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

Average Error: 0.0 → 0

Time: 1.6s

Precision: binary64

Cost: 320

Math

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

↓

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

FPCore

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

↓

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

C

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

↓

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 = x + ((y - x) / 2.0d0)
end function

↓

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

↓

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

Python

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

↓

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

Julia

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

↓

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

MATLAB

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

↓

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

Wolfram

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

↓

code[x_, y_] := N[(0.5 * N[(y + x), $MachinePrecision]), $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. Taylor expanded in x around 0 0

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

3. Simplified 0

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

   [Start] 0	\[ 0.5 \cdot x + 0.5 \cdot y \]
   rational.json-simplify-2 [=>] 0	\[ 0.5 \cdot x + \color{blue}{y \cdot 0.5} \]
   rational.json-simplify-47 [=>] 0	\[ \color{blue}{0.5 \cdot \left(y + x\right)} \]

4. Final simplification 0

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

Alternatives

Alternative 1
Error	17.4
Cost	456

\[\begin{array}{l} \mathbf{if}\;y \leq -6 \cdot 10^{+20}:\\ \;\;\;\;0.5 \cdot y\\ \mathbf{elif}\;y \leq 5.8 \cdot 10^{-86}:\\ \;\;\;\;0.5 \cdot x\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot y\\ \end{array} \]

Alternative 2
Error	31.4
Cost	192

\[0.5 \cdot x \]

Reproduce

herbie shell --seed 2023077 
(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)))