   6. Taylor expanded in x around inf 80.7%

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

      1. associate-/l* 80.8%

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

   8. Simplified 80.8%

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

   9. Taylor expanded in x around 0 62.5%

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

   if 9.4999999999999996e-235 < z < 2.49999999999999994e-138

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf 63.5%

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

      1. associate-*r* 63.5%

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

      2. mul-1-neg 63.5%

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

   5. Simplified 63.5%

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

   6. Taylor expanded in y around inf 53.3%

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

      1. neg-mul-1 53.3%

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

      2. +-commutative 53.3%

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

      3. unsub-neg 53.3%

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

      4. associate-*r/ 53.3%

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

   8. Simplified 53.3%

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

   9. Taylor expanded in x around inf 63.5%

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

       1. mul-1-neg 63.5%

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

       2. unsub-neg 63.5%

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

       3. *-commutative 63.5%

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

       4. associate-/l* 63.5%

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

   11. Simplified 63.5%

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

   if 0.047 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 100.0%

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

      1. sub-neg 100.0%

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

      2. metadata-eval 100.0%

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

      3. +-commutative 100.0%

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

      4. +-commutative 100.0%

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

      5. mul-1-neg 100.0%

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

      6. distribute-frac-neg 100.0%

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

      7. log-rec 100.0%

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

      8. remove-double-neg 100.0%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in z around inf 100.0%

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

      1. +-commutative 100.0%

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

      2. log-rec 100.0%

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

      3. associate-*r/ 100.0%

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

      4. mul-1-neg 100.0%

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

      5. remove-double-neg 100.0%

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

      6. associate--l+ 100.0%

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

      7. distribute-lft-in 100.0%

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

      8. rgt-mult-inverse 100.0%

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

      9. sub-neg 100.0%

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

      10. metadata-eval 100.0%

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

   8. Simplified 100.0%

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

   9. Taylor expanded in z around inf 99.4%

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

4. Final simplification 80.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 9.5 \cdot 10^{-235}:\\ \;\;\;\;y + y \cdot \log z\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{-138}:\\ \;\;\;\;x \cdot \left(0.5 - z \cdot \frac{y}{x}\right)\\ \mathbf{elif}\;z \leq 0.047:\\ \;\;\;\;y + y \cdot \log z\\ \mathbf{else}:\\ \;\;\;\;x \cdot 0.5 + y \cdot \left(1 - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 98.8% accurate, 1.0× speedup

Math

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

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z 0.56)
   (+ (* x 0.5) (* y (+ 1.0 (log z))))
   (+ (* 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 * (1.0 + log(z)));
	} 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 * (1.0d0 + log(z)))
    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 * (1.0 + Math.log(z)));
	} 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 * (1.0 + math.log(z)))
	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(1.0 + log(z))));
	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 * (1.0 + log(z)));
	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[(1.0 + N[Log[z], $MachinePrecision]), $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 99.8%

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

   3. Taylor expanded in z around 0 98.1%

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

      1. *-commutative 98.1%

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

   5. Simplified 98.1%

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

   if 0.56000000000000005 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 100.0%

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

      1. sub-neg 100.0%

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

      2. metadata-eval 100.0%

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

      3. +-commutative 100.0%

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

      4. +-commutative 100.0%

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

      5. mul-1-neg 100.0%

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

      6. distribute-frac-neg 100.0%

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

      7. log-rec 100.0%

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

      8. remove-double-neg 100.0%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in z around inf 100.0%

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

      1. +-commutative 100.0%

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

      2. log-rec 100.0%

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

      3. associate-*r/ 100.0%

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

      4. mul-1-neg 100.0%

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

      5. remove-double-neg 100.0%

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

      6. associate--l+ 100.0%

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

      7. distribute-lft-in 100.0%

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

      8. rgt-mult-inverse 100.0%

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

      9. sub-neg 100.0%

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

      10. metadata-eval 100.0%

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

   8. Simplified 100.0%

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

   9. Taylor expanded in z around inf 99.4%

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

4. Final simplification 98.7%

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

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. Add Preprocessing

3. Final simplification 99.9%

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

Alternative 5: 60.7% accurate, 12.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq 8 \cdot 10^{+16}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (if (<= z 8e+16) (* x 0.5) (* y (- z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= 8e+16) {
		tmp = x * 0.5;
	} else {
		tmp = y * -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 <= 8d+16) then
        tmp = x * 0.5d0
    else
        tmp = y * -z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= 8e+16) {
		tmp = x * 0.5;
	} else {
		tmp = y * -z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= 8e+16:
		tmp = x * 0.5
	else:
		tmp = y * -z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= 8e+16)
		tmp = Float64(x * 0.5);
	else
		tmp = Float64(y * Float64(-z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= 8e+16)
		tmp = x * 0.5;
	else
		tmp = y * -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, 8e+16], N[(x * 0.5), $MachinePrecision], N[(y * (-z)), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 8e16

