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

Percentage Accurate: 100.0% → 100.0%

Time: 2.8s

Alternatives: 7

Speedup: N/A×

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, 1.3× speedup

Math

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

FPCore

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

C

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

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 + ((0.5d0 + y) * x)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

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 0 100.0%

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

5. Final simplification 100.0%

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

Alternative 2: 59.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6 \cdot 10^{+64}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq -3.8 \cdot 10^{-126}:\\ \;\;\;\;z\\ \mathbf{elif}\;y \leq -5.7 \cdot 10^{-241}:\\ \;\;\;\;0.5 \cdot x\\ \mathbf{elif}\;y \leq 5.8 \cdot 10^{-223}:\\ \;\;\;\;z\\ \mathbf{elif}\;y \leq 4.1 \cdot 10^{-52}:\\ \;\;\;\;0.5 \cdot x\\ \mathbf{elif}\;y \leq 8.2 \cdot 10^{+52}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -6e+64)
   (* y x)
   (if (<= y -3.8e-126)
     z
     (if (<= y -5.7e-241)
       (* 0.5 x)
       (if (<= y 5.8e-223)
         z
         (if (<= y 4.1e-52) (* 0.5 x) (if (<= y 8.2e+52) z (* y x))))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -6e+64) {
		tmp = y * x;
	} else if (y <= -3.8e-126) {
		tmp = z;
	} else if (y <= -5.7e-241) {
		tmp = 0.5 * x;
	} else if (y <= 5.8e-223) {
		tmp = z;
	} else if (y <= 4.1e-52) {
		tmp = 0.5 * x;
	} else if (y <= 8.2e+52) {
		tmp = z;
	} else {
		tmp = y * x;
	}
	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 <= (-6d+64)) then
        tmp = y * x
    else if (y <= (-3.8d-126)) then
        tmp = z
    else if (y <= (-5.7d-241)) then
        tmp = 0.5d0 * x
    else if (y <= 5.8d-223) then
        tmp = z
    else if (y <= 4.1d-52) then
        tmp = 0.5d0 * x
    else if (y <= 8.2d+52) then
        tmp = z
    else
        tmp = y * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -6e+64) {
		tmp = y * x;
	} else if (y <= -3.8e-126) {
		tmp = z;
	} else if (y <= -5.7e-241) {
		tmp = 0.5 * x;
	} else if (y <= 5.8e-223) {
		tmp = z;
	} else if (y <= 4.1e-52) {
		tmp = 0.5 * x;
	} else if (y <= 8.2e+52) {
		tmp = z;
	} else {
		tmp = y * x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -6e+64:
		tmp = y * x
	elif y <= -3.8e-126:
		tmp = z
	elif y <= -5.7e-241:
		tmp = 0.5 * x
	elif y <= 5.8e-223:
		tmp = z
	elif y <= 4.1e-52:
		tmp = 0.5 * x
	elif y <= 8.2e+52:
		tmp = z
	else:
		tmp = y * x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -6e+64)
		tmp = Float64(y * x);
	elseif (y <= -3.8e-126)
		tmp = z;
	elseif (y <= -5.7e-241)
		tmp = Float64(0.5 * x);
	elseif (y <= 5.8e-223)
		tmp = z;
	elseif (y <= 4.1e-52)
		tmp = Float64(0.5 * x);
	elseif (y <= 8.2e+52)
		tmp = z;
	else
		tmp = Float64(y * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -6e+64)
		tmp = y * x;
	elseif (y <= -3.8e-126)
		tmp = z;
	elseif (y <= -5.7e-241)
		tmp = 0.5 * x;
	elseif (y <= 5.8e-223)
		tmp = z;
	elseif (y <= 4.1e-52)
		tmp = 0.5 * x;
	elseif (y <= 8.2e+52)
		tmp = z;
	else
		tmp = y * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -6e+64], N[(y * x), $MachinePrecision], If[LessEqual[y, -3.8e-126], z, If[LessEqual[y, -5.7e-241], N[(0.5 * x), $MachinePrecision], If[LessEqual[y, 5.8e-223], z, If[LessEqual[y, 4.1e-52], N[(0.5 * x), $MachinePrecision], If[LessEqual[y, 8.2e+52], z, N[(y * x), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -6.0000000000000004e64 or 8.1999999999999999e52 < 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 y around inf 76.2%

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

   if -6.0000000000000004e64 < y < -3.7999999999999999e-126 or -5.6999999999999998e-241 < y < 5.8000000000000001e-223 or 4.09999999999999988e-52 < y < 8.1999999999999999e52

   1. Initial program 99.9%

      \[\left(\frac{x}{2} + y \cdot x\right) + z \]
   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 0 63.8%

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

   if -3.7999999999999999e-126 < y < -5.6999999999999998e-241 or 5.8000000000000001e-223 < y < 4.09999999999999988e-52

