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

Percentage Accurate: 99.9% → 99.9%

Time: 11.2s

Alternatives: 10

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: 99.9% accurate, 0.5× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z) {
	return fma(y, ((1.0 - z) + log(z)), (x * 0.5));
}

Julia

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

Wolfram

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

Derivation

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%

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

   2. fma-def 99.8%

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

3. Simplified 99.8%

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

4. Final simplification 99.8%

   \[\leadsto \mathsf{fma}\left(y, \left(1 - z\right) + \log z, x \cdot 0.5\right) \]

Alternative 2: 74.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot 0.5 \leq -5 \cdot 10^{-209} \lor \neg \left(x \cdot 0.5 \leq 10^{-276}\right):\\ \;\;\;\;\mathsf{fma}\left(y, -z, x \cdot 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(1 + \log z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= (* x 0.5) -5e-209) (not (<= (* x 0.5) 1e-276)))
   (fma y (- z) (* x 0.5))
   (* y (+ 1.0 (log z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (((x * 0.5) <= -5e-209) || !((x * 0.5) <= 1e-276)) {
		tmp = fma(y, -z, (x * 0.5));
	} else {
		tmp = y * (1.0 + log(z));
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if ((Float64(x * 0.5) <= -5e-209) || !(Float64(x * 0.5) <= 1e-276))
		tmp = fma(y, Float64(-z), Float64(x * 0.5));
	else
		tmp = Float64(y * Float64(1.0 + log(z)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[N[(x * 0.5), $MachinePrecision], -5e-209], N[Not[LessEqual[N[(x * 0.5), $MachinePrecision], 1e-276]], $MachinePrecision]], N[(y * (-z) + N[(x * 0.5), $MachinePrecision]), $MachinePrecision], N[(y * N[(1.0 + N[Log[z], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x 1/2) < -5.0000000000000005e-209 or 1e-276 < (*.f64 x 1/2)

   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%

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

      2. fma-def 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in z around inf 79.2%

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

      1. mul-1-neg 79.2%

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

   6. Simplified 79.2%

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

   if -5.0000000000000005e-209 < (*.f64 x 1/2) < 1e-276

   1. Initial program 99.5%

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

      1. sub-neg 99.5%

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

      2. associate-+l+ 99.5%

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

      3. distribute-rgt-in 99.4%

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

      4. *-lft-identity 99.4%

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

      5. associate-+r+ 99.4%

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

      6. neg-sub0 99.4%

         \[\leadsto \left(x \cdot 0.5 + y\right) + \left(\color{blue}{\left(0 - z\right)} + \log z\right) \cdot y \]

      7. associate-+l- 99.4%

         \[\leadsto \left(x \cdot 0.5 + y\right) + \color{blue}{\left(0 - \left(z - \log z\right)\right)} \cdot y \]

      8. neg-sub0 99.4%

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

      9. distribute-lft-neg-out 99.4%

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

      10. unsub-neg 99.4%

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

      11. fma-def 99.4%

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

      12. *-commutative 99.4%

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

   3. Simplified 99.4%

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

   4. Taylor expanded in y around -inf 98.7%

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

      1. mul-1-neg 98.7%

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

      2. sub-neg 98.7%

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

      3. associate-+l- 98.7%

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

      4. rem-cube-cbrt 97.5%

         \[\leadsto y \cdot \color{blue}{{\left(\sqrt[3]{\left(1 - z\right) + \log z}\right)}^{3}} \]

   6. Applied egg-rr 97.5%

      \[\leadsto y \cdot \color{blue}{{\left(\sqrt[3]{\left(1 - z\right) + \log z}\right)}^{3}} \]

   7. Taylor expanded in z around 0 72.0%

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

      1. *-commutative 72.0%

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

   9. Simplified 72.0%

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

4. Final simplification 78.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot 0.5 \leq -5 \cdot 10^{-209} \lor \neg \left(x \cdot 0.5 \leq 10^{-276}\right):\\ \;\;\;\;\mathsf{fma}\left(y, -z, x \cdot 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(1 + \log z\right)\\ \end{array} \]

