Numeric.Interval.Internal:bisect from intervals-0.7.1, A

Percentage Accurate: 100.0% → 100.0%

Time: 1.8s

Alternatives: 1

Speedup: 1.4×

Specification

Math

\[\begin{array}{l} \\ x + \frac{y - x}{2} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (+ x (/ (- y x) 2.0)))

C

double code(double x, double y) {
	return x + ((y - x) / 2.0);
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = x + ((y - x) / 2.0d0)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 100.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x + \frac{y - x}{2} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (+ x (/ (- y x) 2.0)))

C

double code(double x, double y) {
	return x + ((y - x) / 2.0);
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = x + ((y - x) / 2.0d0)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 100.0% accurate, 1.4× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

   \[x + \frac{y - x}{2} \]
2. Step-by-step derivation

   1. +-commutative 100.0%

      \[\leadsto \color{blue}{\frac{y - x}{2} + x} \]

   2. div-sub 100.0%

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

   3. sub-neg 100.0%

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

   4. associate-+l+ 100.0%

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

   5. *-lft-identity 100.0%

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

   6. metadata-eval 100.0%

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

   7. associate-/l* 99.8%

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

   8. associate-/r/ 100.0%

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

   9. metadata-eval 100.0%

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

   10. metadata-eval 100.0%

       \[\leadsto \color{blue}{0.5} \cdot y + \left(\left(-\frac{x}{2}\right) + x\right) \]

   11. metadata-eval 100.0%

       \[\leadsto \color{blue}{\left(1 + -0.5\right)} \cdot y + \left(\left(-\frac{x}{2}\right) + x\right) \]

   12. metadata-eval 100.0%

       \[\leadsto \left(\color{blue}{\left(--1\right)} + -0.5\right) \cdot y + \left(\left(-\frac{x}{2}\right) + x\right) \]

   13. metadata-eval 100.0%

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

   14. *-commutative 100.0%

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

   15. +-commutative 100.0%

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

   16. *-lft-identity 100.0%

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

   17. metadata-eval 100.0%

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

   18. distribute-neg-frac 100.0%

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

   19. neg-mul-1 100.0%

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

   20. associate-/l* 99.9%

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

   21. associate-/r/ 100.0%

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

   22. distribute-rgt-out 100.0%

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

   23. distribute-rgt-in 100.0%

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

   24. metadata-eval 100.0%

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

   25. metadata-eval 100.0%

       \[\leadsto \left(1 + \color{blue}{-0.5}\right) \cdot \left(y + x\right) \]

   26. metadata-eval 100.0%

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

3. Simplified 100.0%

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

4. Final simplification 100.0%

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

Developer target: 100.0% accurate, 1.4× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2023196 
(FPCore (x y)
  :name "Numeric.Interval.Internal:bisect from intervals-0.7.1, A"
  :precision binary64

  :herbie-target
  (* 0.5 (+ x y))

  (+ x (/ (- y x) 2.0)))