Data.Histogram.Bin.BinF:$cfromIndex from histogram-fill-0.8.4.1

Percentage Accurate: 100.0% → 100.0%

Time: 5.5s

Alternatives: 9

Speedup: 1.0×

Specification

Math

\[\begin{array}{l} \\ \left(\frac{x}{2} + y \cdot x\right) + z \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (+ (+ (/ x 2.0) (* y x)) z))

C

double code(double x, double y, double z) {
	return ((x / 2.0) + (y * x)) + 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 / 2.0d0) + (y * x)) + z
end function

Java

public static double code(double x, double y, double z) {
	return ((x / 2.0) + (y * x)) + z;
}

Python

def code(x, y, z):
	return ((x / 2.0) + (y * x)) + z

Julia

function code(x, y, z)
	return Float64(Float64(Float64(x / 2.0) + Float64(y * x)) + z)
end

MATLAB

function tmp = code(x, y, z)
	tmp = ((x / 2.0) + (y * x)) + z;
end

Wolfram

code[x_, y_, z_] := N[(N[(N[(x / 2.0), $MachinePrecision] + N[(y * x), $MachinePrecision]), $MachinePrecision] + z), $MachinePrecision]

Initial Program: 100.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \left(\frac{x}{2} + y \cdot x\right) + z \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (+ (+ (/ x 2.0) (* y x)) z))

C

double code(double x, double y, double z) {
	return ((x / 2.0) + (y * x)) + 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 / 2.0d0) + (y * x)) + z
end function

Java

public static double code(double x, double y, double z) {
	return ((x / 2.0) + (y * x)) + z;
}

Python

def code(x, y, z):
	return ((x / 2.0) + (y * x)) + z

Julia

function code(x, y, z)
	return Float64(Float64(Float64(x / 2.0) + Float64(y * x)) + z)
end

MATLAB

function tmp = code(x, y, z)
	tmp = ((x / 2.0) + (y * x)) + z;
end

Wolfram

code[x_, y_, z_] := N[(N[(N[(x / 2.0), $MachinePrecision] + N[(y * x), $MachinePrecision]), $MachinePrecision] + z), $MachinePrecision]

Alternative 1: 100.0% accurate, 0.1× speedup

Math

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

FPCore

(FPCore (x y z) :precision binary64 (fma x (+ y 0.5) z))

