Average Error: 0.0 → 0.0
Time: 7.2s
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 r34500 = x;
        double r34501 = 1.0;
        double r34502 = 0.5;
        double r34503 = r34500 * r34502;
        double r34504 = r34501 - r34503;
        double r34505 = r34500 * r34504;
        return r34505;
}
↓
double f(double x) {
        double r34506 = x;
        double r34507 = 1.0;
        double r34508 = r34506 * r34507;
        double r34509 = 0.5;
        double r34510 = 2.0;
        double r34511 = pow(r34506, r34510);
        double r34512 = r34509 * r34511;
        double r34513 = -r34512;
        double r34514 = r34508 + r34513;
        return r34514;
}

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 2019304 +o rules:numerics
(FPCore (x)
  :name "Numeric.SpecFunctions:log1p from math-functions-0.1.5.2, B"
  :precision binary64
  (* x (- 1 (* x 0.5))))