Alternative 3: 74.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot 0.5 \leq -5 \cdot 10^{-209} \lor \neg \left(x \cdot 0.5 \leq 10^{-276}\right):\\ \;\;\;\;x \cdot 0.5 - y \cdot z\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(1 + \log z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= (* x 0.5) -5e-209) (not (<= (* x 0.5) 1e-276)))
   (- (* x 0.5) (* y z))
   (* y (+ 1.0 (log z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (((x * 0.5) <= -5e-209) || !((x * 0.5) <= 1e-276)) {
		tmp = (x * 0.5) - (y * z);
	} else {
		tmp = y * (1.0 + log(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 (((x * 0.5d0) <= (-5d-209)) .or. (.not. ((x * 0.5d0) <= 1d-276))) then
        tmp = (x * 0.5d0) - (y * z)
    else
        tmp = y * (1.0d0 + log(z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (((x * 0.5) <= -5e-209) || !((x * 0.5) <= 1e-276)) {
		tmp = (x * 0.5) - (y * z);
	} else {
		tmp = y * (1.0 + Math.log(z));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if ((x * 0.5) <= -5e-209) or not ((x * 0.5) <= 1e-276):
		tmp = (x * 0.5) - (y * z)
	else:
		tmp = y * (1.0 + math.log(z))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((Float64(x * 0.5) <= -5e-209) || !(Float64(x * 0.5) <= 1e-276))
		tmp = Float64(Float64(x * 0.5) - Float64(y * z));
	else
		tmp = Float64(y * Float64(1.0 + log(z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (((x * 0.5) <= -5e-209) || ~(((x * 0.5) <= 1e-276)))
		tmp = (x * 0.5) - (y * z);
	else
		tmp = y * (1.0 + log(z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[N[(x * 0.5), $MachinePrecision], -5e-209], N[Not[LessEqual[N[(x * 0.5), $MachinePrecision], 1e-276]], $MachinePrecision]], N[(N[(x * 0.5), $MachinePrecision] - N[(y * z), $MachinePrecision]), $MachinePrecision], N[(y * N[(1.0 + N[Log[z], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x 1/2) < -5.0000000000000005e-209 or 1e-276 < (*.f64 x 1/2)

   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 79.1%

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

      1. associate-*r* 79.1%

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

      2. neg-mul-1 79.1%

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

   4. Simplified 79.1%

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

   if -5.0000000000000005e-209 < (*.f64 x 1/2) < 1e-276

   1. Initial program 99.5%

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

      1. sub-neg 99.5%

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

      2. associate-+l+ 99.5%

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

      3. distribute-rgt-in 99.4%

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

      4. *-lft-identity 99.4%

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

      5. associate-+r+ 99.4%

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

      6. neg-sub0 99.4%

         \[\leadsto \left(x \cdot 0.5 + y\right) + \left(\color{blue}{\left(0 - z\right)} + \log z\right) \cdot y \]

      7. associate-+l- 99.4%

         \[\leadsto \left(x \cdot 0.5 + y\right) + \color{blue}{\left(0 - \left(z - \log z\right)\right)} \cdot y \]

      8. neg-sub0 99.4%

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

      9. distribute-lft-neg-out 99.4%

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

      10. unsub-neg 99.4%

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

      11. fma-def 99.4%

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

      12. *-commutative 99.4%

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

   3. Simplified 99.4%

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

   4. Taylor expanded in y around -inf 98.7%

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

      1. mul-1-neg 98.7%

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

      2. sub-neg 98.7%

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

      3. associate-+l- 98.7%

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

      4. rem-cube-cbrt 97.5%

         \[\leadsto y \cdot \color{blue}{{\left(\sqrt[3]{\left(1 - z\right) + \log z}\right)}^{3}} \]

   6. Applied egg-rr 97.5%

      \[\leadsto y \cdot \color{blue}{{\left(\sqrt[3]{\left(1 - z\right) + \log z}\right)}^{3}} \]

   7. Taylor expanded in z around 0 72.0%

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

      1. *-commutative 72.0%

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

   9. Simplified 72.0%

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

4. Final simplification 78.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot 0.5 \leq -5 \cdot 10^{-209} \lor \neg \left(x \cdot 0.5 \leq 10^{-276}\right):\\ \;\;\;\;x \cdot 0.5 - y \cdot z\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(1 + \log z\right)\\ \end{array} \]