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

   1. +-commutative 100.0%

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

   2. remove-double-neg 100.0%

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

   3. distribute-frac-neg 100.0%

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

   4. sub-neg 100.0%

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

   5. neg-mul-1 100.0%

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

   6. *-commutative 100.0%

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

   7. associate-/l* 100.0%

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

   8. *-commutative 100.0%

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

   9. distribute-rgt-out-- 100.0%

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

   10. fma-define 100.0%

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

   11. sub-neg 100.0%

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

   12. metadata-eval 100.0%

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

   13. metadata-eval 100.0%

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

3. Simplified 100.0%

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

5. Final simplification 100.0%

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

Alternative 2: 60.7% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3 \cdot 10^{+23}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;y \leq -6 \cdot 10^{-96}:\\ \;\;\;\;z\\ \mathbf{elif}\;y \leq -1.25 \cdot 10^{-136}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;y \leq 3.15 \cdot 10^{-299}:\\ \;\;\;\;z\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{-282}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;y \leq 2.95 \cdot 10^{-235}:\\ \;\;\;\;z\\ \mathbf{elif}\;y \leq 2.7 \cdot 10^{-178}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;y \leq 4.3 \cdot 10^{-155}:\\ \;\;\;\;z\\ \mathbf{elif}\;y \leq 7.4 \cdot 10^{-92}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;y \leq 1.5 \cdot 10^{+34}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -3e+23)
   (* x y)
   (if (<= y -6e-96)
     z
     (if (<= y -1.25e-136)
       (* x 0.5)
       (if (<= y 3.15e-299)
         z
         (if (<= y 3.2e-282)
           (* x 0.5)
           (if (<= y 2.95e-235)
             z
             (if (<= y 2.7e-178)
               (* x 0.5)
               (if (<= y 4.3e-155)
                 z
                 (if (<= y 7.4e-92)
                   (* x 0.5)
                   (if (<= y 1.5e+34) z (* x y))))))))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -3e+23) {
		tmp = x * y;
	} else if (y <= -6e-96) {
		tmp = z;
	} else if (y <= -1.25e-136) {
		tmp = x * 0.5;
	} else if (y <= 3.15e-299) {
		tmp = z;
	} else if (y <= 3.2e-282) {
		tmp = x * 0.5;
	} else if (y <= 2.95e-235) {
		tmp = z;
	} else if (y <= 2.7e-178) {
		tmp = x * 0.5;
	} else if (y <= 4.3e-155) {
		tmp = z;
	} else if (y <= 7.4e-92) {
		tmp = x * 0.5;
	} else if (y <= 1.5e+34) {
		tmp = z;
	} else {
		tmp = x * y;
	}
	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 <= (-3d+23)) then
        tmp = x * y
    else if (y <= (-6d-96)) then
        tmp = z
    else if (y <= (-1.25d-136)) then
        tmp = x * 0.5d0
    else if (y <= 3.15d-299) then
        tmp = z
    else if (y <= 3.2d-282) then
        tmp = x * 0.5d0
    else if (y <= 2.95d-235) then
        tmp = z
    else if (y <= 2.7d-178) then
        tmp = x * 0.5d0
    else if (y <= 4.3d-155) then
        tmp = z
    else if (y <= 7.4d-92) then
        tmp = x * 0.5d0
    else if (y <= 1.5d+34) then
        tmp = z
    else
        tmp = x * y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -3e+23) {
		tmp = x * y;
	} else if (y <= -6e-96) {
		tmp = z;
	} else if (y <= -1.25e-136) {
		tmp = x * 0.5;
	} else if (y <= 3.15e-299) {
		tmp = z;
	} else if (y <= 3.2e-282) {
		tmp = x * 0.5;
	} else if (y <= 2.95e-235) {
		tmp = z;
	} else if (y <= 2.7e-178) {
		tmp = x * 0.5;
	} else if (y <= 4.3e-155) {
		tmp = z;
	} else if (y <= 7.4e-92) {
		tmp = x * 0.5;
	} else if (y <= 1.5e+34) {
		tmp = z;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -3e+23:
		tmp = x * y
	elif y <= -6e-96:
		tmp = z
	elif y <= -1.25e-136:
		tmp = x * 0.5
	elif y <= 3.15e-299:
		tmp = z
	elif y <= 3.2e-282:
		tmp = x * 0.5
	elif y <= 2.95e-235:
		tmp = z
	elif y <= 2.7e-178:
		tmp = x * 0.5
	elif y <= 4.3e-155:
		tmp = z
	elif y <= 7.4e-92:
		tmp = x * 0.5
	elif y <= 1.5e+34:
		tmp = z
	else:
		tmp = x * y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -3e+23)
		tmp = Float64(x * y);
	elseif (y <= -6e-96)
		tmp = z;
	elseif (y <= -1.25e-136)
		tmp = Float64(x * 0.5);
	elseif (y <= 3.15e-299)
		tmp = z;
	elseif (y <= 3.2e-282)
		tmp = Float64(x * 0.5);
	elseif (y <= 2.95e-235)
		tmp = z;
	elseif (y <= 2.7e-178)
		tmp = Float64(x * 0.5);
	elseif (y <= 4.3e-155)
		tmp = z;
	elseif (y <= 7.4e-92)
		tmp = Float64(x * 0.5);
	elseif (y <= 1.5e+34)
		tmp = z;
	else
		tmp = Float64(x * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -3e+23)
		tmp = x * y;
	elseif (y <= -6e-96)
		tmp = z;
	elseif (y <= -1.25e-136)
		tmp = x * 0.5;
	elseif (y <= 3.15e-299)
		tmp = z;
	elseif (y <= 3.2e-282)
		tmp = x * 0.5;
	elseif (y <= 2.95e-235)
		tmp = z;
	elseif (y <= 2.7e-178)
		tmp = x * 0.5;
	elseif (y <= 4.3e-155)
		tmp = z;
	elseif (y <= 7.4e-92)
		tmp = x * 0.5;
	elseif (y <= 1.5e+34)
		tmp = z;
	else
		tmp = x * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -3e+23], N[(x * y), $MachinePrecision], If[LessEqual[y, -6e-96], z, If[LessEqual[y, -1.25e-136], N[(x * 0.5), $MachinePrecision], If[LessEqual[y, 3.15e-299], z, If[LessEqual[y, 3.2e-282], N[(x * 0.5), $MachinePrecision], If[LessEqual[y, 2.95e-235], z, If[LessEqual[y, 2.7e-178], N[(x * 0.5), $MachinePrecision], If[LessEqual[y, 4.3e-155], z, If[LessEqual[y, 7.4e-92], N[(x * 0.5), $MachinePrecision], If[LessEqual[y, 1.5e+34], z, N[(x * y), $MachinePrecision]]]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.0000000000000001e23 or 1.50000000000000009e34 < y

