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

Percentage Accurate: 100.0% → 100.0%

Time: 4.5s

Alternatives: 5

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, 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: 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* 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. Add Preprocessing

5. Final simplification 100.0%

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

Alternative 3: 60.2% accurate, 1.8× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := N[(x * N[(y + 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. 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. Add Preprocessing

5. Taylor expanded in x around inf 60.7%

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

   1. +-commutative 60.7%

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

7. Simplified 60.7%

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

8. Final simplification 60.7%

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

Alternative 4: 75.8% accurate, 1.8× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := N[(z + N[(x * y), $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* 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. Add Preprocessing

5. Taylor expanded in y around inf 74.1%

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

   1. associate-*r* 74.1%

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

   2. neg-mul-1 74.1%

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

7. Simplified 74.1%

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

   1. cancel-sign-sub 74.1%

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

   2. +-commutative 74.1%

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

9. Applied egg-rr 74.1%

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

10. Final simplification 74.1%

    \[\leadsto z + x \cdot y \]
11. Add Preprocessing

Alternative 5: 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* 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. Add Preprocessing

5. Taylor expanded in y around inf 74.1%

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

   1. associate-*r* 74.1%

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

   2. neg-mul-1 74.1%

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

7. Simplified 74.1%

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

8. Taylor expanded in z around inf 40.7%

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

9. Final simplification 40.7%

   \[\leadsto z \]
10. Add Preprocessing

Reproduce

herbie shell --seed 2024033 
(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))