   1. Initial program 99.8%

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

   3. Taylor expanded in z around inf 50.6%

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

      1. associate-*r* 50.6%

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

      2. mul-1-neg 50.6%

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

   5. Simplified 50.6%

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

   6. Taylor expanded in x around inf 49.3%

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

   if 8e16 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 100.0%

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

      1. associate-*r* 100.0%

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

      2. mul-1-neg 100.0%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in x around 0 81.0%

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

      1. neg-mul-1 81.0%

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

      2. distribute-lft-neg-in 81.0%

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

   8. Simplified 81.0%

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

4. Final simplification 63.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 8 \cdot 10^{+16}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 75.0% accurate, 15.9× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

3. Taylor expanded in z around inf 73.2%

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

   1. associate-*r* 73.2%

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

   2. mul-1-neg 73.2%

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

5. Simplified 73.2%

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

   1. fma-define 73.2%

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

   2. distribute-lft-neg-out 73.2%

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

   3. add-sqr-sqrt 37.1%

      \[\leadsto \mathsf{fma}\left(x, 0.5, -\color{blue}{\left(\sqrt{y} \cdot \sqrt{y}\right)} \cdot z\right) \]

   4. sqrt-unprod 46.7%

      \[\leadsto \mathsf{fma}\left(x, 0.5, -\color{blue}{\sqrt{y \cdot y}} \cdot z\right) \]

   5. sqr-neg 46.7%

      \[\leadsto \mathsf{fma}\left(x, 0.5, -\sqrt{\color{blue}{\left(-y\right) \cdot \left(-y\right)}} \cdot z\right) \]

   6. sqrt-unprod 14.9%

      \[\leadsto \mathsf{fma}\left(x, 0.5, -\color{blue}{\left(\sqrt{-y} \cdot \sqrt{-y}\right)} \cdot z\right) \]

   7. add-sqr-sqrt 35.2%

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

   8. fma-neg 35.2%

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

   9. add-sqr-sqrt 14.9%

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

   10. sqrt-unprod 46.7%

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

   11. sqr-neg 46.7%

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

   12. sqrt-unprod 37.1%

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

   13. add-sqr-sqrt 73.2%

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

7. Applied egg-rr 73.2%

   \[\leadsto \color{blue}{x \cdot 0.5 - y \cdot z} \]
8. Add Preprocessing

Alternative 7: 41.0% 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. Add Preprocessing

3. Taylor expanded in z around inf 73.2%

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

   1. associate-*r* 73.2%

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

   2. mul-1-neg 73.2%

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

5. Simplified 73.2%

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

6. Taylor expanded in x around inf 36.3%

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

7. Final simplification 36.3%

   \[\leadsto x \cdot 0.5 \]
8. Add Preprocessing

Alternative 8: 2.3% 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. Add Preprocessing

3. Taylor expanded in z around inf 73.2%

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

   1. associate-*r* 73.2%

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

   2. mul-1-neg 73.2%

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

5. Simplified 73.2%

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

6. Taylor expanded in y around inf 64.3%

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

   1. neg-mul-1 64.3%

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

   2. +-commutative 64.3%

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

   3. unsub-neg 64.3%

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

   4. associate-*r/ 64.3%

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

8. Simplified 64.3%

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

   1. div-inv 64.2%

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

   2. frac-2neg 64.2%

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

   3. metadata-eval 64.2%

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

   4. mul-1-neg 64.2%

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

   5. add-sqr-sqrt 30.8%

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

   6. sqrt-unprod 42.8%

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

   7. mul-1-neg 42.8%

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

   8. mul-1-neg 42.8%

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

   9. sqr-neg 42.8%

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

   10. sqrt-unprod 17.5%

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

   11. add-sqr-sqrt 38.8%

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

10. Applied egg-rr 38.8%

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

    1. associate-*r/ 38.8%

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

    2. *-commutative 38.8%

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

    3. *-rgt-identity 38.8%

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

    4. neg-mul-1 38.8%

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

    5. distribute-rgt-neg-in 38.8%

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

    6. times-frac 38.8%

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

    7. metadata-eval 38.8%

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

    8. associate-*r/ 38.8%

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

    9. distribute-neg-frac 38.8%

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

    10. /-rgt-identity 38.8%

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

    11. distribute-rgt-neg-in 38.8%

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

    12. *-commutative 38.8%

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

    13. distribute-rgt-neg-in 38.8%

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

    14. associate-*r/ 38.8%

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

    15. metadata-eval 38.8%

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

    16. distribute-neg-frac 38.8%

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

    17. metadata-eval 38.8%

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

12. Simplified 38.8%

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

13. Taylor expanded in y around 0 2.3%

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

14. Final simplification 2.3%

    \[\leadsto x \cdot -0.5 \]
15. Add Preprocessing

Developer Target 1: 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 2024146 
(FPCore (x y z)
  :name "System.Random.MWC.Distributions:gamma from mwc-random-0.13.3.2"
  :precision binary64

  :alt
  (! :herbie-platform default (- (+ y (* 1/2 x)) (* y (- z (log z)))))

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