   1. Initial program 100.0%

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

      1. +-commutative 100.0%

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

      2. remove-double-neg 100.0%

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

      3. distribute-frac-neg 100.0%

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

      4. sub-neg 100.0%

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

      5. neg-mul-1 100.0%

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

      6. *-commutative 100.0%

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

      7. associate-/l* 100.0%

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

      8. *-commutative 100.0%

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

      9. distribute-rgt-out-- 100.0%

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

      10. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in x around inf 89.5%

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

      1. associate-+r+ 89.5%

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

   7. Simplified 89.5%

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

   8. Taylor expanded in y around inf 77.2%

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

   if -3.0000000000000001e23 < y < -6e-96 or -1.25e-136 < y < 3.14999999999999976e-299 or 3.19999999999999983e-282 < y < 2.9500000000000002e-235 or 2.70000000000000009e-178 < y < 4.30000000000000008e-155 or 7.39999999999999954e-92 < y < 1.50000000000000009e34

   1. Initial program 100.0%

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

      1. +-commutative 100.0%

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

      2. remove-double-neg 100.0%

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

      3. distribute-frac-neg 100.0%

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

      4. sub-neg 100.0%

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

      5. neg-mul-1 100.0%

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

      6. *-commutative 100.0%

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

      7. associate-/l* 100.0%

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

      8. *-commutative 100.0%

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

      9. distribute-rgt-out-- 100.0%

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

      10. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in x around 0 70.9%

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

   if -6e-96 < y < -1.25e-136 or 3.14999999999999976e-299 < y < 3.19999999999999983e-282 or 2.9500000000000002e-235 < y < 2.70000000000000009e-178 or 4.30000000000000008e-155 < y < 7.39999999999999954e-92

