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

Percentage Accurate: 99.9% → 99.9%

Time: 10.5s

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 99.9%

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

3. Simplified 99.9%

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

5. Final simplification 99.9%

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

Alternative 2: 72.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y \cdot \left(\log z + 1\right)\\ t_1 := \mathsf{fma}\left(y, -z, x \cdot 0.5\right)\\ \mathbf{if}\;x \cdot 0.5 \leq -5 \cdot 10^{-306}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot 0.5 \leq 5 \cdot 10^{-239}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \cdot 0.5 \leq 2 \cdot 10^{-163}:\\ \;\;\;\;x \cdot 0.5 - y \cdot z\\ \mathbf{elif}\;x \cdot 0.5 \leq 2 \cdot 10^{-87}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* y (+ (log z) 1.0))) (t_1 (fma y (- z) (* x 0.5))))
   (if (<= (* x 0.5) -5e-306)
     t_1
     (if (<= (* x 0.5) 5e-239)
       t_0
       (if (<= (* x 0.5) 2e-163)
         (- (* x 0.5) (* y z))
         (if (<= (* x 0.5) 2e-87) t_0 t_1))))))

C

double code(double x, double y, double z) {
	double t_0 = y * (log(z) + 1.0);
	double t_1 = fma(y, -z, (x * 0.5));
	double tmp;
	if ((x * 0.5) <= -5e-306) {
		tmp = t_1;
	} else if ((x * 0.5) <= 5e-239) {
		tmp = t_0;
	} else if ((x * 0.5) <= 2e-163) {
		tmp = (x * 0.5) - (y * z);
	} else if ((x * 0.5) <= 2e-87) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = Float64(y * Float64(log(z) + 1.0))
	t_1 = fma(y, Float64(-z), Float64(x * 0.5))
	tmp = 0.0
	if (Float64(x * 0.5) <= -5e-306)
		tmp = t_1;
	elseif (Float64(x * 0.5) <= 5e-239)
		tmp = t_0;
	elseif (Float64(x * 0.5) <= 2e-163)
		tmp = Float64(Float64(x * 0.5) - Float64(y * z));
	elseif (Float64(x * 0.5) <= 2e-87)
		tmp = t_0;
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(y * N[(N[Log[z], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(y * (-z) + N[(x * 0.5), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x * 0.5), $MachinePrecision], -5e-306], t$95$1, If[LessEqual[N[(x * 0.5), $MachinePrecision], 5e-239], t$95$0, If[LessEqual[N[(x * 0.5), $MachinePrecision], 2e-163], N[(N[(x * 0.5), $MachinePrecision] - N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * 0.5), $MachinePrecision], 2e-87], t$95$0, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x 1/2) < -4.99999999999999998e-306 or 2.00000000000000004e-87 < (*.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. Add Preprocessing

   5. Taylor expanded in z around inf 82.1%

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

      1. mul-1-neg 82.1%

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

   7. Simplified 82.1%

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

   if -4.99999999999999998e-306 < (*.f64 x 1/2) < 5e-239 or 1.99999999999999985e-163 < (*.f64 x 1/2) < 2.00000000000000004e-87

