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

Average Error: 0.0 → 0

Time: 6.4s

Precision: binary64

Cost: 320

Math

\[x + \frac{y - x}{2} \]

↓

\[\frac{x + y}{2} \]

FPCore

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

↓

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

C

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

↓

double code(double x, double y) {
	return (x + y) / 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

↓

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

Java

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

↓

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

Python

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

↓

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

Julia

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

↓

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

MATLAB

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

↓

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

Wolfram

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

↓

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

Target

Original	0.0
Target	0
Herbie	0

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

Derivation

1. Initial program 0.0

   \[x + \frac{y - x}{2} \]

2. Applied egg-rr 0

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

3. Final simplification 0

   \[\leadsto \frac{x + y}{2} \]

Alternatives

Alternative 1
Error	16.0
Cost	456

\[\begin{array}{l} \mathbf{if}\;x \leq -3.4 \cdot 10^{+49}:\\ \;\;\;\;0.5 \cdot x\\ \mathbf{elif}\;x \leq 7.4 \cdot 10^{+31}:\\ \;\;\;\;0.5 \cdot y\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot x\\ \end{array} \]

Alternative 2
Error	31.8
Cost	192

\[0.5 \cdot x \]

Reproduce

herbie shell --seed 2023069 
(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)))