Average Error: 0.0 → 0
Time: 12.8s
Precision: 64
\[x \cdot \left(x - 1.0\right)\]
↓
\[\mathsf{fma}\left(x, x, x \cdot \left(-1.0\right)\right)\]
x \cdot \left(x - 1.0\right)
↓
\mathsf{fma}\left(x, x, x \cdot \left(-1.0\right)\right)
double f(double x) {
        double r18524917 = x;
        double r18524918 = 1.0;
        double r18524919 = r18524917 - r18524918;
        double r18524920 = r18524917 * r18524919;
        return r18524920;
}
↓
double f(double x) {
        double r18524921 = x;
        double r18524922 = 1.0;
        double r18524923 = -r18524922;
        double r18524924 = r18524921 * r18524923;
        double r18524925 = fma(r18524921, r18524921, r18524924);
        return r18524925;
}

Error

Bits error versus x

Target

Original0.0
Target0.0
Herbie0
\[x \cdot x - x\]

Derivation

  1. Initial program 0.0

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

  3. Applied sub-neg0.0

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

  4. Applied distribute-lft-in0.0

    \[\leadsto \color{blue}{x \cdot x + x \cdot \left(-1.0\right)}\]
  5. Using strategy rm

  6. Applied fma-def0

    \[\leadsto \color{blue}{\mathsf{fma}\left(x, x, x \cdot \left(-1.0\right)\right)}\]

  7. Final simplification0

    \[\leadsto \mathsf{fma}\left(x, x, x \cdot \left(-1.0\right)\right)\]

Reproduce

herbie shell --seed 2019165 +o rules:numerics
(FPCore (x)
  :name "Statistics.Correlation.Kendall:numOfTiesBy from math-functions-0.1.5.2"

  :herbie-target
  (- (* x x) x)

  (* x (- x 1.0)))