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

Percentage Accurate: 99.9% → 99.9%

Time: 13.6s

Alternatives: 8

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := N[(N[(y * N[(N[(1.0 - z), $MachinePrecision] + N[Log[z], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + 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. Final simplification 99.9%

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

Alternative 2: 85.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.8 \cdot 10^{+121}:\\ \;\;\;\;y \cdot \left(\left(1 - z\right) + \log z\right)\\ \mathbf{elif}\;y \leq 2.4 \cdot 10^{+36}:\\ \;\;\;\;x \cdot 0.5 - y \cdot z\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(\left(\log z - z\right) + 1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -2.8e+121)
   (* y (+ (- 1.0 z) (log z)))
   (if (<= y 2.4e+36) (- (* x 0.5) (* y z)) (* y (+ (- (log z) z) 1.0)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -2.8e+121) {
		tmp = y * ((1.0 - z) + log(z));
	} else if (y <= 2.4e+36) {
		tmp = (x * 0.5) - (y * z);
	} else {
		tmp = y * ((log(z) - 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 (y <= (-2.8d+121)) then
        tmp = y * ((1.0d0 - z) + log(z))
    else if (y <= 2.4d+36) then
        tmp = (x * 0.5d0) - (y * z)
    else
        tmp = y * ((log(z) - z) + 1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -2.8e+121) {
		tmp = y * ((1.0 - z) + Math.log(z));
	} else if (y <= 2.4e+36) {
		tmp = (x * 0.5) - (y * z);
	} else {
		tmp = y * ((Math.log(z) - z) + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -2.8e+121:
		tmp = y * ((1.0 - z) + math.log(z))
	elif y <= 2.4e+36:
		tmp = (x * 0.5) - (y * z)
	else:
		tmp = y * ((math.log(z) - z) + 1.0)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -2.8e+121)
		tmp = Float64(y * Float64(Float64(1.0 - z) + log(z)));
	elseif (y <= 2.4e+36)
		tmp = Float64(Float64(x * 0.5) - Float64(y * z));
	else
		tmp = Float64(y * Float64(Float64(log(z) - z) + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -2.8e+121)
		tmp = y * ((1.0 - z) + log(z));
	elseif (y <= 2.4e+36)
		tmp = (x * 0.5) - (y * z);
	else
		tmp = y * ((log(z) - z) + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -2.8e+121], N[(y * N[(N[(1.0 - z), $MachinePrecision] + N[Log[z], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.4e+36], N[(N[(x * 0.5), $MachinePrecision] - N[(y * z), $MachinePrecision]), $MachinePrecision], N[(y * N[(N[(N[Log[z], $MachinePrecision] - z), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.80000000000000006e121

   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. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y, \color{blue}{\left(\left(1 + \log z\right) - z\right)}\right) \]

      2. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(y, \left(1 + \color{blue}{\left(\log z - z\right)}\right)\right) \]

      3. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(y, \left(1 + \left(\log z + \color{blue}{\left(\mathsf{neg}\left(z\right)\right)}\right)\right)\right) \]

      4. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(y, \left(1 + \left(\log z + -1 \cdot \color{blue}{z}\right)\right)\right) \]

      5. *-lft-identity N/A

         \[\leadsto \mathsf{*.f64}\left(y, \left(1 + 1 \cdot \color{blue}{\left(\log z + -1 \cdot z\right)}\right)\right) \]

      6. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(y, \left(1 + \left(\mathsf{neg}\left(-1\right)\right) \cdot \left(\color{blue}{\log z} + -1 \cdot z\right)\right)\right) \]

      7. cancel-sign-sub-inv N/A

         \[\leadsto \mathsf{*.f64}\left(y, \left(1 - \color{blue}{-1 \cdot \left(\log z + -1 \cdot z\right)}\right)\right) \]

      8. neg-mul-1 N/A

         \[\leadsto \mathsf{*.f64}\left(y, \left(1 - \left(\mathsf{neg}\left(\left(\log z + -1 \cdot z\right)\right)\right)\right)\right) \]

      9. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(1, \color{blue}{\left(\mathsf{neg}\left(\left(\log z + -1 \cdot z\right)\right)\right)}\right)\right) \]

      10. mul-1-neg N/A

          \[\leadsto \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(1, \left(\mathsf{neg}\left(\left(\log z + \left(\mathsf{neg}\left(z\right)\right)\right)\right)\right)\right)\right) \]

      11. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(1, \left(\mathsf{neg}\left(\left(\left(\mathsf{neg}\left(z\right)\right) + \log z\right)\right)\right)\right)\right) \]

      12. distribute-neg-in N/A

          \[\leadsto \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(1, \left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(z\right)\right)\right)\right) + \color{blue}{\left(\mathsf{neg}\left(\log z\right)\right)}\right)\right)\right) \]

      13. remove-double-neg N/A

          \[\leadsto \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(1, \left(z + \left(\mathsf{neg}\left(\color{blue}{\log z}\right)\right)\right)\right)\right) \]

      14. sub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(1, \left(z - \color{blue}{\log z}\right)\right)\right) \]

