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

Percentage Accurate: 100.0% → 100.0%

Time: 4.7s

Alternatives: 8

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, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

2. Final simplification 100.0%

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

Alternative 2: 60.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -8500000:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;y \leq -1.08 \cdot 10^{-187}:\\ \;\;\;\;z\\ \mathbf{elif}\;y \leq -5.6 \cdot 10^{-225}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;y \leq -2.8 \cdot 10^{-265}:\\ \;\;\;\;z\\ \mathbf{elif}\;y \leq 3.1 \cdot 10^{-232}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;y \leq 8.6 \cdot 10^{-138}:\\ \;\;\;\;z\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{-47}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;y \leq 3 \cdot 10^{+51}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -8500000.0)
   (* x y)
   (if (<= y -1.08e-187)
     z
     (if (<= y -5.6e-225)
       (* x 0.5)
       (if (<= y -2.8e-265)
         z
         (if (<= y 3.1e-232)
           (* x 0.5)
           (if (<= y 8.6e-138)
             z
             (if (<= y 7.5e-47) (* x 0.5) (if (<= y 3e+51) z (* x y))))))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -8500000.0) {
		tmp = x * y;
	} else if (y <= -1.08e-187) {
		tmp = z;
	} else if (y <= -5.6e-225) {
		tmp = x * 0.5;
	} else if (y <= -2.8e-265) {
		tmp = z;
	} else if (y <= 3.1e-232) {
		tmp = x * 0.5;
	} else if (y <= 8.6e-138) {
		tmp = z;
	} else if (y <= 7.5e-47) {
		tmp = x * 0.5;
	} else if (y <= 3e+51) {
		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 <= (-8500000.0d0)) then
        tmp = x * y
    else if (y <= (-1.08d-187)) then
        tmp = z
    else if (y <= (-5.6d-225)) then
        tmp = x * 0.5d0
    else if (y <= (-2.8d-265)) then
        tmp = z
    else if (y <= 3.1d-232) then
        tmp = x * 0.5d0
    else if (y <= 8.6d-138) then
        tmp = z
    else if (y <= 7.5d-47) then
        tmp = x * 0.5d0
    else if (y <= 3d+51) 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 <= -8500000.0) {
		tmp = x * y;
	} else if (y <= -1.08e-187) {
		tmp = z;
	} else if (y <= -5.6e-225) {
		tmp = x * 0.5;
	} else if (y <= -2.8e-265) {
		tmp = z;
	} else if (y <= 3.1e-232) {
		tmp = x * 0.5;
	} else if (y <= 8.6e-138) {
		tmp = z;
	} else if (y <= 7.5e-47) {
		tmp = x * 0.5;
	} else if (y <= 3e+51) {
		tmp = z;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -8500000.0:
		tmp = x * y
	elif y <= -1.08e-187:
		tmp = z
	elif y <= -5.6e-225:
		tmp = x * 0.5
	elif y <= -2.8e-265:
		tmp = z
	elif y <= 3.1e-232:
		tmp = x * 0.5
	elif y <= 8.6e-138:
		tmp = z
	elif y <= 7.5e-47:
		tmp = x * 0.5
	elif y <= 3e+51:
		tmp = z
	else:
		tmp = x * y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -8500000.0)
		tmp = Float64(x * y);
	elseif (y <= -1.08e-187)
		tmp = z;
	elseif (y <= -5.6e-225)
		tmp = Float64(x * 0.5);
	elseif (y <= -2.8e-265)
		tmp = z;
	elseif (y <= 3.1e-232)
		tmp = Float64(x * 0.5);
	elseif (y <= 8.6e-138)
		tmp = z;
	elseif (y <= 7.5e-47)
		tmp = Float64(x * 0.5);
	elseif (y <= 3e+51)
		tmp = z;
	else
		tmp = Float64(x * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -8500000.0)
		tmp = x * y;
	elseif (y <= -1.08e-187)
		tmp = z;
	elseif (y <= -5.6e-225)
		tmp = x * 0.5;
	elseif (y <= -2.8e-265)
		tmp = z;
	elseif (y <= 3.1e-232)
		tmp = x * 0.5;
	elseif (y <= 8.6e-138)
		tmp = z;
	elseif (y <= 7.5e-47)
		tmp = x * 0.5;
	elseif (y <= 3e+51)
		tmp = z;
	else
		tmp = x * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -8500000.0], N[(x * y), $MachinePrecision], If[LessEqual[y, -1.08e-187], z, If[LessEqual[y, -5.6e-225], N[(x * 0.5), $MachinePrecision], If[LessEqual[y, -2.8e-265], z, If[LessEqual[y, 3.1e-232], N[(x * 0.5), $MachinePrecision], If[LessEqual[y, 8.6e-138], z, If[LessEqual[y, 7.5e-47], N[(x * 0.5), $MachinePrecision], If[LessEqual[y, 3e+51], z, N[(x * y), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -8.5e6 or 3e51 < y

