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

Percentage Accurate: 100.0% → 100.0%

Time: 2.5s

Alternatives: 4

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. Add Preprocessing

3. Final simplification 100.0%

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

Alternative 2: 98.9% accurate, 0.6× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if y < -0.5 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%

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

      2. remove-double-neg 100.0%

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

      3. distribute-frac-neg 100.0%

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

      4. sub-neg 100.0%

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

      5. neg-mul-1 100.0%

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

      6. *-commutative 100.0%

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

      7. associate-/l* 100.0%

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

      8. *-commutative 100.0%

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

      9. distribute-rgt-out-- 100.0%

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

      10. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around inf 98.1%

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

   if -0.5 < 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%

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

      2. remove-double-neg 100.0%

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

      3. distribute-frac-neg 100.0%

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

      4. sub-neg 100.0%

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

      5. neg-mul-1 100.0%

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

      6. *-commutative 100.0%

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

      7. associate-/l* 100.0%

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

      8. *-commutative 100.0%

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

      9. distribute-rgt-out-- 100.0%

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

      10. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around 0 98.7%

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

      1. *-commutative 98.7%

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

   7. Simplified 98.7%

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

4. Final simplification 98.3%

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

Alternative 3: 100.0% accurate, 1.3× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

   1. +-commutative 100.0%

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

   2. remove-double-neg 100.0%

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

   3. distribute-frac-neg 100.0%

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

   4. sub-neg 100.0%

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

   5. neg-mul-1 100.0%

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

   6. *-commutative 100.0%

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

   7. associate-/l* 100.0%

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

   8. *-commutative 100.0%

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

   9. distribute-rgt-out-- 100.0%

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

   10. metadata-eval 100.0%

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

3. Simplified 100.0%

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

5. Final simplification 100.0%

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

Alternative 4: 65.2% accurate, 1.8× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

   1. +-commutative 100.0%

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

   2. remove-double-neg 100.0%

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

   3. distribute-frac-neg 100.0%

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

   4. sub-neg 100.0%

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

   5. neg-mul-1 100.0%

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

   6. *-commutative 100.0%

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

   7. associate-/l* 100.0%

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

   8. *-commutative 100.0%

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

   9. distribute-rgt-out-- 100.0%

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

   10. metadata-eval 100.0%

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

3. Simplified 100.0%

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

5. Taylor expanded in y around 0 60.1%

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

   1. *-commutative 60.1%

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

7. Simplified 60.1%

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

8. Final simplification 60.1%

   \[\leadsto z + x \cdot 0.5 \]
9. Add Preprocessing

Reproduce

herbie shell --seed 2024089 
(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))