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

Percentage Accurate: 99.9% → 99.9%

Time: 16.6s

Alternatives: 9

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, 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 99.9%

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

Alternative 2: 75.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(1 - z\right) + \log z\\ t_1 := x \cdot 0.5 - y \cdot z\\ \mathbf{if}\;t\_0 \leq -350:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_0 \leq -278.5:\\ \;\;\;\;y + y \cdot \log z\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ (- 1.0 z) (log z))) (t_1 (- (* x 0.5) (* y z))))
   (if (<= t_0 -350.0) t_1 (if (<= t_0 -278.5) (+ y (* y (log z))) t_1))))

C

double code(double x, double y, double z) {
	double t_0 = (1.0 - z) + log(z);
	double t_1 = (x * 0.5) - (y * z);
	double tmp;
	if (t_0 <= -350.0) {
		tmp = t_1;
	} else if (t_0 <= -278.5) {
		tmp = y + (y * log(z));
	} else {
		tmp = t_1;
	}
	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) :: t_1
    real(8) :: tmp
    t_0 = (1.0d0 - z) + log(z)
    t_1 = (x * 0.5d0) - (y * z)
    if (t_0 <= (-350.0d0)) then
        tmp = t_1
    else if (t_0 <= (-278.5d0)) then
        tmp = y + (y * log(z))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = (1.0 - z) + Math.log(z);
	double t_1 = (x * 0.5) - (y * z);
	double tmp;
	if (t_0 <= -350.0) {
		tmp = t_1;
	} else if (t_0 <= -278.5) {
		tmp = y + (y * Math.log(z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (1.0 - z) + math.log(z)
	t_1 = (x * 0.5) - (y * z)
	tmp = 0
	if t_0 <= -350.0:
		tmp = t_1
	elif t_0 <= -278.5:
		tmp = y + (y * math.log(z))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(1.0 - z) + log(z))
	t_1 = Float64(Float64(x * 0.5) - Float64(y * z))
	tmp = 0.0
	if (t_0 <= -350.0)
		tmp = t_1;
	elseif (t_0 <= -278.5)
		tmp = Float64(y + Float64(y * log(z)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (1.0 - z) + log(z);
	t_1 = (x * 0.5) - (y * z);
	tmp = 0.0;
	if (t_0 <= -350.0)
		tmp = t_1;
	elseif (t_0 <= -278.5)
		tmp = y + (y * log(z));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(1.0 - z), $MachinePrecision] + N[Log[z], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(x * 0.5), $MachinePrecision] - N[(y * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$0, -350.0], t$95$1, If[LessEqual[t$95$0, -278.5], N[(y + N[(y * N[Log[z], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 (-.f64 #s(literal 1 binary64) z) (log.f64 z)) < -350 or -278.5 < (+.f64 (-.f64 #s(literal 1 binary64) z) (log.f64 z))

   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

      \[\leadsto x \cdot \frac{1}{2} + \color{blue}{-1 \cdot \left(y \cdot z\right)} \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto x \cdot \frac{1}{2} + \color{blue}{\left(\mathsf{neg}\left(y \cdot z\right)\right)} \]

      2. neg-sub0 N/A

         \[\leadsto x \cdot \frac{1}{2} + \color{blue}{\left(0 - y \cdot z\right)} \]

      3. --lowering--.f64 N/A

         \[\leadsto x \cdot \frac{1}{2} + \color{blue}{\left(0 - y \cdot z\right)} \]