   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 63.2%

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

   5. Taylor expanded in y around 0 63.2%

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

4. Final simplification 68.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6 \cdot 10^{+64}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq -3.8 \cdot 10^{-126}:\\ \;\;\;\;z\\ \mathbf{elif}\;y \leq -5.7 \cdot 10^{-241}:\\ \;\;\;\;0.5 \cdot x\\ \mathbf{elif}\;y \leq 5.8 \cdot 10^{-223}:\\ \;\;\;\;z\\ \mathbf{elif}\;y \leq 4.1 \cdot 10^{-52}:\\ \;\;\;\;0.5 \cdot x\\ \mathbf{elif}\;y \leq 8.2 \cdot 10^{+52}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \]

Alternative 3: 71.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.3 \cdot 10^{+177}:\\ \;\;\;\;z\\ \mathbf{elif}\;z \leq -9.5 \cdot 10^{+113} \lor \neg \left(z \leq -9.5 \cdot 10^{-15}\right) \land z \leq 3.8 \cdot 10^{+42}:\\ \;\;\;\;\left(0.5 + y\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -5.3e+177)
   z
   (if (or (<= z -9.5e+113) (and (not (<= z -9.5e-15)) (<= z 3.8e+42)))
     (* (+ 0.5 y) x)
     z)))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -5.3e+177) {
		tmp = z;
	} else if ((z <= -9.5e+113) || (!(z <= -9.5e-15) && (z <= 3.8e+42))) {
		tmp = (0.5 + y) * x;
	} 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 <= (-5.3d+177)) then
        tmp = z
    else if ((z <= (-9.5d+113)) .or. (.not. (z <= (-9.5d-15))) .and. (z <= 3.8d+42)) then
        tmp = (0.5d0 + y) * x
    else
        tmp = z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -5.3e+177) {
		tmp = z;
	} else if ((z <= -9.5e+113) || (!(z <= -9.5e-15) && (z <= 3.8e+42))) {
		tmp = (0.5 + y) * x;
	} else {
		tmp = z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -5.3e+177:
		tmp = z
	elif (z <= -9.5e+113) or (not (z <= -9.5e-15) and (z <= 3.8e+42)):
		tmp = (0.5 + y) * x
	else:
		tmp = z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -5.3e+177)
		tmp = z;
	elseif ((z <= -9.5e+113) || (!(z <= -9.5e-15) && (z <= 3.8e+42)))
		tmp = Float64(Float64(0.5 + y) * x);
	else
		tmp = z;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -5.3e+177)
		tmp = z;
	elseif ((z <= -9.5e+113) || (~((z <= -9.5e-15)) && (z <= 3.8e+42)))
		tmp = (0.5 + y) * x;
	else
		tmp = z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -5.3e+177], z, If[Or[LessEqual[z, -9.5e+113], And[N[Not[LessEqual[z, -9.5e-15]], $MachinePrecision], LessEqual[z, 3.8e+42]]], N[(N[(0.5 + y), $MachinePrecision] * x), $MachinePrecision], z]]

Derivation

1. Split input into 2 regimes

2. if z < -5.2999999999999997e177 or -9.5000000000000001e113 < z < -9.5000000000000005e-15 or 3.7999999999999998e42 < z

   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 0 74.3%

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

   if -5.2999999999999997e177 < z < -9.5000000000000001e113 or -9.5000000000000005e-15 < z < 3.7999999999999998e42

   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 85.1%

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

4. Final simplification 80.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.3 \cdot 10^{+177}:\\ \;\;\;\;z\\ \mathbf{elif}\;z \leq -9.5 \cdot 10^{+113} \lor \neg \left(z \leq -9.5 \cdot 10^{-15}\right) \land z \leq 3.8 \cdot 10^{+42}:\\ \;\;\;\;\left(0.5 + y\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \]

Alternative 4: 85.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -9.5 \cdot 10^{+44} \lor \neg \left(x \leq 1.8 \cdot 10^{+62}\right):\\ \;\;\;\;\left(0.5 + y\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;z + y \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -9.5e+44) (not (<= x 1.8e+62))) (* (+ 0.5 y) x) (+ z (* y x))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -9.5e+44) || !(x <= 1.8e+62)) {
		tmp = (0.5 + y) * x;
	} else {
		tmp = z + (y * x);
	}
	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 <= (-9.5d+44)) .or. (.not. (x <= 1.8d+62))) then
        tmp = (0.5d0 + y) * x
    else
        tmp = z + (y * x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -9.5e+44) || !(x <= 1.8e+62)) {
		tmp = (0.5 + y) * x;
	} else {
		tmp = z + (y * x);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -9.5e+44) or not (x <= 1.8e+62):
		tmp = (0.5 + y) * x
	else:
		tmp = z + (y * x)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -9.5e+44) || !(x <= 1.8e+62))
		tmp = Float64(Float64(0.5 + y) * x);
	else
		tmp = Float64(z + Float64(y * x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -9.5e+44) || ~((x <= 1.8e+62)))
		tmp = (0.5 + y) * x;
	else
		tmp = z + (y * x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -9.5e+44], N[Not[LessEqual[x, 1.8e+62]], $MachinePrecision]], N[(N[(0.5 + y), $MachinePrecision] * x), $MachinePrecision], N[(z + N[(y * x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -9.5000000000000004e44 or 1.8e62 < 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 86.9%