   1. Initial program 100.0%

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

      1. +-commutative 100.0%

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

      2. remove-double-neg 100.0%

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

      3. distribute-frac-neg 100.0%

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

      4. sub-neg 100.0%

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

      5. neg-mul-1 100.0%

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

      6. *-commutative 100.0%

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

      7. associate-/l* 100.0%

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

      8. *-commutative 100.0%

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

      9. distribute-rgt-out-- 100.0%

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

      10. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in x around inf 92.0%

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

      1. associate-+r+ 92.0%

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

   7. Simplified 92.0%

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

   8. Taylor expanded in x around inf 75.5%

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

   9. Taylor expanded in y around 0 75.5%

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

4. Final simplification 74.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3 \cdot 10^{+23}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;y \leq -6 \cdot 10^{-96}:\\ \;\;\;\;z\\ \mathbf{elif}\;y \leq -1.25 \cdot 10^{-136}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;y \leq 3.15 \cdot 10^{-299}:\\ \;\;\;\;z\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{-282}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;y \leq 2.95 \cdot 10^{-235}:\\ \;\;\;\;z\\ \mathbf{elif}\;y \leq 2.7 \cdot 10^{-178}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;y \leq 4.3 \cdot 10^{-155}:\\ \;\;\;\;z\\ \mathbf{elif}\;y \leq 7.4 \cdot 10^{-92}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;y \leq 1.5 \cdot 10^{+34}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 74.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.4 \cdot 10^{-73} \lor \neg \left(x \leq 9.4 \cdot 10^{-51}\right):\\ \;\;\;\;x \cdot \left(y + 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -3.4e-73) (not (<= x 9.4e-51))) (* x (+ y 0.5)) z))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -3.4e-73) || !(x <= 9.4e-51)) {
		tmp = x * (y + 0.5);
	} else {
		tmp = z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((x <= (-3.4d-73)) .or. (.not. (x <= 9.4d-51))) then
        tmp = x * (y + 0.5d0)
    else
        tmp = z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -3.4e-73) || !(x <= 9.4e-51)) {
		tmp = x * (y + 0.5);
	} else {
		tmp = z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -3.4e-73) or not (x <= 9.4e-51):
		tmp = x * (y + 0.5)
	else:
		tmp = z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -3.4e-73) || !(x <= 9.4e-51))
		tmp = Float64(x * Float64(y + 0.5));
	else
		tmp = z;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -3.4e-73) || ~((x <= 9.4e-51)))
		tmp = x * (y + 0.5);
	else
		tmp = z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -3.4e-73], N[Not[LessEqual[x, 9.4e-51]], $MachinePrecision]], N[(x * N[(y + 0.5), $MachinePrecision]), $MachinePrecision], z]