   1. Initial program 100.0%

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

      1. associate-+l+ 100.0%

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

      2. *-commutative 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around inf 77.2%

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

      1. +-commutative 77.2%

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

   6. Simplified 77.2%

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

   7. Taylor expanded in y around inf 76.6%

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

   if -8.5e6 < y < -1.08e-187 or -5.6e-225 < y < -2.80000000000000023e-265 or 3.0999999999999999e-232 < y < 8.6000000000000001e-138 or 7.49999999999999969e-47 < y < 3e51

   1. Initial program 100.0%

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

      1. +-commutative 100.0%

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

      2. remove-double-neg 100.0%

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

      3. distribute-neg-in 100.0%

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

      4. distribute-frac-neg 100.0%

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

      5. distribute-rgt-neg-out 100.0%

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

      6. unsub-neg 100.0%

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

      7. distribute-rgt-neg-out 100.0%

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

      8. unsub-neg 100.0%

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

      9. neg-mul-1 100.0%

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

      10. associate-/l* 99.9%

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

      11. associate-/r/ 100.0%

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

      12. distribute-rgt-out-- 100.0%

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

      13. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around inf 72.4%

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

      1. mul-1-neg 72.4%

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

      2. distribute-rgt-neg-out 72.4%

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

   6. Simplified 72.4%

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

   7. Taylor expanded in z around inf 68.3%

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

   if -1.08e-187 < y < -5.6e-225 or -2.80000000000000023e-265 < y < 3.0999999999999999e-232 or 8.6000000000000001e-138 < y < 7.49999999999999969e-47

   1. Initial program 100.0%

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

      1. associate-+l+ 100.0%

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

      2. *-commutative 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around inf 75.5%

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

      1. +-commutative 75.5%

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

   6. Simplified 75.5%

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

   7. Taylor expanded in y around 0 75.5%

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

      1. *-commutative 75.5%

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

   9. Simplified 75.5%

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

4. Final simplification 73.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8500000:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;y \leq -1.08 \cdot 10^{-187}:\\ \;\;\;\;z\\ \mathbf{elif}\;y \leq -5.6 \cdot 10^{-225}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;y \leq -2.8 \cdot 10^{-265}:\\ \;\;\;\;z\\ \mathbf{elif}\;y \leq 3.1 \cdot 10^{-232}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;y \leq 8.6 \cdot 10^{-138}:\\ \;\;\;\;z\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{-47}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;y \leq 3 \cdot 10^{+51}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]

