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

Percentage Accurate: 100.0% → 100.0%

Time: 4.2s

Alternatives: 8

Speedup: 1.3×

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

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

FPCore

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

C

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

Julia

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

Wolfram

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

   1. +-commutative 100.0%

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

   2. fma-def 100.0%

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

6. Simplified 100.0%

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

7. Final simplification 100.0%

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

Alternative 2: 60.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2600:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq -1.75 \cdot 10^{-168}:\\ \;\;\;\;z\\ \mathbf{elif}\;y \leq 9.8 \cdot 10^{-285}:\\ \;\;\;\;0.5 \cdot x\\ \mathbf{elif}\;y \leq 3.6 \cdot 10^{-230}:\\ \;\;\;\;z\\ \mathbf{elif}\;y \leq 5 \cdot 10^{-73}:\\ \;\;\;\;0.5 \cdot x\\ \mathbf{elif}\;y \leq 3.4 \cdot 10^{-48}:\\ \;\;\;\;z\\ \mathbf{elif}\;y \leq 8.2 \cdot 10^{-13}:\\ \;\;\;\;0.5 \cdot x\\ \mathbf{elif}\;y \leq 1.85 \cdot 10^{+64}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -2600.0)
   (* y x)
   (if (<= y -1.75e-168)
     z
     (if (<= y 9.8e-285)
       (* 0.5 x)
       (if (<= y 3.6e-230)
         z
         (if (<= y 5e-73)
           (* 0.5 x)
           (if (<= y 3.4e-48)
             z
             (if (<= y 8.2e-13)
               (* 0.5 x)
               (if (<= y 1.85e+64) z (* y x))))))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -2600.0) {
		tmp = y * x;
	} else if (y <= -1.75e-168) {
		tmp = z;
	} else if (y <= 9.8e-285) {
		tmp = 0.5 * x;
	} else if (y <= 3.6e-230) {
		tmp = z;
	} else if (y <= 5e-73) {
		tmp = 0.5 * x;
	} else if (y <= 3.4e-48) {
		tmp = z;
	} else if (y <= 8.2e-13) {
		tmp = 0.5 * x;
	} else if (y <= 1.85e+64) {
		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 <= (-2600.0d0)) then
        tmp = y * x
    else if (y <= (-1.75d-168)) then
        tmp = z
    else if (y <= 9.8d-285) then
        tmp = 0.5d0 * x
    else if (y <= 3.6d-230) then
        tmp = z
    else if (y <= 5d-73) then
        tmp = 0.5d0 * x
    else if (y <= 3.4d-48) then
        tmp = z
    else if (y <= 8.2d-13) then
        tmp = 0.5d0 * x
    else if (y <= 1.85d+64) 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 <= -2600.0) {
		tmp = y * x;
	} else if (y <= -1.75e-168) {
		tmp = z;
	} else if (y <= 9.8e-285) {
		tmp = 0.5 * x;
	} else if (y <= 3.6e-230) {
		tmp = z;
	} else if (y <= 5e-73) {
		tmp = 0.5 * x;
	} else if (y <= 3.4e-48) {
		tmp = z;
	} else if (y <= 8.2e-13) {
		tmp = 0.5 * x;
	} else if (y <= 1.85e+64) {
		tmp = z;
	} else {
		tmp = y * x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -2600.0:
		tmp = y * x
	elif y <= -1.75e-168:
		tmp = z
	elif y <= 9.8e-285:
		tmp = 0.5 * x
	elif y <= 3.6e-230:
		tmp = z
	elif y <= 5e-73:
		tmp = 0.5 * x
	elif y <= 3.4e-48:
		tmp = z
	elif y <= 8.2e-13:
		tmp = 0.5 * x
	elif y <= 1.85e+64:
		tmp = z
	else:
		tmp = y * x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -2600.0)
		tmp = Float64(y * x);
	elseif (y <= -1.75e-168)
		tmp = z;
	elseif (y <= 9.8e-285)
		tmp = Float64(0.5 * x);
	elseif (y <= 3.6e-230)
		tmp = z;
	elseif (y <= 5e-73)
		tmp = Float64(0.5 * x);
	elseif (y <= 3.4e-48)
		tmp = z;
	elseif (y <= 8.2e-13)
		tmp = Float64(0.5 * x);
	elseif (y <= 1.85e+64)
		tmp = z;
	else
		tmp = Float64(y * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -2600.0)
		tmp = y * x;
	elseif (y <= -1.75e-168)
		tmp = z;
	elseif (y <= 9.8e-285)
		tmp = 0.5 * x;
	elseif (y <= 3.6e-230)
		tmp = z;
	elseif (y <= 5e-73)
		tmp = 0.5 * x;
	elseif (y <= 3.4e-48)
		tmp = z;
	elseif (y <= 8.2e-13)
		tmp = 0.5 * x;
	elseif (y <= 1.85e+64)
		tmp = z;
	else
		tmp = y * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -2600.0], N[(y * x), $MachinePrecision], If[LessEqual[y, -1.75e-168], z, If[LessEqual[y, 9.8e-285], N[(0.5 * x), $MachinePrecision], If[LessEqual[y, 3.6e-230], z, If[LessEqual[y, 5e-73], N[(0.5 * x), $MachinePrecision], If[LessEqual[y, 3.4e-48], z, If[LessEqual[y, 8.2e-13], N[(0.5 * x), $MachinePrecision], If[LessEqual[y, 1.85e+64], z, N[(y * x), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2600 or 1.84999999999999992e64 < 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 73.4%