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

   if -9.5000000000000004e44 < x < 1.8e62

   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 0 100.0%

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

   5. Taylor expanded in y around inf 88.1%

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

4. Final simplification 87.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -9.5 \cdot 10^{+44} \lor \neg \left(x \leq 1.8 \cdot 10^{+62}\right):\\ \;\;\;\;\left(0.5 + y\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;z + y \cdot x\\ \end{array} \]

Alternative 5: 98.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.9 \cdot 10^{+14} \lor \neg \left(y \leq 1.25 \cdot 10^{-6}\right):\\ \;\;\;\;z + y \cdot x\\ \mathbf{else}:\\ \;\;\;\;z + 0.5 \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -1.9e+14) (not (<= y 1.25e-6))) (+ z (* y x)) (+ z (* 0.5 x))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.9e+14) || !(y <= 1.25e-6)) {
		tmp = z + (y * x);
	} else {
		tmp = z + (0.5 * x);
	}
	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 <= (-1.9d+14)) .or. (.not. (y <= 1.25d-6))) then
        tmp = z + (y * x)
    else
        tmp = z + (0.5d0 * x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.9e+14) || !(y <= 1.25e-6)) {
		tmp = z + (y * x);
	} else {
		tmp = z + (0.5 * x);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -1.9e+14) or not (y <= 1.25e-6):
		tmp = z + (y * x)
	else:
		tmp = z + (0.5 * x)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -1.9e+14) || !(y <= 1.25e-6))
		tmp = Float64(z + Float64(y * x));
	else
		tmp = Float64(z + Float64(0.5 * x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -1.9e+14) || ~((y <= 1.25e-6)))
		tmp = z + (y * x);
	else
		tmp = z + (0.5 * x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -1.9e+14], N[Not[LessEqual[y, 1.25e-6]], $MachinePrecision]], N[(z + N[(y * x), $MachinePrecision]), $MachinePrecision], N[(z + N[(0.5 * x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.9e14 or 1.2500000000000001e-6 < 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 0 100.0%

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

   5. Taylor expanded in y around inf 100.0%

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

   if -1.9e14 < y < 1.2500000000000001e-6

   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 y around 0 98.5%

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

4. Final simplification 99.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.9 \cdot 10^{+14} \lor \neg \left(y \leq 1.25 \cdot 10^{-6}\right):\\ \;\;\;\;z + y \cdot x\\ \mathbf{else}:\\ \;\;\;\;z + 0.5 \cdot x\\ \end{array} \]

Alternative 6: 49.8% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{-32}:\\ \;\;\;\;z\\ \mathbf{elif}\;z \leq 7 \cdot 10^{+35}:\\ \;\;\;\;0.5 \cdot x\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -2e-32) z (if (<= z 7e+35) (* 0.5 x) z)))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -2e-32) {
		tmp = z;
	} else if (z <= 7e+35) {
		tmp = 0.5 * x;
	} 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 <= (-2d-32)) then
        tmp = z
    else if (z <= 7d+35) then
        tmp = 0.5d0 * x
    else
        tmp = z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -2e-32) {
		tmp = z;
	} else if (z <= 7e+35) {
		tmp = 0.5 * x;
	} else {
		tmp = z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -2e-32:
		tmp = z
	elif z <= 7e+35:
		tmp = 0.5 * x
	else:
		tmp = z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -2e-32)
		tmp = z;
	elseif (z <= 7e+35)
		tmp = Float64(0.5 * x);
	else
		tmp = z;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -2e-32)
		tmp = z;
	elseif (z <= 7e+35)
		tmp = 0.5 * x;
	else
		tmp = z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -2e-32], z, If[LessEqual[z, 7e+35], N[(0.5 * x), $MachinePrecision], z]]

Derivation

1. Split input into 2 regimes

2. if z < -2.00000000000000011e-32 or 7.0000000000000001e35 < z

   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 0 68.4%

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

   if -2.00000000000000011e-32 < z < 7.0000000000000001e35

   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 85.1%

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

   5. Taylor expanded in y around 0 37.5%

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

4. Final simplification 52.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{-32}:\\ \;\;\;\;z\\ \mathbf{elif}\;z \leq 7 \cdot 10^{+35}:\\ \;\;\;\;0.5 \cdot x\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \]

Alternative 7: 40.2% 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. 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 0 42.7%

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

5. Final simplification 42.7%

   \[\leadsto z \]

Reproduce

herbie shell --seed 2023176 
(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))