      15. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(1, \mathsf{\_.f64}\left(z, \color{blue}{\log z}\right)\right)\right) \]

      16. log-lowering-log.f64 91.0%

          \[\leadsto \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(1, \mathsf{\_.f64}\left(z, \mathsf{log.f64}\left(z\right)\right)\right)\right) \]

   5. Simplified 91.0%

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

      1. associate-+l- N/A

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

      2. *-commutative N/A

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

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

         \[\leadsto \mathsf{*.f64}\left(\left(\left(1 - z\right) + \log z\right), \color{blue}{y}\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(\left(1 - z\right), \log z\right), y\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{\_.f64}\left(1, z\right), \log z\right), y\right) \]

      6. log-lowering-log.f64 91.0%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{\_.f64}\left(1, z\right), \mathsf{log.f64}\left(z\right)\right), y\right) \]

   7. Applied egg-rr 91.0%

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

   if -2.80000000000000006e121 < y < 2.39999999999999992e36

   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. flip-+ N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \frac{1}{2}\right), \left(y \cdot \frac{\left(1 - z\right) \cdot \left(1 - z\right) - \log z \cdot \log z}{\color{blue}{\left(1 - z\right) - \log z}}\right)\right) \]

      2. clear-num N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \frac{1}{2}\right), \left(y \cdot \frac{1}{\color{blue}{\frac{\left(1 - z\right) - \log z}{\left(1 - z\right) \cdot \left(1 - z\right) - \log z \cdot \log z}}}\right)\right) \]

      3. un-div-inv N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \frac{1}{2}\right), \left(\frac{y}{\color{blue}{\frac{\left(1 - z\right) - \log z}{\left(1 - z\right) \cdot \left(1 - z\right) - \log z \cdot \log z}}}\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \frac{1}{2}\right), \mathsf{/.f64}\left(y, \color{blue}{\left(\frac{\left(1 - z\right) - \log z}{\left(1 - z\right) \cdot \left(1 - z\right) - \log z \cdot \log z}\right)}\right)\right) \]

      5. clear-num N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \frac{1}{2}\right), \mathsf{/.f64}\left(y, \left(\frac{1}{\color{blue}{\frac{\left(1 - z\right) \cdot \left(1 - z\right) - \log z \cdot \log z}{\left(1 - z\right) - \log z}}}\right)\right)\right) \]

      6. flip-+ N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \frac{1}{2}\right), \mathsf{/.f64}\left(y, \left(\frac{1}{\left(1 - z\right) + \color{blue}{\log z}}\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \frac{1}{2}\right), \mathsf{/.f64}\left(y, \mathsf{/.f64}\left(1, \color{blue}{\left(\left(1 - z\right) + \log z\right)}\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \frac{1}{2}\right), \mathsf{/.f64}\left(y, \mathsf{/.f64}\left(1, \mathsf{+.f64}\left(\left(1 - z\right), \color{blue}{\log z}\right)\right)\right)\right) \]

      9. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \frac{1}{2}\right), \mathsf{/.f64}\left(y, \mathsf{/.f64}\left(1, \mathsf{+.f64}\left(\mathsf{\_.f64}\left(1, z\right), \log \color{blue}{z}\right)\right)\right)\right) \]

      10. log-lowering-log.f64 99.8%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \frac{1}{2}\right), \mathsf{/.f64}\left(y, \mathsf{/.f64}\left(1, \mathsf{+.f64}\left(\mathsf{\_.f64}\left(1, z\right), \mathsf{log.f64}\left(z\right)\right)\right)\right)\right) \]

   4. Applied egg-rr 99.8%

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

   5. Taylor expanded in z around inf

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \frac{1}{2}\right), \mathsf{/.f64}\left(y, \color{blue}{\left(\frac{-1}{z}\right)}\right)\right) \]
   6. Step-by-step derivation

      1. /-lowering-/.f64 88.6%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \frac{1}{2}\right), \mathsf{/.f64}\left(y, \mathsf{/.f64}\left(-1, \color{blue}{z}\right)\right)\right) \]

   7. Simplified 88.6%

      \[\leadsto x \cdot 0.5 + \frac{y}{\color{blue}{\frac{-1}{z}}} \]

   8. Taylor expanded in x around 0

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

      1. +-commutative N/A

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

      2. mul-1-neg N/A

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

      3. unsub-neg N/A

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

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

         \[\leadsto \mathsf{\_.f64}\left(\left(\frac{1}{2} \cdot x\right), \color{blue}{\left(y \cdot z\right)}\right) \]

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

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\frac{1}{2}, x\right), \left(\color{blue}{y} \cdot z\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\frac{1}{2}, x\right), \left(z \cdot \color{blue}{y}\right)\right) \]

      7. *-lowering-*.f64 88.7%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\frac{1}{2}, x\right), \mathsf{*.f64}\left(z, \color{blue}{y}\right)\right) \]

   10. Simplified 88.7%

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

   if 2.39999999999999992e36 < y

   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. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y, \color{blue}{\left(\left(1 + \log z\right) - z\right)}\right) \]

      2. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(y, \left(1 + \color{blue}{\left(\log z - z\right)}\right)\right) \]