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

   if -2600 < y < -1.74999999999999991e-168 or 9.79999999999999949e-285 < y < 3.5999999999999998e-230 or 4.9999999999999998e-73 < y < 3.40000000000000028e-48 or 8.2000000000000004e-13 < y < 1.84999999999999992e64

   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 61.7%

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

   if -1.74999999999999991e-168 < y < 9.79999999999999949e-285 or 3.5999999999999998e-230 < y < 4.9999999999999998e-73 or 3.40000000000000028e-48 < y < 8.2000000000000004e-13

   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 67.9%

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

   5. Taylor expanded in y around 0 67.6%

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

4. Final simplification 68.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2600:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq -1.75 \cdot 10^{-168}:\\ \;\;\;\;z\\ \mathbf{elif}\;y \leq 9.8 \cdot 10^{-285}:\\ \;\;\;\;0.5 \cdot x\\ \mathbf{elif}\;y \leq 3.6 \cdot 10^{-230}:\\ \;\;\;\;z\\ \mathbf{elif}\;y \leq 5 \cdot 10^{-73}:\\ \;\;\;\;0.5 \cdot x\\ \mathbf{elif}\;y \leq 3.4 \cdot 10^{-48}:\\ \;\;\;\;z\\ \mathbf{elif}\;y \leq 8.2 \cdot 10^{-13}:\\ \;\;\;\;0.5 \cdot x\\ \mathbf{elif}\;y \leq 1.85 \cdot 10^{+64}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \]

Alternative 3: 84.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.65 \cdot 10^{-155} \lor \neg \left(z \leq 1.9 \cdot 10^{-6}\right):\\ \;\;\;\;z + y \cdot x\\ \mathbf{else}:\\ \;\;\;\;\left(0.5 + y\right) \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -2.65e-155) (not (<= z 1.9e-6))) (+ z (* y x)) (* (+ 0.5 y) x)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -2.65e-155) || !(z <= 1.9e-6)) {
		tmp = z + (y * x);
	} else {
		tmp = (0.5 + 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 ((z <= (-2.65d-155)) .or. (.not. (z <= 1.9d-6))) then
        tmp = z + (y * x)
    else
        tmp = (0.5d0 + y) * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -2.65e-155) || !(z <= 1.9e-6)) {
		tmp = z + (y * x);
	} else {
		tmp = (0.5 + y) * x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -2.65e-155) or not (z <= 1.9e-6):
		tmp = z + (y * x)
	else:
		tmp = (0.5 + y) * x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -2.65e-155) || !(z <= 1.9e-6))
		tmp = Float64(z + Float64(y * x));
	else
		tmp = Float64(Float64(0.5 + y) * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -2.65e-155) || ~((z <= 1.9e-6)))
		tmp = z + (y * x);
	else
		tmp = (0.5 + y) * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -2.65e-155], N[Not[LessEqual[z, 1.9e-6]], $MachinePrecision]], N[(z + N[(y * x), $MachinePrecision]), $MachinePrecision], N[(N[(0.5 + y), $MachinePrecision] * x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.6499999999999999e-155 or 1.9e-6 < 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 0 100.0%