Alternative 3: 84.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -6.8 \cdot 10^{+187} \lor \neg \left(x \leq 1100000000\right):\\ \;\;\;\;x \cdot \left(y + 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;z + x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -6.8e+187) (not (<= x 1100000000.0)))
   (* x (+ y 0.5))
   (+ z (* x y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -6.8e+187) || !(x <= 1100000000.0)) {
		tmp = x * (y + 0.5);
	} else {
		tmp = z + (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 ((x <= (-6.8d+187)) .or. (.not. (x <= 1100000000.0d0))) then
        tmp = x * (y + 0.5d0)
    else
        tmp = z + (x * y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -6.8e+187) || !(x <= 1100000000.0)) {
		tmp = x * (y + 0.5);
	} else {
		tmp = z + (x * y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -6.8e+187) or not (x <= 1100000000.0):
		tmp = x * (y + 0.5)
	else:
		tmp = z + (x * y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -6.8e+187) || !(x <= 1100000000.0))
		tmp = Float64(x * Float64(y + 0.5));
	else
		tmp = Float64(z + Float64(x * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -6.8e+187) || ~((x <= 1100000000.0)))
		tmp = x * (y + 0.5);
	else
		tmp = z + (x * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -6.8e+187], N[Not[LessEqual[x, 1100000000.0]], $MachinePrecision]], N[(x * N[(y + 0.5), $MachinePrecision]), $MachinePrecision], N[(z + N[(x * y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -6.7999999999999999e187 or 1.1e9 < x

   1. Initial program 100.0%

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

      1. associate-+l+ 100.0%

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

      2. *-commutative 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around inf 92.6%

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

      1. +-commutative 92.6%

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

   6. Simplified 92.6%

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

   if -6.7999999999999999e187 < x < 1.1e9

   1. Initial program 100.0%

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

      1. +-commutative 100.0%

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

      2. remove-double-neg 100.0%

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

      3. distribute-neg-in 100.0%

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

      4. distribute-frac-neg 100.0%

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

      5. distribute-rgt-neg-out 100.0%

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

      6. unsub-neg 100.0%

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

      7. distribute-rgt-neg-out 100.0%

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

      8. unsub-neg 100.0%

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

      9. neg-mul-1 100.0%

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

      10. associate-/l* 100.0%

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

      11. associate-/r/ 100.0%

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

      12. distribute-rgt-out-- 100.0%

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

      13. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around inf 87.3%

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

      1. mul-1-neg 87.3%

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

      2. distribute-rgt-neg-out 87.3%

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

   6. Simplified 87.3%

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

      1. *-commutative 87.3%

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

      2. cancel-sign-sub 87.3%

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

      3. *-commutative 87.3%

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

      4. +-commutative 87.3%

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

   8. Applied egg-rr 87.3%

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

4. Final simplification 89.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6.8 \cdot 10^{+187} \lor \neg \left(x \leq 1100000000\right):\\ \;\;\;\;x \cdot \left(y + 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;z + x \cdot y\\ \end{array} \]

Alternative 4: 99.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.9 \lor \neg \left(y \leq 0.5\right):\\ \;\;\;\;z + x \cdot y\\ \mathbf{else}:\\ \;\;\;\;z - x \cdot -0.5\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -3.9) (not (<= y 0.5))) (+ z (* x y)) (- z (* x -0.5))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -3.9) || !(y <= 0.5)) {
		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 <= (-3.9d0)) .or. (.not. (y <= 0.5d0))) 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 <= -3.9) || !(y <= 0.5)) {
		tmp = z + (x * y);
	} else {
		tmp = z - (x * -0.5);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -3.9) or not (y <= 0.5):
		tmp = z + (x * y)
	else:
		tmp = z - (x * -0.5)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -3.9) || !(y <= 0.5))
		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 <= -3.9) || ~((y <= 0.5)))
		tmp = z + (x * y);
	else
		tmp = z - (x * -0.5);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -3.9], N[Not[LessEqual[y, 0.5]], $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 < -3.89999999999999991 or 0.5 < y