      3. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(y, \left(1 + \left(\log z + \color{blue}{\left(\mathsf{neg}\left(z\right)\right)}\right)\right)\right) \]

      4. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(y, \left(1 + \left(\log z + -1 \cdot \color{blue}{z}\right)\right)\right) \]

      5. *-lft-identity N/A

         \[\leadsto \mathsf{*.f64}\left(y, \left(1 + 1 \cdot \color{blue}{\left(\log z + -1 \cdot z\right)}\right)\right) \]

      6. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(y, \left(1 + \left(\mathsf{neg}\left(-1\right)\right) \cdot \left(\color{blue}{\log z} + -1 \cdot z\right)\right)\right) \]

      7. cancel-sign-sub-inv N/A

         \[\leadsto \mathsf{*.f64}\left(y, \left(1 - \color{blue}{-1 \cdot \left(\log z + -1 \cdot z\right)}\right)\right) \]

      8. neg-mul-1 N/A

         \[\leadsto \mathsf{*.f64}\left(y, \left(1 - \left(\mathsf{neg}\left(\left(\log z + -1 \cdot z\right)\right)\right)\right)\right) \]

      9. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(1, \color{blue}{\left(\mathsf{neg}\left(\left(\log z + -1 \cdot z\right)\right)\right)}\right)\right) \]

      10. mul-1-neg N/A

          \[\leadsto \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(1, \left(\mathsf{neg}\left(\left(\log z + \left(\mathsf{neg}\left(z\right)\right)\right)\right)\right)\right)\right) \]

      11. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(1, \left(\mathsf{neg}\left(\left(\left(\mathsf{neg}\left(z\right)\right) + \log z\right)\right)\right)\right)\right) \]

      12. distribute-neg-in N/A

          \[\leadsto \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(1, \left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(z\right)\right)\right)\right) + \color{blue}{\left(\mathsf{neg}\left(\log z\right)\right)}\right)\right)\right) \]

      13. remove-double-neg N/A

          \[\leadsto \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(1, \left(z + \left(\mathsf{neg}\left(\color{blue}{\log z}\right)\right)\right)\right)\right) \]

      14. sub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(1, \left(z - \color{blue}{\log z}\right)\right)\right) \]

      15. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(1, \mathsf{\_.f64}\left(z, \color{blue}{\log z}\right)\right)\right) \]

      16. log-lowering-log.f64 82.3%

          \[\leadsto \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(1, \mathsf{\_.f64}\left(z, \mathsf{log.f64}\left(z\right)\right)\right)\right) \]

   5. Simplified 82.3%

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

4. Final simplification 88.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.8 \cdot 10^{+121}:\\ \;\;\;\;y \cdot \left(\left(1 - z\right) + \log z\right)\\ \mathbf{elif}\;y \leq 2.4 \cdot 10^{+36}:\\ \;\;\;\;x \cdot 0.5 - y \cdot z\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(\left(\log z - z\right) + 1\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 85.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y \cdot \left(\left(\log z - z\right) + 1\right)\\ \mathbf{if}\;y \leq -3.95 \cdot 10^{+121}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 4.1 \cdot 10^{+36}:\\ \;\;\;\;x \cdot 0.5 - y \cdot z\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* y (+ (- (log z) z) 1.0))))
   (if (<= y -3.95e+121) t_0 (if (<= y 4.1e+36) (- (* x 0.5) (* y z)) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = y * ((log(z) - z) + 1.0);
	double tmp;
	if (y <= -3.95e+121) {
		tmp = t_0;
	} else if (y <= 4.1e+36) {
		tmp = (x * 0.5) - (y * z);
	} else {
		tmp = t_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) :: t_0
    real(8) :: tmp
    t_0 = y * ((log(z) - z) + 1.0d0)
    if (y <= (-3.95d+121)) then
        tmp = t_0
    else if (y <= 4.1d+36) then
        tmp = (x * 0.5d0) - (y * z)
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = y * ((Math.log(z) - z) + 1.0);
	double tmp;
	if (y <= -3.95e+121) {
		tmp = t_0;
	} else if (y <= 4.1e+36) {
		tmp = (x * 0.5) - (y * z);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = y * ((math.log(z) - z) + 1.0)
	tmp = 0
	if y <= -3.95e+121:
		tmp = t_0
	elif y <= 4.1e+36:
		tmp = (x * 0.5) - (y * z)
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(y * Float64(Float64(log(z) - z) + 1.0))
	tmp = 0.0
	if (y <= -3.95e+121)
		tmp = t_0;
	elseif (y <= 4.1e+36)
		tmp = Float64(Float64(x * 0.5) - Float64(y * z));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = y * ((log(z) - z) + 1.0);
	tmp = 0.0;
	if (y <= -3.95e+121)
		tmp = t_0;
	elseif (y <= 4.1e+36)
		tmp = (x * 0.5) - (y * z);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(y * N[(N[(N[Log[z], $MachinePrecision] - z), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -3.95e+121], t$95$0, If[LessEqual[y, 4.1e+36], N[(N[(x * 0.5), $MachinePrecision] - N[(y * z), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if y < -3.95e121 or 4.10000000000000013e36 < y