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

      1. *-commutative 100.0%

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

      2. flip-+ 87.0%

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

      3. associate-*r/ 85.2%

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

      4. metadata-eval 85.2%

         \[\leadsto z + \frac{x \cdot \left(\color{blue}{0.25} - y \cdot y\right)}{0.5 - y} \]

   6. Applied egg-rr 85.2%

      \[\leadsto z + \color{blue}{\frac{x \cdot \left(0.25 - y \cdot y\right)}{0.5 - y}} \]
   7. Step-by-step derivation

      1. *-commutative 85.2%

         \[\leadsto z + \frac{\color{blue}{\left(0.25 - y \cdot y\right) \cdot x}}{0.5 - y} \]

      2. associate-/l* 86.5%

         \[\leadsto z + \color{blue}{\frac{0.25 - y \cdot y}{\frac{0.5 - y}{x}}} \]

   8. Simplified 86.5%

      \[\leadsto z + \color{blue}{\frac{0.25 - y \cdot y}{\frac{0.5 - y}{x}}} \]

   9. Taylor expanded in y around inf 82.5%

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

   if -2.6499999999999999e-155 < z < 1.9e-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 x around inf 89.5%

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

4. Final simplification 85.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.65 \cdot 10^{-155} \lor \neg \left(z \leq 1.9 \cdot 10^{-6}\right):\\ \;\;\;\;z + y \cdot x\\ \mathbf{else}:\\ \;\;\;\;\left(0.5 + y\right) \cdot x\\ \end{array} \]

Alternative 4: 98.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -0.5 \lor \neg \left(y \leq 2.85 \cdot 10^{-8}\right):\\ \;\;\;\;z + y \cdot x\\ \mathbf{else}:\\ \;\;\;\;z + 0.5 \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -0.5) (not (<= y 2.85e-8))) (+ z (* y x)) (+ z (* 0.5 x))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -0.5) || !(y <= 2.85e-8)) {
		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 <= (-0.5d0)) .or. (.not. (y <= 2.85d-8))) 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 <= -0.5) || !(y <= 2.85e-8)) {
		tmp = z + (y * x);
	} else {
		tmp = z + (0.5 * x);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -0.5) or not (y <= 2.85e-8):
		tmp = z + (y * x)
	else:
		tmp = z + (0.5 * x)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -0.5) || !(y <= 2.85e-8))
		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 <= -0.5) || ~((y <= 2.85e-8)))
		tmp = z + (y * x);
	else
		tmp = z + (0.5 * x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -0.5], N[Not[LessEqual[y, 2.85e-8]], $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 < -0.5 or 2.85000000000000004e-8 < 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. Step-by-step derivation

      1. *-commutative 100.0%

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

      2. flip-+ 71.5%

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

      3. associate-*r/ 65.0%

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

      4. metadata-eval 65.0%

         \[\leadsto z + \frac{x \cdot \left(\color{blue}{0.25} - y \cdot y\right)}{0.5 - y} \]

   6. Applied egg-rr 65.0%

      \[\leadsto z + \color{blue}{\frac{x \cdot \left(0.25 - y \cdot y\right)}{0.5 - y}} \]
   7. Step-by-step derivation

      1. *-commutative 65.0%

         \[\leadsto z + \frac{\color{blue}{\left(0.25 - y \cdot y\right) \cdot x}}{0.5 - y} \]

      2. associate-/l* 70.7%

         \[\leadsto z + \color{blue}{\frac{0.25 - y \cdot y}{\frac{0.5 - y}{x}}} \]

