Average Error: 0.0 → 0.0
Time: 9.1s
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 r56616 = x;
        double r56617 = 1.0;
        double r56618 = 0.5;
        double r56619 = r56616 * r56618;
        double r56620 = r56617 - r56619;
        double r56621 = r56616 * r56620;
        return r56621;
}
↓
double f(double x) {
        double r56622 = x;
        double r56623 = 1.0;
        double r56624 = r56622 * r56623;
        double r56625 = 0.5;
        double r56626 = 2.0;
        double r56627 = pow(r56622, r56626);
        double r56628 = r56625 * r56627;
        double r56629 = -r56628;
        double r56630 = r56624 + r56629;
        return r56630;
}

Error

Bits error versus x

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