Alternative 4: 83.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7.2 \cdot 10^{+27} \lor \neg \left(y \leq 1.1 \cdot 10^{+154}\right):\\ \;\;\;\;y \cdot \left(\left(1 - z\right) + \log z\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, -z, x \cdot 0.5\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -7.2e+27) (not (<= y 1.1e+154)))
   (* y (+ (- 1.0 z) (log z)))
   (fma y (- z) (* x 0.5))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -7.2e+27) || !(y <= 1.1e+154)) {
		tmp = y * ((1.0 - z) + log(z));
	} else {
		tmp = fma(y, -z, (x * 0.5));
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -7.2e+27) || !(y <= 1.1e+154))
		tmp = Float64(y * Float64(Float64(1.0 - z) + log(z)));
	else
		tmp = fma(y, Float64(-z), Float64(x * 0.5));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -7.2e+27], N[Not[LessEqual[y, 1.1e+154]], $MachinePrecision]], N[(y * N[(N[(1.0 - z), $MachinePrecision] + N[Log[z], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * (-z) + N[(x * 0.5), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -7.19999999999999966e27 or 1.1000000000000001e154 < y

   1. Initial program 99.7%

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

      1. sub-neg 99.7%

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

      2. associate-+l+ 99.7%

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

      3. distribute-rgt-in 99.6%

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

      4. *-lft-identity 99.6%

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

      5. associate-+r+ 99.5%

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

      6. neg-sub0 99.5%

         \[\leadsto \left(x \cdot 0.5 + y\right) + \left(\color{blue}{\left(0 - z\right)} + \log z\right) \cdot y \]

      7. associate-+l- 99.5%

         \[\leadsto \left(x \cdot 0.5 + y\right) + \color{blue}{\left(0 - \left(z - \log z\right)\right)} \cdot y \]

      8. neg-sub0 99.5%

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

      9. distribute-lft-neg-out 99.5%

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

      10. unsub-neg 99.5%

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

      11. fma-def 99.5%

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

      12. *-commutative 99.5%

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

   3. Simplified 99.5%

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

   4. Taylor expanded in y around -inf 89.1%

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

   5. Taylor expanded in z around 0 89.1%

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

      1. neg-mul-1 89.1%

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

      2. associate-+r+ 89.1%

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

      3. +-commutative 89.1%

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

      4. associate-+l+ 89.1%

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

      5. sub-neg 89.1%

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

   7. Simplified 89.1%

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

   if -7.19999999999999966e27 < y < 1.1000000000000001e154

   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%

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

      2. fma-def 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in z around inf 85.0%

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

      1. mul-1-neg 85.0%

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

   6. Simplified 85.0%

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

4. Final simplification 86.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.2 \cdot 10^{+27} \lor \neg \left(y \leq 1.1 \cdot 10^{+154}\right):\\ \;\;\;\;y \cdot \left(\left(1 - z\right) + \log z\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, -z, x \cdot 0.5\right)\\ \end{array} \]

Alternative 5: 98.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq 0.28:\\ \;\;\;\;x \cdot 0.5 + y \cdot \left(1 + \log z\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, -z, x \cdot 0.5\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z 0.28) (+ (* x 0.5) (* y (+ 1.0 (log z)))) (fma y (- z) (* x 0.5))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= 0.28) {
		tmp = (x * 0.5) + (y * (1.0 + log(z)));
	} else {
		tmp = fma(y, -z, (x * 0.5));
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= 0.28)
		tmp = Float64(Float64(x * 0.5) + Float64(y * Float64(1.0 + log(z))));
	else
		tmp = fma(y, Float64(-z), Float64(x * 0.5));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, 0.28], N[(N[(x * 0.5), $MachinePrecision] + N[(y * N[(1.0 + N[Log[z], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * (-z) + N[(x * 0.5), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 0.28000000000000003

   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 98.7%

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

   if 0.28000000000000003 < 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%

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

      2. fma-def 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in z around inf 99.3%

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

      1. mul-1-neg 99.3%

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

   6. Simplified 99.3%

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

4. Final simplification 99.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 0.28:\\ \;\;\;\;x \cdot 0.5 + y \cdot \left(1 + \log z\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, -z, x \cdot 0.5\right)\\ \end{array} \]

Alternative 6: 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]

