Average Error: 0.0 → 0.0
Time: 10.0s
Precision: 64
\[x \cdot \left(1 - x \cdot 0.5\right)\]
↓
\[1 \cdot x + \left(-x \cdot 0.5\right) \cdot x\]
x \cdot \left(1 - x \cdot 0.5\right)
↓
1 \cdot x + \left(-x \cdot 0.5\right) \cdot x
double f(double x) {
        double r6376215 = x;
        double r6376216 = 1.0;
        double r6376217 = 0.5;
        double r6376218 = r6376215 * r6376217;
        double r6376219 = r6376216 - r6376218;
        double r6376220 = r6376215 * r6376219;
        return r6376220;
}
↓
double f(double x) {
        double r6376221 = 1.0;
        double r6376222 = x;
        double r6376223 = r6376221 * r6376222;
        double r6376224 = 0.5;
        double r6376225 = r6376222 * r6376224;
        double r6376226 = -r6376225;
        double r6376227 = r6376226 * r6376222;
        double r6376228 = r6376223 + r6376227;
        return r6376228;
}

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-rgt-in0.0

    \[\leadsto \color{blue}{1 \cdot x + \left(-x \cdot 0.5\right) \cdot x}\]

  5. Final simplification0.0

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

Reproduce

herbie shell --seed 2019173 +o rules:numerics
(FPCore (x)
  :name "Numeric.SpecFunctions:log1p from math-functions-0.1.5.2, B"
  (* x (- 1.0 (* x 0.5))))