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 r46487 = x;
        double r46488 = 1.0;
        double r46489 = 0.5;
        double r46490 = r46487 * r46489;
        double r46491 = r46488 - r46490;
        double r46492 = r46487 * r46491;
        return r46492;
}
↓
double f(double x) {
        double r46493 = x;
        double r46494 = 1.0;
        double r46495 = r46493 * r46494;
        double r46496 = 0.5;
        double r46497 = 2.0;
        double r46498 = pow(r46493, r46497);
        double r46499 = r46496 * r46498;
        double r46500 = -r46499;
        double r46501 = r46495 + r46500;
        return r46501;
}

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 2019306 
(FPCore (x)
  :name "Numeric.SpecFunctions:log1p from math-functions-0.1.5.2, B"
  :precision binary64
  (* x (- 1 (* x 0.5))))