Average Error: 0.0 → 0.0
Time: 858.0ms
Precision: 64
\[x \cdot \left(1 - x \cdot 0.5\right)\]
↓
\[x \cdot 1 + x \cdot \left(-x \cdot 0.5\right)\]
x \cdot \left(1 - x \cdot 0.5\right)
↓
x \cdot 1 + x \cdot \left(-x \cdot 0.5\right)
double f(double x) {
        double r37955 = x;
        double r37956 = 1.0;
        double r37957 = 0.5;
        double r37958 = r37955 * r37957;
        double r37959 = r37956 - r37958;
        double r37960 = r37955 * r37959;
        return r37960;
}
↓
double f(double x) {
        double r37961 = x;
        double r37962 = 1.0;
        double r37963 = r37961 * r37962;
        double r37964 = 0.5;
        double r37965 = r37961 * r37964;
        double r37966 = -r37965;
        double r37967 = r37961 * r37966;
        double r37968 = r37963 + r37967;
        return r37968;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.0

    \[x \cdot \left(1 - x \cdot 0.5\right)\]
  2. Using strategy rm

  3. Applied sub-neg0.0

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

  4. Applied distribute-lft-in0.0

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

  5. Final simplification0.0

    \[\leadsto x \cdot 1 + x \cdot \left(-x \cdot 0.5\right)\]

Reproduce

herbie shell --seed 2020039 +o rules:numerics
(FPCore (x)
  :name "Numeric.SpecFunctions:log1p from math-functions-0.1.5.2, B"
  :precision binary64
  (* x (- 1 (* x 0.5))))