   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. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y, \color{blue}{\left(\left(1 + \log z\right) - z\right)}\right) \]

      2. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(y, \left(1 + \color{blue}{\left(\log z - z\right)}\right)\right) \]

      3. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(y, \left(1 + \left(\log z + \color{blue}{\left(\mathsf{neg}\left(z\right)\right)}\right)\right)\right) \]

      4. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(y, \left(1 + \left(\log z + -1 \cdot \color{blue}{z}\right)\right)\right) \]

      5. *-lft-identity N/A

         \[\leadsto \mathsf{*.f64}\left(y, \left(1 + 1 \cdot \color{blue}{\left(\log z + -1 \cdot z\right)}\right)\right) \]

      6. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(y, \left(1 + \left(\mathsf{neg}\left(-1\right)\right) \cdot \left(\color{blue}{\log z} + -1 \cdot z\right)\right)\right) \]

      7. cancel-sign-sub-inv N/A

         \[\leadsto \mathsf{*.f64}\left(y, \left(1 - \color{blue}{-1 \cdot \left(\log z + -1 \cdot z\right)}\right)\right) \]

      8. neg-mul-1 N/A

         \[\leadsto \mathsf{*.f64}\left(y, \left(1 - \left(\mathsf{neg}\left(\left(\log z + -1 \cdot z\right)\right)\right)\right)\right) \]

      9. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(1, \color{blue}{\left(\mathsf{neg}\left(\left(\log z + -1 \cdot z\right)\right)\right)}\right)\right) \]

      10. mul-1-neg N/A

          \[\leadsto \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(1, \left(\mathsf{neg}\left(\left(\log z + \left(\mathsf{neg}\left(z\right)\right)\right)\right)\right)\right)\right) \]

      11. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(1, \left(\mathsf{neg}\left(\left(\left(\mathsf{neg}\left(z\right)\right) + \log z\right)\right)\right)\right)\right) \]

      12. distribute-neg-in N/A

          \[\leadsto \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(1, \left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(z\right)\right)\right)\right) + \color{blue}{\left(\mathsf{neg}\left(\log z\right)\right)}\right)\right)\right) \]

      13. remove-double-neg N/A

          \[\leadsto \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(1, \left(z + \left(\mathsf{neg}\left(\color{blue}{\log z}\right)\right)\right)\right)\right) \]

      14. sub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(1, \left(z - \color{blue}{\log z}\right)\right)\right) \]

      15. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(1, \mathsf{\_.f64}\left(z, \color{blue}{\log z}\right)\right)\right) \]

      16. log-lowering-log.f64 86.8%

          \[\leadsto \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(1, \mathsf{\_.f64}\left(z, \mathsf{log.f64}\left(z\right)\right)\right)\right) \]

   5. Simplified 86.8%

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

   if -3.95e121 < y < 4.10000000000000013e36

   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. flip-+ N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \frac{1}{2}\right), \left(y \cdot \frac{\left(1 - z\right) \cdot \left(1 - z\right) - \log z \cdot \log z}{\color{blue}{\left(1 - z\right) - \log z}}\right)\right) \]

      2. clear-num N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \frac{1}{2}\right), \left(y \cdot \frac{1}{\color{blue}{\frac{\left(1 - z\right) - \log z}{\left(1 - z\right) \cdot \left(1 - z\right) - \log z \cdot \log z}}}\right)\right) \]

      3. un-div-inv N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \frac{1}{2}\right), \left(\frac{y}{\color{blue}{\frac{\left(1 - z\right) - \log z}{\left(1 - z\right) \cdot \left(1 - z\right) - \log z \cdot \log z}}}\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \frac{1}{2}\right), \mathsf{/.f64}\left(y, \color{blue}{\left(\frac{\left(1 - z\right) - \log z}{\left(1 - z\right) \cdot \left(1 - z\right) - \log z \cdot \log z}\right)}\right)\right) \]

      5. clear-num N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \frac{1}{2}\right), \mathsf{/.f64}\left(y, \left(\frac{1}{\color{blue}{\frac{\left(1 - z\right) \cdot \left(1 - z\right) - \log z \cdot \log z}{\left(1 - z\right) - \log z}}}\right)\right)\right) \]

      6. flip-+ N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \frac{1}{2}\right), \mathsf{/.f64}\left(y, \left(\frac{1}{\left(1 - z\right) + \color{blue}{\log z}}\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \frac{1}{2}\right), \mathsf{/.f64}\left(y, \mathsf{/.f64}\left(1, \color{blue}{\left(\left(1 - z\right) + \log z\right)}\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \frac{1}{2}\right), \mathsf{/.f64}\left(y, \mathsf{/.f64}\left(1, \mathsf{+.f64}\left(\left(1 - z\right), \color{blue}{\log z}\right)\right)\right)\right) \]

      9. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \frac{1}{2}\right), \mathsf{/.f64}\left(y, \mathsf{/.f64}\left(1, \mathsf{+.f64}\left(\mathsf{\_.f64}\left(1, z\right), \log \color{blue}{z}\right)\right)\right)\right) \]

