Average Error: 0.1 → 0.1
Time: 5.9s
Precision: 64
\[x \cdot \left(1 - x \cdot y\right)\]
↓
\[\left(1 - x \cdot y\right) \cdot x\]
x \cdot \left(1 - x \cdot y\right)
↓
\left(1 - x \cdot y\right) \cdot x
double f(double x, double y) {
        double r59942 = x;
        double r59943 = 1.0;
        double r59944 = y;
        double r59945 = r59942 * r59944;
        double r59946 = r59943 - r59945;
        double r59947 = r59942 * r59946;
        return r59947;
}
↓
double f(double x, double y) {
        double r59948 = 1.0;
        double r59949 = x;
        double r59950 = y;
        double r59951 = r59949 * r59950;
        double r59952 = r59948 - r59951;
        double r59953 = r59952 * r59949;
        return r59953;
}

Error

Bits error versus x

Bits error versus y

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Results

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Derivation

  1. Initial program 0.1

    \[x \cdot \left(1 - x \cdot y\right)\]
  2. Using strategy rm

  3. Applied sub-neg0.1

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

  4. Applied distribute-lft-in0.1

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

  5. Final simplification0.1

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

Reproduce

herbie shell --seed 2019304 
(FPCore (x y)
  :name "Numeric.SpecFunctions:log1p from math-functions-0.1.5.2, A"
  :precision binary64
  (* x (- 1 (* x y))))