   8. Simplified 70.7%

      \[\leadsto z + \color{blue}{\frac{0.25 - y \cdot y}{\frac{0.5 - y}{x}}} \]

   9. Taylor expanded in y around inf 97.9%

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

   if -0.5 < y < 2.85000000000000004e-8

   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 99.6%

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

4. Final simplification 98.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.5 \lor \neg \left(y \leq 2.85 \cdot 10^{-8}\right):\\ \;\;\;\;z + y \cdot x\\ \mathbf{else}:\\ \;\;\;\;z + 0.5 \cdot x\\ \end{array} \]

Alternative 5: 74.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.3 \cdot 10^{+71}:\\ \;\;\;\;z\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{+125}:\\ \;\;\;\;\left(0.5 + y\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -1.3e+71) z (if (<= z 2.3e+125) (* (+ 0.5 y) x) z)))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.3e+71) {
		tmp = z;
	} else if (z <= 2.3e+125) {
		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 <= (-1.3d+71)) then
        tmp = z
    else if (z <= 2.3d+125) 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 <= -1.3e+71) {
		tmp = z;
	} else if (z <= 2.3e+125) {
		tmp = (0.5 + y) * x;
	} else {
		tmp = z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -1.3e+71:
		tmp = z
	elif z <= 2.3e+125:
		tmp = (0.5 + y) * x
	else:
		tmp = z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -1.3e+71)
		tmp = z;
	elseif (z <= 2.3e+125)
		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 <= -1.3e+71)
		tmp = z;
	elseif (z <= 2.3e+125)
		tmp = (0.5 + y) * x;
	else
		tmp = z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -1.3e+71], z, If[LessEqual[z, 2.3e+125], N[(N[(0.5 + y), $MachinePrecision] * x), $MachinePrecision], z]]

Derivation

1. Split input into 2 regimes

2. if z < -1.29999999999999996e71 or 2.30000000000000013e125 < 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 78.4%

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

   if -1.29999999999999996e71 < z < 2.30000000000000013e125

   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 79.8%

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

4. Final simplification 79.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.3 \cdot 10^{+71}:\\ \;\;\;\;z\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{+125}:\\ \;\;\;\;\left(0.5 + y\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \]

Alternative 6: 49.1% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.2 \cdot 10^{-159}:\\ \;\;\;\;z\\ \mathbf{elif}\;z \leq 22500000:\\ \;\;\;\;0.5 \cdot x\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -2.2e-159) z (if (<= z 22500000.0) (* 0.5 x) z)))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -2.2e-159) {
		tmp = z;
	} else if (z <= 22500000.0) {
		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 <= (-2.2d-159)) then
        tmp = z
    else if (z <= 22500000.0d0) 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 <= -2.2e-159) {
		tmp = z;
	} else if (z <= 22500000.0) {
		tmp = 0.5 * x;
	} else {
		tmp = z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -2.2e-159:
		tmp = z
	elif z <= 22500000.0:
		tmp = 0.5 * x
	else:
		tmp = z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -2.2e-159)
		tmp = z;
	elseif (z <= 22500000.0)
		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 <= -2.2e-159)
		tmp = z;
	elseif (z <= 22500000.0)
		tmp = 0.5 * x;
	else
		tmp = z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -2.2e-159], z, If[LessEqual[z, 22500000.0], N[(0.5 * x), $MachinePrecision], z]]

Derivation

1. Split input into 2 regimes

2. if z < -2.2e-159 or 2.25e7 < 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 57.6%

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

   if -2.2e-159 < z < 2.25e7

   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 89.5%

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

   5. Taylor expanded in y around 0 49.6%

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

4. Final simplification 54.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.2 \cdot 10^{-159}:\\ \;\;\;\;z\\ \mathbf{elif}\;z \leq 22500000:\\ \;\;\;\;0.5 \cdot x\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \]

Alternative 7: 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 8: 39.9% 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. 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 39.7%

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

5. Final simplification 39.7%

   \[\leadsto z \]

Reproduce

herbie shell --seed 2023228 
(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))