Average Error: 0.1 → 0.1
Time: 15.6s
Precision: 64
\[x \cdot \left(1.0 - x \cdot y\right)\]
↓
\[x \cdot 1.0 + \left(-y \cdot x\right) \cdot x\]
x \cdot \left(1.0 - x \cdot y\right)
↓
x \cdot 1.0 + \left(-y \cdot x\right) \cdot x
double f(double x, double y) {
        double r3851218 = x;
        double r3851219 = 1.0;
        double r3851220 = y;
        double r3851221 = r3851218 * r3851220;
        double r3851222 = r3851219 - r3851221;
        double r3851223 = r3851218 * r3851222;
        return r3851223;
}
↓
double f(double x, double y) {
        double r3851224 = x;
        double r3851225 = 1.0;
        double r3851226 = r3851224 * r3851225;
        double r3851227 = y;
        double r3851228 = r3851227 * r3851224;
        double r3851229 = -r3851228;
        double r3851230 = r3851229 * r3851224;
        double r3851231 = r3851226 + r3851230;
        return r3851231;
}

Error

Bits error versus x

Bits error versus y

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Your Program's Arguments

Results

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Derivation

  1. Initial program 0.1

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

  3. Applied sub-neg0.1

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

  4. Applied distribute-lft-in0.1

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

  5. Final simplification0.1

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

Reproduce

herbie shell --seed 2019162 
(FPCore (x y)
  :name "Numeric.SpecFunctions:log1p from math-functions-0.1.5.2, A"
  (* x (- 1.0 (* x y))))