Derivation

1. Split input into 2 regimes

2. if x < -3.40000000000000021e-73 or 9.3999999999999995e-51 < x

   1. Initial program 100.0%

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

      1. +-commutative 100.0%

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

      2. remove-double-neg 100.0%

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

      3. distribute-frac-neg 100.0%

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

      4. sub-neg 100.0%

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

      5. neg-mul-1 100.0%

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

      6. *-commutative 100.0%

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

      7. associate-/l* 100.0%

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

      8. *-commutative 100.0%

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

      9. distribute-rgt-out-- 100.0%

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

      10. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in x around inf 99.4%

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

      1. associate-+r+ 99.4%

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

   7. Simplified 99.4%

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

   8. Taylor expanded in x around inf 79.8%

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

   if -3.40000000000000021e-73 < x < 9.3999999999999995e-51

   1. Initial program 100.0%

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

      1. +-commutative 100.0%

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

      2. remove-double-neg 100.0%

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

      3. distribute-frac-neg 100.0%

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

      4. sub-neg 100.0%

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

      5. neg-mul-1 100.0%

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

      6. *-commutative 100.0%

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

      7. associate-/l* 100.0%

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

      8. *-commutative 100.0%

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

      9. distribute-rgt-out-- 100.0%

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

      10. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in x around 0 71.1%

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

4. Final simplification 76.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.4 \cdot 10^{-73} \lor \neg \left(x \leq 9.4 \cdot 10^{-51}\right):\\ \;\;\;\;x \cdot \left(y + 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 98.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -0.5 \lor \neg \left(y \leq 0.00088\right):\\ \;\;\;\;z + x \cdot y\\ \mathbf{else}:\\ \;\;\;\;z + x \cdot 0.5\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -0.5) (not (<= y 0.00088))) (+ z (* x y)) (+ z (* x 0.5))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -0.5) || !(y <= 0.00088)) {
		tmp = z + (x * y);
	} else {
		tmp = z + (x * 0.5);
	}
	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 <= (-0.5d0)) .or. (.not. (y <= 0.00088d0))) then
        tmp = z + (x * y)
    else
        tmp = z + (x * 0.5d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -0.5) || !(y <= 0.00088)) {
		tmp = z + (x * y);
	} else {
		tmp = z + (x * 0.5);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -0.5) or not (y <= 0.00088):
		tmp = z + (x * y)
	else:
		tmp = z + (x * 0.5)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -0.5) || !(y <= 0.00088))
		tmp = Float64(z + Float64(x * y));
	else
		tmp = Float64(z + Float64(x * 0.5));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -0.5) || ~((y <= 0.00088)))
		tmp = z + (x * y);
	else
		tmp = z + (x * 0.5);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -0.5], N[Not[LessEqual[y, 0.00088]], $MachinePrecision]], N[(z + N[(x * y), $MachinePrecision]), $MachinePrecision], N[(z + N[(x * 0.5), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -0.5 or 8.80000000000000031e-4 < y

   1. Initial program 100.0%

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

      1. +-commutative 100.0%

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

      2. remove-double-neg 100.0%

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

      3. distribute-frac-neg 100.0%

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

      4. sub-neg 100.0%

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

      5. neg-mul-1 100.0%

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

      6. *-commutative 100.0%

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

      7. associate-/l* 100.0%

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

      8. *-commutative 100.0%

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

      9. distribute-rgt-out-- 100.0%

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

      10. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around inf 99.6%

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

   if -0.5 < y < 8.80000000000000031e-4

   1. Initial program 100.0%

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

      1. +-commutative 100.0%

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

      2. remove-double-neg 100.0%

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

      3. distribute-frac-neg 100.0%

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

      4. sub-neg 100.0%

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

      5. neg-mul-1 100.0%

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

      6. *-commutative 100.0%

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

      7. associate-/l* 100.0%

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

      8. *-commutative 100.0%

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

      9. distribute-rgt-out-- 100.0%

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

      10. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around 0 99.5%

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

      1. *-commutative 99.5%

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

   7. Simplified 99.5%

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

4. Final simplification 99.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.5 \lor \neg \left(y \leq 0.00088\right):\\ \;\;\;\;z + x \cdot y\\ \mathbf{else}:\\ \;\;\;\;z + x \cdot 0.5\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 84.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.9 \cdot 10^{+23}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;y \leq 3.8 \cdot 10^{+33}:\\ \;\;\;\;z + x \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y + 0.5\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -3.9e+23)
   (* x y)
   (if (<= y 3.8e+33) (+ z (* x 0.5)) (* x (+ y 0.5)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -3.9e+23) {
		tmp = x * y;
	} else if (y <= 3.8e+33) {
		tmp = z + (x * 0.5);
	} else {
		tmp = x * (y + 0.5);
	}
	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 <= (-3.9d+23)) then
        tmp = x * y
    else if (y <= 3.8d+33) then
        tmp = z + (x * 0.5d0)
    else
        tmp = x * (y + 0.5d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -3.9e+23) {
		tmp = x * y;
	} else if (y <= 3.8e+33) {
		tmp = z + (x * 0.5);
	} else {
		tmp = x * (y + 0.5);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -3.9e+23:
		tmp = x * y
	elif y <= 3.8e+33:
		tmp = z + (x * 0.5)
	else:
		tmp = x * (y + 0.5)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -3.9e+23)
		tmp = Float64(x * y);
	elseif (y <= 3.8e+33)
		tmp = Float64(z + Float64(x * 0.5));
	else
		tmp = Float64(x * Float64(y + 0.5));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -3.9e+23)
		tmp = x * y;
	elseif (y <= 3.8e+33)
		tmp = z + (x * 0.5);
	else
		tmp = x * (y + 0.5);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -3.9e+23], N[(x * y), $MachinePrecision], If[LessEqual[y, 3.8e+33], N[(z + N[(x * 0.5), $MachinePrecision]), $MachinePrecision], N[(x * N[(y + 0.5), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.9e23