      10. log-lowering-log.f64 99.8%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \frac{1}{2}\right), \mathsf{/.f64}\left(y, \mathsf{/.f64}\left(1, \mathsf{+.f64}\left(\mathsf{\_.f64}\left(1, z\right), \mathsf{log.f64}\left(z\right)\right)\right)\right)\right) \]

   4. Applied egg-rr 99.8%

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

   5. Taylor expanded in z around inf

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \frac{1}{2}\right), \mathsf{/.f64}\left(y, \color{blue}{\left(\frac{-1}{z}\right)}\right)\right) \]
   6. Step-by-step derivation

      1. /-lowering-/.f64 88.6%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \frac{1}{2}\right), \mathsf{/.f64}\left(y, \mathsf{/.f64}\left(-1, \color{blue}{z}\right)\right)\right) \]

   7. Simplified 88.6%

      \[\leadsto x \cdot 0.5 + \frac{y}{\color{blue}{\frac{-1}{z}}} \]

   8. Taylor expanded in x around 0

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

      1. +-commutative N/A

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

      2. mul-1-neg N/A

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

      3. unsub-neg N/A

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

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

         \[\leadsto \mathsf{\_.f64}\left(\left(\frac{1}{2} \cdot x\right), \color{blue}{\left(y \cdot z\right)}\right) \]

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

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\frac{1}{2}, x\right), \left(\color{blue}{y} \cdot z\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\frac{1}{2}, x\right), \left(z \cdot \color{blue}{y}\right)\right) \]

      7. *-lowering-*.f64 88.7%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\frac{1}{2}, x\right), \mathsf{*.f64}\left(z, \color{blue}{y}\right)\right) \]

   10. Simplified 88.7%

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

4. Final simplification 88.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.95 \cdot 10^{+121}:\\ \;\;\;\;y \cdot \left(\left(\log z - z\right) + 1\right)\\ \mathbf{elif}\;y \leq 4.1 \cdot 10^{+36}:\\ \;\;\;\;x \cdot 0.5 - y \cdot z\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(\left(\log z - z\right) + 1\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 98.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= 0.28) {
		tmp = (y * (log(z) + 1.0)) + (x * 0.5);
	} else {
		tmp = (x * 0.5) - (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 <= 0.28d0) then
        tmp = (y * (log(z) + 1.0d0)) + (x * 0.5d0)
    else
        tmp = (x * 0.5d0) - (y * z)
    end if
    code = tmp
end function

Java

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

Python

def code(x, y, z):
	tmp = 0
	if z <= 0.28:
		tmp = (y * (math.log(z) + 1.0)) + (x * 0.5)
	else:
		tmp = (x * 0.5) - (y * z)
	return tmp

Julia

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

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= 0.28)
		tmp = (y * (log(z) + 1.0)) + (x * 0.5);
	else
		tmp = (x * 0.5) - (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if z < 0.28000000000000003

   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

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \frac{1}{2}\right), \color{blue}{\left(y \cdot \left(1 + \log z\right)\right)}\right) \]
   4. Step-by-step derivation

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \frac{1}{2}\right), \mathsf{*.f64}\left(y, \color{blue}{\left(1 + \log z\right)}\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \frac{1}{2}\right), \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(1, \color{blue}{\log z}\right)\right)\right) \]

      3. log-lowering-log.f64 98.7%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \frac{1}{2}\right), \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(1, \mathsf{log.f64}\left(z\right)\right)\right)\right) \]

   5. Simplified 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. Add Preprocessing
   3. Step-by-step derivation

      1. flip-+ N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \frac{1}{2}\right), \left(y \cdot \frac{\left(1 - z\right) \cdot \left(1 - z\right) - \log z \cdot \log z}{\color{blue}{\left(1 - z\right) - \log z}}\right)\right) \]

      2. clear-num N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \frac{1}{2}\right), \left(y \cdot \frac{1}{\color{blue}{\frac{\left(1 - z\right) - \log z}{\left(1 - z\right) \cdot \left(1 - z\right) - \log z \cdot \log z}}}\right)\right) \]

      3. un-div-inv N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \frac{1}{2}\right), \left(\frac{y}{\color{blue}{\frac{\left(1 - z\right) - \log z}{\left(1 - z\right) \cdot \left(1 - z\right) - \log z \cdot \log z}}}\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \frac{1}{2}\right), \mathsf{/.f64}\left(y, \color{blue}{\left(\frac{\left(1 - z\right) - \log z}{\left(1 - z\right) \cdot \left(1 - z\right) - \log z \cdot \log z}\right)}\right)\right) \]

      5. clear-num N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \frac{1}{2}\right), \mathsf{/.f64}\left(y, \left(\frac{1}{\color{blue}{\frac{\left(1 - z\right) \cdot \left(1 - z\right) - \log z \cdot \log z}{\left(1 - z\right) - \log z}}}\right)\right)\right) \]