   1. Initial program 100.0%

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

      1. +-commutative 100.0%

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

      2. remove-double-neg 100.0%

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

      3. distribute-neg-in 100.0%

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

      4. distribute-frac-neg 100.0%

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

      5. distribute-rgt-neg-out 100.0%

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

      6. unsub-neg 100.0%

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

      7. distribute-rgt-neg-out 100.0%

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

      8. unsub-neg 100.0%

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

      9. neg-mul-1 100.0%

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

      10. associate-/l* 100.0%

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

      11. associate-/r/ 100.0%

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

      12. distribute-rgt-out-- 100.0%

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

      13. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around inf 99.0%

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

      1. mul-1-neg 99.0%

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

      2. distribute-rgt-neg-out 99.0%

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

   6. Simplified 99.0%

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

      1. *-commutative 99.0%

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

      2. cancel-sign-sub 99.0%

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

      3. *-commutative 99.0%

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

      4. +-commutative 99.0%

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

   8. Applied egg-rr 99.0%

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

   if -3.89999999999999991 < y < 0.5

   1. Initial program 100.0%

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

      1. +-commutative 100.0%

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

      2. remove-double-neg 100.0%

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

      3. distribute-neg-in 100.0%

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

      4. distribute-frac-neg 100.0%

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

      5. distribute-rgt-neg-out 100.0%

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

      6. unsub-neg 100.0%

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

      7. distribute-rgt-neg-out 100.0%

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

      8. unsub-neg 100.0%

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

      9. neg-mul-1 100.0%

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

      10. associate-/l* 99.9%

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

      11. associate-/r/ 100.0%

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

      12. distribute-rgt-out-- 100.0%

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

      13. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around 0 99.3%

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

      1. *-commutative 99.3%

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

   6. Simplified 99.3%

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

4. Final simplification 99.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.9 \lor \neg \left(y \leq 0.5\right):\\ \;\;\;\;z + x \cdot y\\ \mathbf{else}:\\ \;\;\;\;z - x \cdot -0.5\\ \end{array} \]

Alternative 5: 73.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8 \cdot 10^{+49}:\\ \;\;\;\;z\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{+113}:\\ \;\;\;\;x \cdot \left(y + 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -8e+49) z (if (<= z 2.3e+113) (* x (+ y 0.5)) z)))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -8e+49) {
		tmp = z;
	} else if (z <= 2.3e+113) {
		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 (z <= (-8d+49)) then
        tmp = z
    else if (z <= 2.3d+113) 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 (z <= -8e+49) {
		tmp = z;
	} else if (z <= 2.3e+113) {
		tmp = x * (y + 0.5);
	} else {
		tmp = z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -8e+49:
		tmp = z
	elif z <= 2.3e+113:
		tmp = x * (y + 0.5)
	else:
		tmp = z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -8e+49)
		tmp = z;
	elseif (z <= 2.3e+113)
		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 (z <= -8e+49)
		tmp = z;
	elseif (z <= 2.3e+113)
		tmp = x * (y + 0.5);
	else
		tmp = z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -8e+49], z, If[LessEqual[z, 2.3e+113], N[(x * N[(y + 0.5), $MachinePrecision]), $MachinePrecision], z]]

Derivation

1. Split input into 2 regimes

2. if z < -7.99999999999999957e49 or 2.29999999999999997e113 < z

   1. Initial program 100.0%

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

      1. +-commutative 100.0%

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

      2. remove-double-neg 100.0%

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

      3. distribute-neg-in 100.0%

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

      4. distribute-frac-neg 100.0%

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

      5. distribute-rgt-neg-out 100.0%

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

      6. unsub-neg 100.0%

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

      7. distribute-rgt-neg-out 100.0%

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

      8. unsub-neg 100.0%

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

      9. neg-mul-1 100.0%

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

      10. associate-/l* 100.0%

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

      11. associate-/r/ 100.0%

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

      12. distribute-rgt-out-- 100.0%

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

      13. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around inf 92.2%

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

      1. mul-1-neg 92.2%

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

      2. distribute-rgt-neg-out 92.2%

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

   6. Simplified 92.2%

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

   7. Taylor expanded in z around inf 74.3%

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

   if -7.99999999999999957e49 < z < 2.29999999999999997e113

   1. Initial program 100.0%

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

      1. associate-+l+ 100.0%

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

      2. *-commutative 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around inf 80.1%

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

      1. +-commutative 80.1%

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

   6. Simplified 80.1%

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

4. Final simplification 78.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8 \cdot 10^{+49}:\\ \;\;\;\;z\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{+113}:\\ \;\;\;\;x \cdot \left(y + 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \]