   1. Initial program 99.9%

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

      1. +-commutative 99.9%

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

      2. remove-double-neg 99.9%

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

      3. distribute-frac-neg 99.9%

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

      4. sub-neg 99.9%

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

      5. neg-mul-1 99.9%

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

      6. *-commutative 99.9%

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

      7. associate-/l* 99.9%

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

      8. *-commutative 99.9%

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

      9. distribute-rgt-out-- 99.9%

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

      10. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in x around inf 88.8%

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

      1. associate-+r+ 88.8%

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

   7. Simplified 88.8%

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

   8. Taylor expanded in y around inf 78.6%

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

   if -3.9e23 < y < 3.80000000000000002e33

   1. Initial program 100.0%

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

      1. +-commutative 100.0%

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

      2. remove-double-neg 100.0%

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

      3. distribute-frac-neg 100.0%

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

      4. sub-neg 100.0%

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

      5. neg-mul-1 100.0%

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

      6. *-commutative 100.0%

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

      7. associate-/l* 100.0%

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

      8. *-commutative 100.0%

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

      9. distribute-rgt-out-- 100.0%

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

      10. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around 0 98.8%

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

      1. *-commutative 98.8%

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

   7. Simplified 98.8%

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

   if 3.80000000000000002e33 < y

   1. Initial program 100.0%

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

      1. +-commutative 100.0%

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

      2. remove-double-neg 100.0%

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

      3. distribute-frac-neg 100.0%

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

      4. sub-neg 100.0%

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

      5. neg-mul-1 100.0%

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

      6. *-commutative 100.0%

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

      7. associate-/l* 100.0%

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

      8. *-commutative 100.0%

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

      9. distribute-rgt-out-- 100.0%

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

      10. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in x around inf 90.3%

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

      1. associate-+r+ 90.3%

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

   7. Simplified 90.3%

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

   8. Taylor expanded in x around inf 75.7%

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

4. Final simplification 88.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.9 \cdot 10^{+23}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;y \leq 3.8 \cdot 10^{+33}:\\ \;\;\;\;z + x \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y + 0.5\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 50.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.9 \cdot 10^{+111} \lor \neg \left(x \leq 8.2 \cdot 10^{+95}\right):\\ \;\;\;\;x \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -1.9e+111) (not (<= x 8.2e+95))) (* x 0.5) z))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.9e+111) || !(x <= 8.2e+95)) {
		tmp = x * 0.5;
	} else {
		tmp = z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((x <= (-1.9d+111)) .or. (.not. (x <= 8.2d+95))) then
        tmp = x * 0.5d0
    else
        tmp = z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.9e+111) || !(x <= 8.2e+95)) {
		tmp = x * 0.5;
	} else {
		tmp = z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -1.9e+111) or not (x <= 8.2e+95):
		tmp = x * 0.5
	else:
		tmp = z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -1.9e+111) || !(x <= 8.2e+95))
		tmp = Float64(x * 0.5);
	else
		tmp = z;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -1.9e+111) || ~((x <= 8.2e+95)))
		tmp = x * 0.5;
	else
		tmp = z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -1.9e+111], N[Not[LessEqual[x, 8.2e+95]], $MachinePrecision]], N[(x * 0.5), $MachinePrecision], z]