      4. *-lowering-*.f64 80.2

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

   5. Simplified 80.2%

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

   if -350 < (+.f64 (-.f64 #s(literal 1 binary64) z) (log.f64 z)) < -278.5

   1. Initial program 99.5%

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

   3. Taylor expanded in x around 0

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

      1. sub-neg N/A

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

      2. mul-1-neg N/A

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

      3. associate-+r+ N/A

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

      4. +-commutative N/A

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

      5. distribute-lft-in N/A

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

      6. *-rgt-identity N/A

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

      7. accelerator-lowering-fma.f64 N/A

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

      8. mul-1-neg N/A

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

      9. sub-neg N/A

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

      10. --lowering--.f64 N/A

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

      11. log-lowering-log.f64 81.5

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

   5. Simplified 81.5%

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

      1. +-lowering-+.f64 N/A

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

      2. *-lowering-*.f64 N/A

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

      3. --lowering--.f64 N/A

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

      4. log-lowering-log.f64 81.8

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

   7. Applied egg-rr 81.8%

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

   8. Taylor expanded in z around 0

      \[\leadsto y \cdot \color{blue}{\log z} + y \]
   9. Step-by-step derivation

      1. log-lowering-log.f64 81.8

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

   10. Simplified 81.8%

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

4. Final simplification 80.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(1 - z\right) + \log z \leq -350:\\ \;\;\;\;x \cdot 0.5 - y \cdot z\\ \mathbf{elif}\;\left(1 - z\right) + \log z \leq -278.5:\\ \;\;\;\;y + y \cdot \log z\\ \mathbf{else}:\\ \;\;\;\;x \cdot 0.5 - y \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 75.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(1 - z\right) + \log z\\ t_1 := x \cdot 0.5 - y \cdot z\\ \mathbf{if}\;t\_0 \leq -350:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_0 \leq -278.5:\\ \;\;\;\;\mathsf{fma}\left(y, \log z, y\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ (- 1.0 z) (log z))) (t_1 (- (* x 0.5) (* y z))))
   (if (<= t_0 -350.0) t_1 (if (<= t_0 -278.5) (fma y (log z) y) t_1))))

C

double code(double x, double y, double z) {
	double t_0 = (1.0 - z) + log(z);
	double t_1 = (x * 0.5) - (y * z);
	double tmp;
	if (t_0 <= -350.0) {
		tmp = t_1;
	} else if (t_0 <= -278.5) {
		tmp = fma(y, log(z), y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = Float64(Float64(1.0 - z) + log(z))
	t_1 = Float64(Float64(x * 0.5) - Float64(y * z))
	tmp = 0.0
	if (t_0 <= -350.0)
		tmp = t_1;
	elseif (t_0 <= -278.5)
		tmp = fma(y, log(z), y);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(1.0 - z), $MachinePrecision] + N[Log[z], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(x * 0.5), $MachinePrecision] - N[(y * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$0, -350.0], t$95$1, If[LessEqual[t$95$0, -278.5], N[(y * N[Log[z], $MachinePrecision] + y), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 (-.f64 #s(literal 1 binary64) z) (log.f64 z)) < -350 or -278.5 < (+.f64 (-.f64 #s(literal 1 binary64) z) (log.f64 z))

   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

      \[\leadsto x \cdot \frac{1}{2} + \color{blue}{-1 \cdot \left(y \cdot z\right)} \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto x \cdot \frac{1}{2} + \color{blue}{\left(\mathsf{neg}\left(y \cdot z\right)\right)} \]

      2. neg-sub0 N/A

         \[\leadsto x \cdot \frac{1}{2} + \color{blue}{\left(0 - y \cdot z\right)} \]

      3. --lowering--.f64 N/A

         \[\leadsto x \cdot \frac{1}{2} + \color{blue}{\left(0 - y \cdot z\right)} \]

      4. *-lowering-*.f64 80.2

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

   5. Simplified 80.2%

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

   if -350 < (+.f64 (-.f64 #s(literal 1 binary64) z) (log.f64 z)) < -278.5

   1. Initial program 99.5%

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

   3. Taylor expanded in x around 0

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

      1. sub-neg N/A

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

      2. mul-1-neg N/A

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

      3. associate-+r+ N/A

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

      4. +-commutative N/A

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

      5. distribute-lft-in N/A

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

      6. *-rgt-identity N/A

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

      7. accelerator-lowering-fma.f64 N/A

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

      8. mul-1-neg N/A

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

      9. sub-neg N/A

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

      10. --lowering--.f64 N/A

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

      11. log-lowering-log.f64 81.5

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

   5. Simplified 81.5%

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

   6. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. accelerator-lowering-fma.f64 N/A

