Average Error: 0.0 → 0.0
Time: 7.5s
Precision: 64
\[x \cdot \left(1.0 - x \cdot 0.5\right)\]
↓
\[x \cdot 1.0 + \left(-0.5 \cdot x\right) \cdot x\]
x \cdot \left(1.0 - x \cdot 0.5\right)
↓
x \cdot 1.0 + \left(-0.5 \cdot x\right) \cdot x
double f(double x) {
        double r2422046 = x;
        double r2422047 = 1.0;
        double r2422048 = 0.5;
        double r2422049 = r2422046 * r2422048;
        double r2422050 = r2422047 - r2422049;
        double r2422051 = r2422046 * r2422050;
        return r2422051;
}
↓
double f(double x) {
        double r2422052 = x;
        double r2422053 = 1.0;
        double r2422054 = r2422052 * r2422053;
        double r2422055 = 0.5;
        double r2422056 = r2422055 * r2422052;
        double r2422057 = -r2422056;
        double r2422058 = r2422057 * r2422052;
        double r2422059 = r2422054 + r2422058;
        return r2422059;
}

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

    \[x \cdot \left(1.0 - x \cdot 0.5\right)\]
  2. Using strategy rm

  3. Applied sub-neg0.0

    \[\leadsto x \cdot \color{blue}{\left(1.0 + \left(-x \cdot 0.5\right)\right)}\]

  4. Applied distribute-lft-in0.0

    \[\leadsto \color{blue}{x \cdot 1.0 + x \cdot \left(-x \cdot 0.5\right)}\]

  5. Final simplification0.0

    \[\leadsto x \cdot 1.0 + \left(-0.5 \cdot x\right) \cdot x\]

Reproduce

herbie shell --seed 2019158 +o rules:numerics
(FPCore (x)
  :name "Numeric.SpecFunctions:log1p from math-functions-0.1.5.2, B"
  (* x (- 1.0 (* x 0.5))))