Derivation

1. Split input into 2 regimes

2. if x < -1.89999999999999988e111 or 8.19999999999999972e95 < x

   1. Initial program 100.0%

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

      1. +-commutative 100.0%

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

      2. remove-double-neg 100.0%

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

      3. distribute-frac-neg 100.0%

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

      4. sub-neg 100.0%

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

      5. neg-mul-1 100.0%

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

      6. *-commutative 100.0%

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

      7. associate-/l* 100.0%

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

      8. *-commutative 100.0%

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

      9. distribute-rgt-out-- 100.0%

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

      10. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in x around inf 100.0%

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

      1. associate-+r+ 100.0%

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

   7. Simplified 100.0%

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

   8. Taylor expanded in x around inf 92.0%

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

   9. Taylor expanded in y around 0 48.3%

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

   if -1.89999999999999988e111 < x < 8.19999999999999972e95

   1. Initial program 100.0%

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

      1. +-commutative 100.0%

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

      2. remove-double-neg 100.0%

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

      3. distribute-frac-neg 100.0%

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

      4. sub-neg 100.0%

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

      5. neg-mul-1 100.0%

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

      6. *-commutative 100.0%

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

      7. associate-/l* 100.0%

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

      8. *-commutative 100.0%

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

      9. distribute-rgt-out-- 100.0%

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

      10. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in x around 0 55.9%

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

4. Final simplification 53.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.9 \cdot 10^{+111} \lor \neg \left(x \leq 8.2 \cdot 10^{+95}\right):\\ \;\;\;\;x \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 100.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ z + \left(\frac{x}{2} + x \cdot y\right) \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (+ z (+ (/ x 2.0) (* x y))))

C

double code(double x, double y, double z) {
	return z + ((x / 2.0) + (x * 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 = z + ((x / 2.0d0) + (x * y))
end function

Java

public static double code(double x, double y, double z) {
	return z + ((x / 2.0) + (x * y));
}

Python

def code(x, y, z):
	return z + ((x / 2.0) + (x * y))

Julia

function code(x, y, z)
	return Float64(z + Float64(Float64(x / 2.0) + Float64(x * y)))
end

MATLAB

function tmp = code(x, y, z)
	tmp = z + ((x / 2.0) + (x * y));
end

Wolfram

code[x_, y_, z_] := N[(z + N[(N[(x / 2.0), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 100.0%

   \[\left(\frac{x}{2} + y \cdot x\right) + z \]
2. Add Preprocessing

3. Final simplification 100.0%

   \[\leadsto z + \left(\frac{x}{2} + x \cdot y\right) \]
4. Add Preprocessing

Alternative 8: 100.0% accurate, 1.3× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

   1. +-commutative 100.0%

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

   2. remove-double-neg 100.0%

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

   3. distribute-frac-neg 100.0%

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

   4. sub-neg 100.0%

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

   5. neg-mul-1 100.0%

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

   6. *-commutative 100.0%

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

   7. associate-/l* 100.0%

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

   8. *-commutative 100.0%

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

   9. distribute-rgt-out-- 100.0%

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

   10. metadata-eval 100.0%

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

3. Simplified 100.0%

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

5. Final simplification 100.0%

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

Alternative 9: 40.3% accurate, 9.0× speedup

Math

\[\begin{array}{l} \\ z \end{array} \]

FPCore

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

C

double code(double x, double y, double z) {
	return 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 = z
end function

Java

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

Python

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

Julia

function code(x, y, z)
	return z
end

MATLAB

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

Wolfram

code[x_, y_, z_] := z

Derivation

1. Initial program 100.0%

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

   1. +-commutative 100.0%

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

   2. remove-double-neg 100.0%

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

   3. distribute-frac-neg 100.0%

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

   4. sub-neg 100.0%

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

   5. neg-mul-1 100.0%

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

   6. *-commutative 100.0%

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

   7. associate-/l* 100.0%

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

   8. *-commutative 100.0%

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

   9. distribute-rgt-out-- 100.0%

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

   10. metadata-eval 100.0%

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

3. Simplified 100.0%

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

5. Taylor expanded in x around 0 40.0%

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

6. Final simplification 40.0%

   \[\leadsto z \]
7. Add Preprocessing

Reproduce

herbie shell --seed 2024096 
(FPCore (x y z)
  :name "Data.Histogram.Bin.BinF:$cfromIndex from histogram-fill-0.8.4.1"
  :precision binary64
  (+ (+ (/ x 2.0) (* y x)) z))