Average Error: 0.0 → 0.0
Time: 7.0s
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 r54412 = x;
        double r54413 = 1.0;
        double r54414 = 0.5;
        double r54415 = r54412 * r54414;
        double r54416 = r54413 - r54415;
        double r54417 = r54412 * r54416;
        return r54417;
}
↓
double f(double x) {
        double r54418 = x;
        double r54419 = 1.0;
        double r54420 = r54418 * r54419;
        double r54421 = 0.5;
        double r54422 = 2.0;
        double r54423 = pow(r54418, r54422);
        double r54424 = r54421 * r54423;
        double r54425 = -r54424;
        double r54426 = r54420 + r54425;
        return r54426;
}

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 2019350 
(FPCore (x)
  :name "Numeric.SpecFunctions:log1p from math-functions-0.1.5.2, B"
  :precision binary64
  (* x (- 1 (* x 0.5))))