      6. flip-+ N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \frac{1}{2}\right), \mathsf{/.f64}\left(y, \left(\frac{1}{\left(1 - z\right) + \color{blue}{\log z}}\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \frac{1}{2}\right), \mathsf{/.f64}\left(y, \mathsf{/.f64}\left(1, \color{blue}{\left(\left(1 - z\right) + \log z\right)}\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \frac{1}{2}\right), \mathsf{/.f64}\left(y, \mathsf{/.f64}\left(1, \mathsf{+.f64}\left(\left(1 - z\right), \color{blue}{\log z}\right)\right)\right)\right) \]

      9. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \frac{1}{2}\right), \mathsf{/.f64}\left(y, \mathsf{/.f64}\left(1, \mathsf{+.f64}\left(\mathsf{\_.f64}\left(1, z\right), \log \color{blue}{z}\right)\right)\right)\right) \]

      10. log-lowering-log.f64 99.8%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \frac{1}{2}\right), \mathsf{/.f64}\left(y, \mathsf{/.f64}\left(1, \mathsf{+.f64}\left(\mathsf{\_.f64}\left(1, z\right), \mathsf{log.f64}\left(z\right)\right)\right)\right)\right) \]

   4. Applied egg-rr 99.8%

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

   5. Taylor expanded in z around inf

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \frac{1}{2}\right), \mathsf{/.f64}\left(y, \color{blue}{\left(\frac{-1}{z}\right)}\right)\right) \]
   6. Step-by-step derivation

      1. /-lowering-/.f64 98.0%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \frac{1}{2}\right), \mathsf{/.f64}\left(y, \mathsf{/.f64}\left(-1, \color{blue}{z}\right)\right)\right) \]

   7. Simplified 98.0%

      \[\leadsto x \cdot 0.5 + \frac{y}{\color{blue}{\frac{-1}{z}}} \]

   8. Taylor expanded in x around 0

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

      1. +-commutative N/A

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

      2. mul-1-neg N/A

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

      3. unsub-neg N/A

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

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

         \[\leadsto \mathsf{\_.f64}\left(\left(\frac{1}{2} \cdot x\right), \color{blue}{\left(y \cdot z\right)}\right) \]

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

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\frac{1}{2}, x\right), \left(\color{blue}{y} \cdot z\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\frac{1}{2}, x\right), \left(z \cdot \color{blue}{y}\right)\right) \]

      7. *-lowering-*.f64 98.2%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\frac{1}{2}, x\right), \mathsf{*.f64}\left(z, \color{blue}{y}\right)\right) \]

   10. Simplified 98.2%

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

4. Final simplification 98.4%

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

Alternative 5: 58.8% accurate, 11.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq 2.3 \cdot 10^{+81}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(1 - z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z 2.3e+81) (* x 0.5) (* y (- 1.0 z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= 2.3e+81) {
		tmp = x * 0.5;
	} else {
		tmp = y * (1.0 - z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z <= 2.3d+81) then
        tmp = x * 0.5d0
    else
        tmp = y * (1.0d0 - z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= 2.3e+81) {
		tmp = x * 0.5;
	} else {
		tmp = y * (1.0 - z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= 2.3e+81:
		tmp = x * 0.5
	else:
		tmp = y * (1.0 - z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= 2.3e+81)
		tmp = Float64(x * 0.5);
	else
		tmp = Float64(y * Float64(1.0 - z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= 2.3e+81)
		tmp = x * 0.5;
	else
		tmp = y * (1.0 - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, 2.3e+81], N[(x * 0.5), $MachinePrecision], N[(y * N[(1.0 - z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 2.2999999999999999e81

   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

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

      1. *-lowering-*.f64 58.8%

         \[\leadsto \mathsf{*.f64}\left(\frac{1}{2}, \color{blue}{x}\right) \]

   5. Simplified 58.8%

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

   if 2.2999999999999999e81 < 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 x around 0

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

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

         \[\leadsto \mathsf{*.f64}\left(y, \color{blue}{\left(\left(1 + \log z\right) - z\right)}\right) \]

      2. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(y, \left(1 + \color{blue}{\left(\log z - z\right)}\right)\right) \]

      3. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(y, \left(1 + \left(\log z + \color{blue}{\left(\mathsf{neg}\left(z\right)\right)}\right)\right)\right) \]

      4. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(y, \left(1 + \left(\log z + -1 \cdot \color{blue}{z}\right)\right)\right) \]

      5. *-lft-identity N/A

         \[\leadsto \mathsf{*.f64}\left(y, \left(1 + 1 \cdot \color{blue}{\left(\log z + -1 \cdot z\right)}\right)\right) \]

      6. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(y, \left(1 + \left(\mathsf{neg}\left(-1\right)\right) \cdot \left(\color{blue}{\log z} + -1 \cdot z\right)\right)\right) \]

      7. cancel-sign-sub-inv N/A

         \[\leadsto \mathsf{*.f64}\left(y, \left(1 - \color{blue}{-1 \cdot \left(\log z + -1 \cdot z\right)}\right)\right) \]

      8. neg-mul-1 N/A

         \[\leadsto \mathsf{*.f64}\left(y, \left(1 - \left(\mathsf{neg}\left(\left(\log z + -1 \cdot z\right)\right)\right)\right)\right) \]