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

      3. log-lowering-log.f64 81.5

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

   8. Simplified 81.5%

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

4. Final simplification 80.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(1 - z\right) + \log z \leq -350:\\ \;\;\;\;x \cdot 0.5 - y \cdot z\\ \mathbf{elif}\;\left(1 - z\right) + \log z \leq -278.5:\\ \;\;\;\;\mathsf{fma}\left(y, \log z, y\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 0.5 - y \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 60.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y \cdot \left(\left(1 - z\right) + \log z\right)\\ t_1 := 0 - y \cdot z\\ \mathbf{if}\;t\_0 \leq -2 \cdot 10^{+191}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_0 \leq 2 \cdot 10^{+47}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* y (+ (- 1.0 z) (log z)))) (t_1 (- 0.0 (* y z))))
   (if (<= t_0 -2e+191) t_1 (if (<= t_0 2e+47) (* x 0.5) t_1))))

C

double code(double x, double y, double z) {
	double t_0 = y * ((1.0 - z) + log(z));
	double t_1 = 0.0 - (y * z);
	double tmp;
	if (t_0 <= -2e+191) {
		tmp = t_1;
	} else if (t_0 <= 2e+47) {
		tmp = x * 0.5;
	} else {
		tmp = t_1;
	}
	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) :: t_1
    real(8) :: tmp
    t_0 = y * ((1.0d0 - z) + log(z))
    t_1 = 0.0d0 - (y * z)
    if (t_0 <= (-2d+191)) then
        tmp = t_1
    else if (t_0 <= 2d+47) then
        tmp = x * 0.5d0
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = y * ((1.0 - z) + Math.log(z));
	double t_1 = 0.0 - (y * z);
	double tmp;
	if (t_0 <= -2e+191) {
		tmp = t_1;
	} else if (t_0 <= 2e+47) {
		tmp = x * 0.5;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = y * ((1.0 - z) + math.log(z))
	t_1 = 0.0 - (y * z)
	tmp = 0
	if t_0 <= -2e+191:
		tmp = t_1
	elif t_0 <= 2e+47:
		tmp = x * 0.5
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(y * Float64(Float64(1.0 - z) + log(z)))
	t_1 = Float64(0.0 - Float64(y * z))
	tmp = 0.0
	if (t_0 <= -2e+191)
		tmp = t_1;
	elseif (t_0 <= 2e+47)
		tmp = Float64(x * 0.5);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = y * ((1.0 - z) + log(z));
	t_1 = 0.0 - (y * z);
	tmp = 0.0;
	if (t_0 <= -2e+191)
		tmp = t_1;
	elseif (t_0 <= 2e+47)
		tmp = x * 0.5;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(y * N[(N[(1.0 - z), $MachinePrecision] + N[Log[z], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(0.0 - N[(y * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$0, -2e+191], t$95$1, If[LessEqual[t$95$0, 2e+47], N[(x * 0.5), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 y (+.f64 (-.f64 #s(literal 1 binary64) z) (log.f64 z))) < -2.00000000000000015e191 or 2.0000000000000001e47 < (*.f64 y (+.f64 (-.f64 #s(literal 1 binary64) z) (log.f64 z)))

   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

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

      1. mul-1-neg N/A

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

      2. neg-sub0 N/A

         \[\leadsto \color{blue}{0 - y \cdot z} \]

      3. --lowering--.f64 N/A

         \[\leadsto \color{blue}{0 - y \cdot z} \]

      4. *-lowering-*.f64 69.1

         \[\leadsto 0 - \color{blue}{y \cdot z} \]

   5. Simplified 69.1%

      \[\leadsto \color{blue}{0 - y \cdot z} \]

   if -2.00000000000000015e191 < (*.f64 y (+.f64 (-.f64 #s(literal 1 binary64) z) (log.f64 z))) < 2.0000000000000001e47

   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 x around inf

      \[\leadsto \color{blue}{\frac{1}{2} \cdot x} \]
   4. Step-by-step derivation

      1. +-rgt-identity N/A

         \[\leadsto \color{blue}{\frac{1}{2} \cdot x + 0} \]

      2. accelerator-lowering-fma.f64 64.0

         \[\leadsto \color{blue}{\mathsf{fma}\left(0.5, x, 0\right)} \]

   5. Simplified 64.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(0.5, x, 0\right)} \]
   6. Step-by-step derivation

      1. +-rgt-identity N/A

         \[\leadsto \color{blue}{\frac{1}{2} \cdot x} \]

