Average Error: 0.0 → 0.0
Time: 8.8s
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 r46477 = x;
        double r46478 = 1.0;
        double r46479 = 0.5;
        double r46480 = r46477 * r46479;
        double r46481 = r46478 - r46480;
        double r46482 = r46477 * r46481;
        return r46482;
}
↓
double f(double x) {
        double r46483 = x;
        double r46484 = 1.0;
        double r46485 = r46483 * r46484;
        double r46486 = 0.5;
        double r46487 = 2.0;
        double r46488 = pow(r46483, r46487);
        double r46489 = r46486 * r46488;
        double r46490 = -r46489;
        double r46491 = r46485 + r46490;
        return r46491;
}

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