      9. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(1, \color{blue}{\left(\mathsf{neg}\left(\left(\log z + -1 \cdot z\right)\right)\right)}\right)\right) \]

      10. mul-1-neg N/A

          \[\leadsto \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(1, \left(\mathsf{neg}\left(\left(\log z + \left(\mathsf{neg}\left(z\right)\right)\right)\right)\right)\right)\right) \]

      11. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(1, \left(\mathsf{neg}\left(\left(\left(\mathsf{neg}\left(z\right)\right) + \log z\right)\right)\right)\right)\right) \]

      12. distribute-neg-in N/A

          \[\leadsto \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(1, \left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(z\right)\right)\right)\right) + \color{blue}{\left(\mathsf{neg}\left(\log z\right)\right)}\right)\right)\right) \]

      13. remove-double-neg N/A

          \[\leadsto \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(1, \left(z + \left(\mathsf{neg}\left(\color{blue}{\log z}\right)\right)\right)\right)\right) \]

      14. sub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(1, \left(z - \color{blue}{\log z}\right)\right)\right) \]

      15. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(1, \mathsf{\_.f64}\left(z, \color{blue}{\log z}\right)\right)\right) \]

      16. log-lowering-log.f64 79.7%

          \[\leadsto \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(1, \mathsf{\_.f64}\left(z, \mathsf{log.f64}\left(z\right)\right)\right)\right) \]

   5. Simplified 79.7%

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

   6. Taylor expanded in z around inf

      \[\leadsto \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(1, \color{blue}{z}\right)\right) \]
   7. Step-by-step derivation

   8. Simplified 79.7%

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

4. Final simplification 66.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 2.3 \cdot 10^{+81}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(1 - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 75.0% accurate, 15.9× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

   1. flip-+ N/A

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \frac{1}{2}\right), \left(y \cdot \frac{\left(1 - z\right) \cdot \left(1 - z\right) - \log z \cdot \log z}{\color{blue}{\left(1 - z\right) - \log z}}\right)\right) \]

   2. clear-num N/A

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \frac{1}{2}\right), \left(y \cdot \frac{1}{\color{blue}{\frac{\left(1 - z\right) - \log z}{\left(1 - z\right) \cdot \left(1 - z\right) - \log z \cdot \log z}}}\right)\right) \]

   3. un-div-inv N/A

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \frac{1}{2}\right), \left(\frac{y}{\color{blue}{\frac{\left(1 - z\right) - \log z}{\left(1 - z\right) \cdot \left(1 - z\right) - \log z \cdot \log z}}}\right)\right) \]

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

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \frac{1}{2}\right), \mathsf{/.f64}\left(y, \color{blue}{\left(\frac{\left(1 - z\right) - \log z}{\left(1 - z\right) \cdot \left(1 - z\right) - \log z \cdot \log z}\right)}\right)\right) \]

   5. clear-num N/A

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \frac{1}{2}\right), \mathsf{/.f64}\left(y, \left(\frac{1}{\color{blue}{\frac{\left(1 - z\right) \cdot \left(1 - z\right) - \log z \cdot \log z}{\left(1 - z\right) - \log z}}}\right)\right)\right) \]

   6. flip-+ N/A

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \frac{1}{2}\right), \mathsf{/.f64}\left(y, \left(\frac{1}{\left(1 - z\right) + \color{blue}{\log z}}\right)\right)\right) \]

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

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \frac{1}{2}\right), \mathsf{/.f64}\left(y, \mathsf{/.f64}\left(1, \color{blue}{\left(\left(1 - z\right) + \log z\right)}\right)\right)\right) \]

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

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \frac{1}{2}\right), \mathsf{/.f64}\left(y, \mathsf{/.f64}\left(1, \mathsf{+.f64}\left(\left(1 - z\right), \color{blue}{\log z}\right)\right)\right)\right) \]

   9. --lowering--.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \frac{1}{2}\right), \mathsf{/.f64}\left(y, \mathsf{/.f64}\left(1, \mathsf{+.f64}\left(\mathsf{\_.f64}\left(1, z\right), \log \color{blue}{z}\right)\right)\right)\right) \]

   10. log-lowering-log.f64 99.8%

       \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \frac{1}{2}\right), \mathsf{/.f64}\left(y, \mathsf{/.f64}\left(1, \mathsf{+.f64}\left(\mathsf{\_.f64}\left(1, z\right), \mathsf{log.f64}\left(z\right)\right)\right)\right)\right) \]

4. Applied egg-rr 99.8%

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

5. Taylor expanded in z around inf

   \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \frac{1}{2}\right), \mathsf{/.f64}\left(y, \color{blue}{\left(\frac{-1}{z}\right)}\right)\right) \]
6. Step-by-step derivation

   1. /-lowering-/.f64 77.9%

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \frac{1}{2}\right), \mathsf{/.f64}\left(y, \mathsf{/.f64}\left(-1, \color{blue}{z}\right)\right)\right) \]

7. Simplified 77.9%

   \[\leadsto x \cdot 0.5 + \frac{y}{\color{blue}{\frac{-1}{z}}} \]