   1. Initial program 99.4%

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

   3. Taylor expanded in z around 0 78.9%

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

   4. Taylor expanded in x around 0 71.7%

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

   if 5e-239 < (*.f64 x 1/2) < 1.99999999999999985e-163

   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 80.9%

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

      1. mul-1-neg 80.9%

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

      2. distribute-rgt-neg-in 80.9%

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

   5. Simplified 80.9%

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

      1. distribute-rgt-neg-out 80.9%

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

      2. unsub-neg 80.9%

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

      3. add-sqr-sqrt 80.7%

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

      4. sqrt-unprod 65.7%

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

      5. sqr-neg 65.7%

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

      6. sqrt-unprod 0.0%

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

      7. add-sqr-sqrt 25.8%

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

      8. *-commutative 25.8%

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

      9. add-sqr-sqrt 0.0%

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

      10. sqrt-unprod 65.7%

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

      11. sqr-neg 65.7%

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

      12. sqrt-unprod 80.7%

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

      13. add-sqr-sqrt 80.9%

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

   7. Applied egg-rr 80.9%

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

4. Final simplification 80.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot 0.5 \leq -5 \cdot 10^{-306}:\\ \;\;\;\;\mathsf{fma}\left(y, -z, x \cdot 0.5\right)\\ \mathbf{elif}\;x \cdot 0.5 \leq 5 \cdot 10^{-239}:\\ \;\;\;\;y \cdot \left(\log z + 1\right)\\ \mathbf{elif}\;x \cdot 0.5 \leq 2 \cdot 10^{-163}:\\ \;\;\;\;x \cdot 0.5 - y \cdot z\\ \mathbf{elif}\;x \cdot 0.5 \leq 2 \cdot 10^{-87}:\\ \;\;\;\;y \cdot \left(\log z + 1\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, -z, x \cdot 0.5\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 72.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot 0.5 \leq -5 \cdot 10^{-306} \lor \neg \left(x \cdot 0.5 \leq 5 \cdot 10^{-239} \lor \neg \left(x \cdot 0.5 \leq 2 \cdot 10^{-163}\right) \land x \cdot 0.5 \leq 2 \cdot 10^{-87}\right):\\ \;\;\;\;x \cdot 0.5 - y \cdot z\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(\log z + 1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= (* x 0.5) -5e-306)
         (not
          (or (<= (* x 0.5) 5e-239)
              (and (not (<= (* x 0.5) 2e-163)) (<= (* x 0.5) 2e-87)))))
   (- (* x 0.5) (* y z))
   (* y (+ (log z) 1.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if (((x * 0.5) <= -5e-306) || !(((x * 0.5) <= 5e-239) || (!((x * 0.5) <= 2e-163) && ((x * 0.5) <= 2e-87)))) {
		tmp = (x * 0.5) - (y * z);
	} else {
		tmp = y * (log(z) + 1.0);
	}
	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-306)) .or. (.not. ((x * 0.5d0) <= 5d-239) .or. (.not. ((x * 0.5d0) <= 2d-163)) .and. ((x * 0.5d0) <= 2d-87))) then
        tmp = (x * 0.5d0) - (y * z)
    else
        tmp = y * (log(z) + 1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (((x * 0.5) <= -5e-306) || !(((x * 0.5) <= 5e-239) || (!((x * 0.5) <= 2e-163) && ((x * 0.5) <= 2e-87)))) {
		tmp = (x * 0.5) - (y * z);
	} else {
		tmp = y * (Math.log(z) + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if ((x * 0.5) <= -5e-306) or not (((x * 0.5) <= 5e-239) or (not ((x * 0.5) <= 2e-163) and ((x * 0.5) <= 2e-87))):
		tmp = (x * 0.5) - (y * z)
	else:
		tmp = y * (math.log(z) + 1.0)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((Float64(x * 0.5) <= -5e-306) || !((Float64(x * 0.5) <= 5e-239) || (!(Float64(x * 0.5) <= 2e-163) && (Float64(x * 0.5) <= 2e-87))))
		tmp = Float64(Float64(x * 0.5) - Float64(y * z));
	else
		tmp = Float64(y * Float64(log(z) + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (((x * 0.5) <= -5e-306) || ~((((x * 0.5) <= 5e-239) || (~(((x * 0.5) <= 2e-163)) && ((x * 0.5) <= 2e-87)))))
		tmp = (x * 0.5) - (y * z);
	else
		tmp = y * (log(z) + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[N[(x * 0.5), $MachinePrecision], -5e-306], N[Not[Or[LessEqual[N[(x * 0.5), $MachinePrecision], 5e-239], And[N[Not[LessEqual[N[(x * 0.5), $MachinePrecision], 2e-163]], $MachinePrecision], LessEqual[N[(x * 0.5), $MachinePrecision], 2e-87]]]], $MachinePrecision]], N[(N[(x * 0.5), $MachinePrecision] - N[(y * z), $MachinePrecision]), $MachinePrecision], N[(y * N[(N[Log[z], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x 1/2) < -4.99999999999999998e-306 or 5e-239 < (*.f64 x 1/2) < 1.99999999999999985e-163 or 2.00000000000000004e-87 < (*.f64 x 1/2)

   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 82.0%

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

      1. mul-1-neg 82.0%

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

      2. distribute-rgt-neg-in 82.0%

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

   5. Simplified 82.0%

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

      1. distribute-rgt-neg-out 82.0%

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

      2. unsub-neg 82.0%

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

      3. add-sqr-sqrt 81.8%

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

      4. sqrt-unprod 66.7%

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

      5. sqr-neg 66.7%

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

      6. sqrt-unprod 0.0%

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

      7. add-sqr-sqrt 50.3%

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

      8. *-commutative 50.3%

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

      9. add-sqr-sqrt 0.0%

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

      10. sqrt-unprod 66.7%

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

      11. sqr-neg 66.7%

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

      12. sqrt-unprod 81.8%

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

      13. add-sqr-sqrt 82.0%

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

   7. Applied egg-rr 82.0%

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

   if -4.99999999999999998e-306 < (*.f64 x 1/2) < 5e-239 or 1.99999999999999985e-163 < (*.f64 x 1/2) < 2.00000000000000004e-87