      2. *-commutative N/A

         \[\leadsto \color{blue}{x \cdot \frac{1}{2}} \]

      3. *-lowering-*.f64 64.0

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

   7. Applied egg-rr 64.0%

      \[\leadsto \color{blue}{x \cdot 0.5} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 5: 98.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\left(1 - z\right) + \log z \leq -200000000000:\\ \;\;\;\;\mathsf{fma}\left(1 - z, y, x \cdot 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(x, 0.5, \mathsf{fma}\left(y, \log z, y\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= (+ (- 1.0 z) (log z)) -200000000000.0)
   (fma (- 1.0 z) y (* x 0.5))
   (fma x 0.5 (fma y (log z) y))))

C

double code(double x, double y, double z) {
	double tmp;
	if (((1.0 - z) + log(z)) <= -200000000000.0) {
		tmp = fma((1.0 - z), y, (x * 0.5));
	} else {
		tmp = fma(x, 0.5, fma(y, log(z), y));
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (Float64(Float64(1.0 - z) + log(z)) <= -200000000000.0)
		tmp = fma(Float64(1.0 - z), y, Float64(x * 0.5));
	else
		tmp = fma(x, 0.5, fma(y, log(z), y));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[N[(N[(1.0 - z), $MachinePrecision] + N[Log[z], $MachinePrecision]), $MachinePrecision], -200000000000.0], N[(N[(1.0 - z), $MachinePrecision] * y + N[(x * 0.5), $MachinePrecision]), $MachinePrecision], N[(x * 0.5 + N[(y * N[Log[z], $MachinePrecision] + y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 (-.f64 #s(literal 1 binary64) z) (log.f64 z)) < -2e11

   1. Initial program 100.0%

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

      1. +-commutative N/A

         \[\leadsto \color{blue}{y \cdot \left(\left(1 - z\right) + \log z\right) + x \cdot \frac{1}{2}} \]

      2. distribute-rgt-in N/A

         \[\leadsto \color{blue}{\left(\left(1 - z\right) \cdot y + \log z \cdot y\right)} + x \cdot \frac{1}{2} \]

      3. associate-+l+ N/A

         \[\leadsto \color{blue}{\left(1 - z\right) \cdot y + \left(\log z \cdot y + x \cdot \frac{1}{2}\right)} \]

      4. accelerator-lowering-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(1 - z, y, \log z \cdot y + x \cdot \frac{1}{2}\right)} \]

      5. --lowering--.f64 N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{1 - z}, y, \log z \cdot y + x \cdot \frac{1}{2}\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(1 - z, y, \color{blue}{y \cdot \log z} + x \cdot \frac{1}{2}\right) \]

      7. accelerator-lowering-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(1 - z, y, \color{blue}{\mathsf{fma}\left(y, \log z, x \cdot \frac{1}{2}\right)}\right) \]

      8. log-lowering-log.f64 N/A

         \[\leadsto \mathsf{fma}\left(1 - z, y, \mathsf{fma}\left(y, \color{blue}{\log z}, x \cdot \frac{1}{2}\right)\right) \]

      9. *-lowering-*.f64 100.0

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

   4. Applied egg-rr 100.0%

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

   5. Taylor expanded in y around 0

      \[\leadsto \mathsf{fma}\left(1 - z, y, \color{blue}{\frac{1}{2} \cdot x}\right) \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 99.7

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

   7. Simplified 99.7%

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

   if -2e11 < (+.f64 (-.f64 #s(literal 1 binary64) z) (log.f64 z))

   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

      \[\leadsto x \cdot \frac{1}{2} + \color{blue}{y \cdot \left(1 + \log z\right)} \]
   4. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto x \cdot \frac{1}{2} + y \cdot \color{blue}{\left(\log z + 1\right)} \]

      2. distribute-lft-in N/A

         \[\leadsto x \cdot \frac{1}{2} + \color{blue}{\left(y \cdot \log z + y \cdot 1\right)} \]

      3. *-rgt-identity N/A

         \[\leadsto x \cdot \frac{1}{2} + \left(y \cdot \log z + \color{blue}{y}\right) \]

      4. accelerator-lowering-fma.f64 N/A

         \[\leadsto x \cdot \frac{1}{2} + \color{blue}{\mathsf{fma}\left(y, \log z, y\right)} \]