8. Taylor expanded in x around 0

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

   1. +-commutative N/A

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

   2. mul-1-neg N/A

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

   3. unsub-neg N/A

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

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

      \[\leadsto \mathsf{\_.f64}\left(\left(\frac{1}{2} \cdot x\right), \color{blue}{\left(y \cdot z\right)}\right) \]

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

      \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\frac{1}{2}, x\right), \left(\color{blue}{y} \cdot z\right)\right) \]

   6. *-commutative N/A

      \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\frac{1}{2}, x\right), \left(z \cdot \color{blue}{y}\right)\right) \]

   7. *-lowering-*.f64 78.0%

      \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\frac{1}{2}, x\right), \mathsf{*.f64}\left(z, \color{blue}{y}\right)\right) \]

10. Simplified 78.0%

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

11. Final simplification 78.0%

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

Alternative 7: 40.7% accurate, 37.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

3. Taylor expanded in x around inf

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

   1. *-lowering-*.f64 45.9%

      \[\leadsto \mathsf{*.f64}\left(\frac{1}{2}, \color{blue}{x}\right) \]

5. Simplified 45.9%

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

6. Final simplification 45.9%

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

Alternative 8: 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 99.9%

   \[x \cdot 0.5 + y \cdot \left(\left(1 - z\right) + \log z\right) \]
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. *-lowering-*.f64 N/A

      \[\leadsto \mathsf{*.f64}\left(y, \color{blue}{\left(\left(1 + \log z\right) - z\right)}\right) \]

   2. associate--l+ N/A

      \[\leadsto \mathsf{*.f64}\left(y, \left(1 + \color{blue}{\left(\log z - z\right)}\right)\right) \]

   3. sub-neg N/A

      \[\leadsto \mathsf{*.f64}\left(y, \left(1 + \left(\log z + \color{blue}{\left(\mathsf{neg}\left(z\right)\right)}\right)\right)\right) \]

   4. mul-1-neg N/A

      \[\leadsto \mathsf{*.f64}\left(y, \left(1 + \left(\log z + -1 \cdot \color{blue}{z}\right)\right)\right) \]

   5. *-lft-identity N/A

      \[\leadsto \mathsf{*.f64}\left(y, \left(1 + 1 \cdot \color{blue}{\left(\log z + -1 \cdot z\right)}\right)\right) \]

   6. metadata-eval N/A

      \[\leadsto \mathsf{*.f64}\left(y, \left(1 + \left(\mathsf{neg}\left(-1\right)\right) \cdot \left(\color{blue}{\log z} + -1 \cdot z\right)\right)\right) \]

   7. cancel-sign-sub-inv N/A

      \[\leadsto \mathsf{*.f64}\left(y, \left(1 - \color{blue}{-1 \cdot \left(\log z + -1 \cdot z\right)}\right)\right) \]

   8. neg-mul-1 N/A

      \[\leadsto \mathsf{*.f64}\left(y, \left(1 - \left(\mathsf{neg}\left(\left(\log z + -1 \cdot z\right)\right)\right)\right)\right) \]

   9. --lowering--.f64 N/A

      \[\leadsto \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(1, \color{blue}{\left(\mathsf{neg}\left(\left(\log z + -1 \cdot z\right)\right)\right)}\right)\right) \]

   10. mul-1-neg N/A

       \[\leadsto \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(1, \left(\mathsf{neg}\left(\left(\log z + \left(\mathsf{neg}\left(z\right)\right)\right)\right)\right)\right)\right) \]

   11. +-commutative N/A

       \[\leadsto \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(1, \left(\mathsf{neg}\left(\left(\left(\mathsf{neg}\left(z\right)\right) + \log z\right)\right)\right)\right)\right) \]

   12. distribute-neg-in N/A

       \[\leadsto \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(1, \left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(z\right)\right)\right)\right) + \color{blue}{\left(\mathsf{neg}\left(\log z\right)\right)}\right)\right)\right) \]

   13. remove-double-neg N/A

       \[\leadsto \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(1, \left(z + \left(\mathsf{neg}\left(\color{blue}{\log z}\right)\right)\right)\right)\right) \]

   14. sub-neg N/A

       \[\leadsto \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(1, \left(z - \color{blue}{\log z}\right)\right)\right) \]

   15. --lowering--.f64 N/A

       \[\leadsto \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(1, \mathsf{\_.f64}\left(z, \color{blue}{\log z}\right)\right)\right) \]

   16. log-lowering-log.f64 56.0%

       \[\leadsto \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(1, \mathsf{\_.f64}\left(z, \mathsf{log.f64}\left(z\right)\right)\right)\right) \]

5. Simplified 56.0%

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

6. Taylor expanded in z around inf

   \[\leadsto \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(1, \color{blue}{z}\right)\right) \]
7. Step-by-step derivation

8. Simplified 33.9%

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

9. Taylor expanded in z around 0

   \[\leadsto \color{blue}{y} \]
10. Step-by-step derivation

11. Simplified 2.0%

    \[\leadsto \color{blue}{y} \]
12. 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 2024161 
(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)))))