   1. Initial program 99.4%

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

   3. Taylor expanded in z around 0 78.9%

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

   4. Taylor expanded in x around 0 71.7%

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

4. Final simplification 80.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot 0.5 \leq -5 \cdot 10^{-306} \lor \neg \left(x \cdot 0.5 \leq 5 \cdot 10^{-239} \lor \neg \left(x \cdot 0.5 \leq 2 \cdot 10^{-163}\right) \land x \cdot 0.5 \leq 2 \cdot 10^{-87}\right):\\ \;\;\;\;x \cdot 0.5 - y \cdot z\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(\log z + 1\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 85.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot 0.5 \leq -5 \cdot 10^{-41}:\\ \;\;\;\;x \cdot 0.5 - y \cdot z\\ \mathbf{elif}\;x \cdot 0.5 \leq 2 \cdot 10^{-87}:\\ \;\;\;\;y - y \cdot \left(z - \log z\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, -z, x \cdot 0.5\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= (* x 0.5) -5e-41)
   (- (* x 0.5) (* y z))
   (if (<= (* x 0.5) 2e-87)
     (- y (* y (- z (log z))))
     (fma y (- z) (* x 0.5)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x * 0.5) <= -5e-41) {
		tmp = (x * 0.5) - (y * z);
	} else if ((x * 0.5) <= 2e-87) {
		tmp = y - (y * (z - log(z)));
	} else {
		tmp = fma(y, -z, (x * 0.5));
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (Float64(x * 0.5) <= -5e-41)
		tmp = Float64(Float64(x * 0.5) - Float64(y * z));
	elseif (Float64(x * 0.5) <= 2e-87)
		tmp = Float64(y - Float64(y * Float64(z - log(z))));
	else
		tmp = fma(y, Float64(-z), Float64(x * 0.5));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[N[(x * 0.5), $MachinePrecision], -5e-41], N[(N[(x * 0.5), $MachinePrecision] - N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * 0.5), $MachinePrecision], 2e-87], N[(y - N[(y * N[(z - N[Log[z], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * (-z) + N[(x * 0.5), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x 1/2) < -4.9999999999999996e-41

   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 87.2%

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

      1. mul-1-neg 87.2%

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

      2. distribute-rgt-neg-in 87.2%

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

   5. Simplified 87.2%

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

      1. distribute-rgt-neg-out 87.2%

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

      2. unsub-neg 87.2%

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

      3. add-sqr-sqrt 87.1%

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

      4. sqrt-unprod 65.0%

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

      5. sqr-neg 65.0%

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

      6. sqrt-unprod 0.0%

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

      7. add-sqr-sqrt 65.2%

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

      8. *-commutative 65.2%

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

      9. add-sqr-sqrt 0.0%

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

      10. sqrt-unprod 65.0%

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

      11. sqr-neg 65.0%

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

      12. sqrt-unprod 87.1%

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

      13. add-sqr-sqrt 87.2%

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

   7. Applied egg-rr 87.2%

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

   if -4.9999999999999996e-41 < (*.f64 x 1/2) < 2.00000000000000004e-87

   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. associate-+l- 99.7%

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

   4. Applied egg-rr 99.7%

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

      1. sub-neg 99.7%

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

      2. distribute-rgt-in 99.7%

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

      3. *-un-lft-identity 99.7%

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

   6. Applied egg-rr 99.7%

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

   7. Taylor expanded in x around 0 86.8%

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

   if 2.00000000000000004e-87 < (*.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. Add Preprocessing

   5. Taylor expanded in z around inf 90.3%

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

      1. mul-1-neg 90.3%

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

   7. Simplified 90.3%

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

4. Final simplification 87.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot 0.5 \leq -5 \cdot 10^{-41}:\\ \;\;\;\;x \cdot 0.5 - y \cdot z\\ \mathbf{elif}\;x \cdot 0.5 \leq 2 \cdot 10^{-87}:\\ \;\;\;\;y - y \cdot \left(z - \log z\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, -z, x \cdot 0.5\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 98.7% accurate, 1.0× speedup

Math

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

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z 0.28) (+ (* x 0.5) (* y (+ (log z) 1.0))) (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 * (log(z) + 1.0));
	} 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(log(z) + 1.0)));
	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[(N[Log[z], $MachinePrecision] + 1.0), $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. Add Preprocessing

   3. Taylor expanded in z around 0 99.4%

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

   if 0.28000000000000003 < z

   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 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. Add Preprocessing

