Average Error: 0.0 → 0.0
Time: 846.0ms
Precision: 64
\[x \cdot \left(1 - x \cdot 0.5\right)\]
↓
\[x \cdot 1 + x \cdot \left(-x \cdot 0.5\right)\]
x \cdot \left(1 - x \cdot 0.5\right)
↓
x \cdot 1 + x \cdot \left(-x \cdot 0.5\right)
double f(double x) {
        double r62959 = x;
        double r62960 = 1.0;
        double r62961 = 0.5;
        double r62962 = r62959 * r62961;
        double r62963 = r62960 - r62962;
        double r62964 = r62959 * r62963;
        return r62964;
}
↓
double f(double x) {
        double r62965 = x;
        double r62966 = 1.0;
        double r62967 = r62965 * r62966;
        double r62968 = 0.5;
        double r62969 = r62965 * r62968;
        double r62970 = -r62969;
        double r62971 = r62965 * r62970;
        double r62972 = r62967 + r62971;
        return r62972;
}

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. Final simplification0.0

    \[\leadsto x \cdot 1 + x \cdot \left(-x \cdot 0.5\right)\]

Reproduce

herbie shell --seed 2019346 
(FPCore (x)
  :name "Numeric.SpecFunctions:log1p from math-functions-0.1.5.2, B"
  :precision binary64
  (* x (- 1 (* x 0.5))))