Derivation

1. Initial program 99.8%

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

2. Final simplification 99.8%

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

Alternative 7: 58.7% accurate, 10.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq 6 \cdot 10^{+21} \lor \neg \left(z \leq 1.9 \cdot 10^{+89}\right) \land z \leq 3.2 \cdot 10^{+120}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z 6e+21) (and (not (<= z 1.9e+89)) (<= z 3.2e+120)))
   (* x 0.5)
   (* y (- z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= 6e+21) || (!(z <= 1.9e+89) && (z <= 3.2e+120))) {
		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 <= 6d+21) .or. (.not. (z <= 1.9d+89)) .and. (z <= 3.2d+120)) 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 <= 6e+21) || (!(z <= 1.9e+89) && (z <= 3.2e+120))) {
		tmp = x * 0.5;
	} else {
		tmp = y * -z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= 6e+21) or (not (z <= 1.9e+89) and (z <= 3.2e+120)):
		tmp = x * 0.5
	else:
		tmp = y * -z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= 6e+21) || (!(z <= 1.9e+89) && (z <= 3.2e+120)))
		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 <= 6e+21) || (~((z <= 1.9e+89)) && (z <= 3.2e+120)))
		tmp = x * 0.5;
	else
		tmp = y * -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, 6e+21], And[N[Not[LessEqual[z, 1.9e+89]], $MachinePrecision], LessEqual[z, 3.2e+120]]], N[(x * 0.5), $MachinePrecision], N[(y * (-z)), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 6e21 or 1.90000000000000012e89 < z < 3.19999999999999982e120

   1. Initial program 99.7%

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

   2. Taylor expanded in x around inf 54.7%

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

   if 6e21 < z < 1.90000000000000012e89 or 3.19999999999999982e120 < 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. sub-neg 100.0%

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

      2. associate-+l+ 100.0%

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

      3. distribute-rgt-in 100.0%

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

      4. *-lft-identity 100.0%

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

      5. associate-+r+ 100.0%

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

      6. neg-sub0 100.0%

         \[\leadsto \left(x \cdot 0.5 + y\right) + \left(\color{blue}{\left(0 - z\right)} + \log z\right) \cdot y \]

      7. associate-+l- 100.0%

         \[\leadsto \left(x \cdot 0.5 + y\right) + \color{blue}{\left(0 - \left(z - \log z\right)\right)} \cdot y \]

      8. neg-sub0 100.0%

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

      9. distribute-lft-neg-out 100.0%

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

      10. unsub-neg 100.0%

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

      11. fma-def 100.0%

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

      12. *-commutative 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around -inf 75.9%

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

   5. Taylor expanded in z around inf 75.9%

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

      1. neg-mul-1 75.9%

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

   7. Simplified 75.9%

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

4. Final simplification 63.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 6 \cdot 10^{+21} \lor \neg \left(z \leq 1.9 \cdot 10^{+89}\right) \land z \leq 3.2 \cdot 10^{+120}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \end{array} \]

Alternative 8: 74.7% 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 99.8%

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

2. Taylor expanded in z around inf 74.9%

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

   1. associate-*r* 74.9%

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

   2. neg-mul-1 74.9%

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

4. Simplified 74.9%

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

5. Final simplification 74.9%

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

Alternative 9: 40.5% 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 99.8%

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

2. Taylor expanded in x around inf 42.2%

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

3. Final simplification 42.2%

   \[\leadsto x \cdot 0.5 \]

Alternative 10: 1.9% accurate, 111.0× 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 y
end

MATLAB

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

Wolfram

code[x_, y_, z_] := y

Derivation

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. sub-neg 99.8%

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

   2. associate-+l+ 99.8%

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

   3. distribute-rgt-in 99.8%

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

   4. *-lft-identity 99.8%

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

   5. associate-+r+ 99.8%

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

   6. neg-sub0 99.8%

      \[\leadsto \left(x \cdot 0.5 + y\right) + \left(\color{blue}{\left(0 - z\right)} + \log z\right) \cdot y \]

   7. associate-+l- 99.8%

      \[\leadsto \left(x \cdot 0.5 + y\right) + \color{blue}{\left(0 - \left(z - \log z\right)\right)} \cdot y \]

   8. neg-sub0 99.8%

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

   9. distribute-lft-neg-out 99.8%

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

   10. unsub-neg 99.8%

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

   11. fma-def 99.8%

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

   12. *-commutative 99.8%

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

3. Simplified 99.8%

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

4. Taylor expanded in y around -inf 58.2%

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

5. Taylor expanded in z around inf 33.2%

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

6. Taylor expanded in z around 0 1.9%

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

7. Final simplification 1.9%

   \[\leadsto y \]

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 2023271 
(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)))))