      5. log-lowering-log.f64 99.1

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

   5. Simplified 99.1%

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

      1. accelerator-lowering-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(x, \frac{1}{2}, y \cdot \log z + y\right)} \]

      2. accelerator-lowering-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(x, \frac{1}{2}, \color{blue}{\mathsf{fma}\left(y, \log z, y\right)}\right) \]

      3. log-lowering-log.f64 99.1

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

   7. Applied egg-rr 99.1%

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

4. Final simplification 99.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(1 - z\right) + \log z \leq -200000000000:\\ \;\;\;\;\mathsf{fma}\left(1 - z, y, x \cdot 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(x, 0.5, \mathsf{fma}\left(y, \log z, y\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 85.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot 0.5 - y \cdot z\\ \mathbf{if}\;x \cdot 0.5 \leq -2 \cdot 10^{-13}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \cdot 0.5 \leq 10^{-39}:\\ \;\;\;\;\mathsf{fma}\left(y, \log z - z, y\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- (* x 0.5) (* y z))))
   (if (<= (* x 0.5) -2e-13)
     t_0
     (if (<= (* x 0.5) 1e-39) (fma y (- (log z) z) y) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = (x * 0.5) - (y * z);
	double tmp;
	if ((x * 0.5) <= -2e-13) {
		tmp = t_0;
	} else if ((x * 0.5) <= 1e-39) {
		tmp = fma(y, (log(z) - z), y);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = Float64(Float64(x * 0.5) - Float64(y * z))
	tmp = 0.0
	if (Float64(x * 0.5) <= -2e-13)
		tmp = t_0;
	elseif (Float64(x * 0.5) <= 1e-39)
		tmp = fma(y, Float64(log(z) - z), y);
	else
		tmp = t_0;
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(x * 0.5), $MachinePrecision] - N[(y * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x * 0.5), $MachinePrecision], -2e-13], t$95$0, If[LessEqual[N[(x * 0.5), $MachinePrecision], 1e-39], N[(y * N[(N[Log[z], $MachinePrecision] - z), $MachinePrecision] + y), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x #s(literal 1/2 binary64)) < -2.0000000000000001e-13 or 9.99999999999999929e-40 < (*.f64 x #s(literal 1/2 binary64))

   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

      \[\leadsto x \cdot \frac{1}{2} + \color{blue}{-1 \cdot \left(y \cdot z\right)} \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto x \cdot \frac{1}{2} + \color{blue}{\left(\mathsf{neg}\left(y \cdot z\right)\right)} \]

      2. neg-sub0 N/A

         \[\leadsto x \cdot \frac{1}{2} + \color{blue}{\left(0 - y \cdot z\right)} \]

      3. --lowering--.f64 N/A

         \[\leadsto x \cdot \frac{1}{2} + \color{blue}{\left(0 - y \cdot z\right)} \]

      4. *-lowering-*.f64 89.1

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

   5. Simplified 89.1%

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

   if -2.0000000000000001e-13 < (*.f64 x #s(literal 1/2 binary64)) < 9.99999999999999929e-40

   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 x around 0

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

      1. sub-neg N/A

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

      2. mul-1-neg N/A

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

      3. associate-+r+ N/A

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

      4. +-commutative N/A

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

      5. distribute-lft-in N/A

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

      6. *-rgt-identity N/A

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

      7. accelerator-lowering-fma.f64 N/A

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

      8. mul-1-neg N/A

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

      9. sub-neg N/A

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

      10. --lowering--.f64 N/A

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

      11. log-lowering-log.f64 87.6

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

   5. Simplified 87.6%

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

4. Final simplification 88.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot 0.5 \leq -2 \cdot 10^{-13}:\\ \;\;\;\;x \cdot 0.5 - y \cdot z\\ \mathbf{elif}\;x \cdot 0.5 \leq 10^{-39}:\\ \;\;\;\;\mathsf{fma}\left(y, \log z - z, y\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 0.5 - y \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 74.1% accurate, 8.0× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

code[x_, y_, z_] := N[(N[(1.0 - z), $MachinePrecision] * y + N[(x * 0.5), $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. Step-by-step derivation

