Average Error: 0.0 → 0.0
Time: 9.4s
Precision: 64
\[x \cdot \left(1 - x \cdot 0.5\right)\]
↓
\[x \cdot 1 + \left(-0.5 \cdot {x}^{2}\right)\]
x \cdot \left(1 - x \cdot 0.5\right)
↓
x \cdot 1 + \left(-0.5 \cdot {x}^{2}\right)
double f(double x) {
        double r59011 = x;
        double r59012 = 1.0;
        double r59013 = 0.5;
        double r59014 = r59011 * r59013;
        double r59015 = r59012 - r59014;
        double r59016 = r59011 * r59015;
        return r59016;
}
↓
double f(double x) {
        double r59017 = x;
        double r59018 = 1.0;
        double r59019 = r59017 * r59018;
        double r59020 = 0.5;
        double r59021 = 2.0;
        double r59022 = pow(r59017, r59021);
        double r59023 = r59020 * r59022;
        double r59024 = -r59023;
        double r59025 = r59019 + r59024;
        return r59025;
}

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. Simplified0.0

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

  6. Final simplification0.0

    \[\leadsto x \cdot 1 + \left(-0.5 \cdot {x}^{2}\right)\]

Reproduce

herbie shell --seed 2019325 +o rules:numerics
(FPCore (x)
  :name "Numeric.SpecFunctions:log1p from math-functions-0.1.5.2, B"
  :precision binary64
  (* x (- 1 (* x 0.5))))