   5. Taylor expanded in z around inf 98.6%

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

      1. mul-1-neg 98.6%

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

   7. Simplified 98.6%

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

4. Final simplification 99.0%

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

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. Add Preprocessing

3. Final simplification 99.8%

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

Alternative 7: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = (x * 0.5d0) + (y * ((log(z) - z) + 1.0d0))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.8%

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

   1. associate-+l- 99.8%

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

4. Applied egg-rr 99.8%

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

5. Final simplification 99.8%

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

Alternative 8: 60.0% accurate, 5.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq 720000000000 \lor \neg \left(z \leq 5.8 \cdot 10^{+95}\right) \land z \leq 1.46 \cdot 10^{+110}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z 720000000000.0) (and (not (<= z 5.8e+95)) (<= z 1.46e+110)))
   (* x 0.5)
   (* y (- z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= 720000000000.0) || (!(z <= 5.8e+95) && (z <= 1.46e+110))) {
		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 <= 720000000000.0d0) .or. (.not. (z <= 5.8d+95)) .and. (z <= 1.46d+110)) 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 <= 720000000000.0) || (!(z <= 5.8e+95) && (z <= 1.46e+110))) {
		tmp = x * 0.5;
	} else {
		tmp = y * -z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= 720000000000.0) or (not (z <= 5.8e+95) and (z <= 1.46e+110)):
		tmp = x * 0.5
	else:
		tmp = y * -z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= 720000000000.0) || (!(z <= 5.8e+95) && (z <= 1.46e+110)))
		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 <= 720000000000.0) || (~((z <= 5.8e+95)) && (z <= 1.46e+110)))
		tmp = x * 0.5;
	else
		tmp = y * -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, 720000000000.0], And[N[Not[LessEqual[z, 5.8e+95]], $MachinePrecision], LessEqual[z, 1.46e+110]]], N[(x * 0.5), $MachinePrecision], N[(y * (-z)), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 7.2e11 or 5.80000000000000027e95 < z < 1.46e110

   1. Initial program 99.7%

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

   3. Taylor expanded in x around inf 54.9%

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

   if 7.2e11 < z < 5.80000000000000027e95 or 1.46e110 < 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 99.6%

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

      1. mul-1-neg 99.6%

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

      2. distribute-rgt-neg-in 99.6%

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

   5. Simplified 99.6%

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

      1. distribute-rgt-neg-out 99.6%

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

      2. unsub-neg 99.6%

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

      3. add-sqr-sqrt 99.3%

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

      4. sqrt-unprod 68.6%

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

      5. sqr-neg 68.6%

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

      6. sqrt-unprod 0.0%

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

      7. add-sqr-sqrt 32.7%

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

      8. *-commutative 32.7%

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

      9. add-sqr-sqrt 0.0%

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

      10. sqrt-unprod 68.6%

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

      11. sqr-neg 68.6%

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

      12. sqrt-unprod 99.3%

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

      13. add-sqr-sqrt 99.6%

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

   7. Applied egg-rr 99.6%

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

   8. Taylor expanded in x around 0 67.6%

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

      1. associate-*r* 67.6%

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

      2. neg-mul-1 67.6%

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

      3. *-commutative 67.6%

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

   10. Simplified 67.6%

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

4. Final simplification 60.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 720000000000 \lor \neg \left(z \leq 5.8 \cdot 10^{+95}\right) \land z \leq 1.46 \cdot 10^{+110}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 75.2% 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. Add Preprocessing

3. Taylor expanded in z around inf 75.3%

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

   1. mul-1-neg 75.3%

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

   2. distribute-rgt-neg-in 75.3%

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

5. Simplified 75.3%

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

   1. distribute-rgt-neg-out 75.3%

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

   2. unsub-neg 75.3%

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

   3. add-sqr-sqrt 75.2%

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

   4. sqrt-unprod 61.8%

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

   5. sqr-neg 61.8%

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

   6. sqrt-unprod 0.0%

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

   7. add-sqr-sqrt 45.0%

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

   8. *-commutative 45.0%

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

   9. add-sqr-sqrt 0.0%

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

   10. sqrt-unprod 61.8%

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

   11. sqr-neg 61.8%

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

   12. sqrt-unprod 75.2%

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

   13. add-sqr-sqrt 75.3%

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

7. Applied egg-rr 75.3%

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

8. Final simplification 75.3%

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

Alternative 10: 40.3% 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 99.8%

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

3. Taylor expanded in x around inf 45.9%

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

4. Final simplification 45.9%

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

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 2024033 
(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)))))