   1. +-commutative N/A

      \[\leadsto \color{blue}{y \cdot \left(\left(1 - z\right) + \log z\right) + x \cdot \frac{1}{2}} \]

   2. distribute-rgt-in N/A

      \[\leadsto \color{blue}{\left(\left(1 - z\right) \cdot y + \log z \cdot y\right)} + x \cdot \frac{1}{2} \]

   3. associate-+l+ N/A

      \[\leadsto \color{blue}{\left(1 - z\right) \cdot y + \left(\log z \cdot y + x \cdot \frac{1}{2}\right)} \]

   4. accelerator-lowering-fma.f64 N/A

      \[\leadsto \color{blue}{\mathsf{fma}\left(1 - z, y, \log z \cdot y + x \cdot \frac{1}{2}\right)} \]

   5. --lowering--.f64 N/A

      \[\leadsto \mathsf{fma}\left(\color{blue}{1 - z}, y, \log z \cdot y + x \cdot \frac{1}{2}\right) \]

   6. *-commutative N/A

      \[\leadsto \mathsf{fma}\left(1 - z, y, \color{blue}{y \cdot \log z} + x \cdot \frac{1}{2}\right) \]

   7. accelerator-lowering-fma.f64 N/A

      \[\leadsto \mathsf{fma}\left(1 - z, y, \color{blue}{\mathsf{fma}\left(y, \log z, x \cdot \frac{1}{2}\right)}\right) \]

   8. log-lowering-log.f64 N/A

      \[\leadsto \mathsf{fma}\left(1 - z, y, \mathsf{fma}\left(y, \color{blue}{\log z}, x \cdot \frac{1}{2}\right)\right) \]

   9. *-lowering-*.f64 99.9

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

4. Applied egg-rr 99.9%

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

5. Taylor expanded in y around 0

   \[\leadsto \mathsf{fma}\left(1 - z, y, \color{blue}{\frac{1}{2} \cdot x}\right) \]
6. Step-by-step derivation

   1. *-lowering-*.f64 76.2

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

7. Simplified 76.2%

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

8. Final simplification 76.2%

   \[\leadsto \mathsf{fma}\left(1 - z, y, x \cdot 0.5\right) \]
9. Add Preprocessing

Alternative 8: 75.2% accurate, 8.6× 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

   \[\leadsto x \cdot \frac{1}{2} + \color{blue}{-1 \cdot \left(y \cdot z\right)} \]
4. Step-by-step derivation

   1. mul-1-neg N/A

      \[\leadsto x \cdot \frac{1}{2} + \color{blue}{\left(\mathsf{neg}\left(y \cdot z\right)\right)} \]

   2. neg-sub0 N/A

      \[\leadsto x \cdot \frac{1}{2} + \color{blue}{\left(0 - y \cdot z\right)} \]

   3. --lowering--.f64 N/A

      \[\leadsto x \cdot \frac{1}{2} + \color{blue}{\left(0 - y \cdot z\right)} \]

   4. *-lowering-*.f64 77.1

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

5. Simplified 77.1%

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

6. Final simplification 77.1%

   \[\leadsto x \cdot 0.5 - y \cdot z \]
7. Add Preprocessing

Alternative 9: 40.5% accurate, 20.0× 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 x around inf

   \[\leadsto \color{blue}{\frac{1}{2} \cdot x} \]
4. Step-by-step derivation

   1. +-rgt-identity N/A

      \[\leadsto \color{blue}{\frac{1}{2} \cdot x + 0} \]

   2. accelerator-lowering-fma.f64 41.8

      \[\leadsto \color{blue}{\mathsf{fma}\left(0.5, x, 0\right)} \]

5. Simplified 41.8%

   \[\leadsto \color{blue}{\mathsf{fma}\left(0.5, x, 0\right)} \]
6. Step-by-step derivation

   1. +-rgt-identity N/A

      \[\leadsto \color{blue}{\frac{1}{2} \cdot x} \]

   2. *-commutative N/A

      \[\leadsto \color{blue}{x \cdot \frac{1}{2}} \]

   3. *-lowering-*.f64 41.8

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

7. Applied egg-rr 41.8%

   \[\leadsto \color{blue}{x \cdot 0.5} \]
8. 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 2024196 
(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)))))