Alternative 6: 50.0% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.12 \cdot 10^{+174} \lor \neg \left(x \leq 3.65 \cdot 10^{+22}\right):\\ \;\;\;\;x \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -1.12e+174) (not (<= x 3.65e+22))) (* x 0.5) z))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.12e+174) || !(x <= 3.65e+22)) {
		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 <= (-1.12d+174)) .or. (.not. (x <= 3.65d+22))) 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 <= -1.12e+174) || !(x <= 3.65e+22)) {
		tmp = x * 0.5;
	} else {
		tmp = z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -1.12e+174) or not (x <= 3.65e+22):
		tmp = x * 0.5
	else:
		tmp = z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -1.12e+174) || !(x <= 3.65e+22))
		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 <= -1.12e+174) || ~((x <= 3.65e+22)))
		tmp = x * 0.5;
	else
		tmp = z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -1.12e+174], N[Not[LessEqual[x, 3.65e+22]], $MachinePrecision]], N[(x * 0.5), $MachinePrecision], z]

Derivation

1. Split input into 2 regimes

2. if x < -1.11999999999999993e174 or 3.6499999999999999e22 < x

   1. Initial program 100.0%

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

      1. associate-+l+ 100.0%

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

      2. *-commutative 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around inf 92.8%

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

      1. +-commutative 92.8%

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

   6. Simplified 92.8%

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

   7. Taylor expanded in y around 0 45.1%

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

      1. *-commutative 45.1%

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

   9. Simplified 45.1%

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

   if -1.11999999999999993e174 < x < 3.6499999999999999e22

   1. Initial program 100.0%

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

      1. +-commutative 100.0%

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

      2. remove-double-neg 100.0%

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

      3. distribute-neg-in 100.0%

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

      4. distribute-frac-neg 100.0%

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

      5. distribute-rgt-neg-out 100.0%

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

      6. unsub-neg 100.0%

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

      7. distribute-rgt-neg-out 100.0%

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

      8. unsub-neg 100.0%

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

      9. neg-mul-1 100.0%

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

      10. associate-/l* 100.0%

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

      11. associate-/r/ 100.0%

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

      12. distribute-rgt-out-- 100.0%

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

      13. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around inf 87.0%

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

      1. mul-1-neg 87.0%

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

      2. distribute-rgt-neg-out 87.0%

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

   6. Simplified 87.0%

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

   7. Taylor expanded in z around inf 58.5%

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

4. Final simplification 53.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.12 \cdot 10^{+174} \lor \neg \left(x \leq 3.65 \cdot 10^{+22}\right):\\ \;\;\;\;x \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \]

Alternative 7: 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%

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

   2. remove-double-neg 100.0%

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

   3. distribute-neg-in 100.0%

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

   4. distribute-frac-neg 100.0%

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

   5. distribute-rgt-neg-out 100.0%

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

   6. unsub-neg 100.0%

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

   7. distribute-rgt-neg-out 100.0%

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

   8. unsub-neg 100.0%

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

   9. neg-mul-1 100.0%

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

   10. associate-/l* 100.0%

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

   11. associate-/r/ 100.0%

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

   12. distribute-rgt-out-- 100.0%

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

   13. metadata-eval 100.0%

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

3. Simplified 100.0%

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

4. Final simplification 100.0%

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

Alternative 8: 40.9% 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%

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

   2. remove-double-neg 100.0%

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

   3. distribute-neg-in 100.0%

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

   4. distribute-frac-neg 100.0%

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

   5. distribute-rgt-neg-out 100.0%

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

   6. unsub-neg 100.0%

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

   7. distribute-rgt-neg-out 100.0%

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

   8. unsub-neg 100.0%

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

   9. neg-mul-1 100.0%

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

   10. associate-/l* 100.0%

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

   11. associate-/r/ 100.0%

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

   12. distribute-rgt-out-- 100.0%

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

   13. metadata-eval 100.0%

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

3. Simplified 100.0%

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

4. Taylor expanded in y around inf 75.4%

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

   1. mul-1-neg 75.4%

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

   2. distribute-rgt-neg-out 75.4%

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

6. Simplified 75.4%

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

7. Taylor expanded in z around inf 39.3%

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

8. Final simplification 39.3%

   \[\leadsto z \]

Reproduce

herbie shell --seed 2023321 
(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))