Average Error: 0.0 → 0
Time: 3.6s
Precision: 64
\[x \cdot \left(x - 1\right)\]
↓
\[\mathsf{fma}\left(x, x, \left(-1\right) \cdot x\right)\]
x \cdot \left(x - 1\right)
↓
\mathsf{fma}\left(x, x, \left(-1\right) \cdot x\right)
double f(double x) {
        double r330659 = x;
        double r330660 = 1.0;
        double r330661 = r330659 - r330660;
        double r330662 = r330659 * r330661;
        return r330662;
}
↓
double f(double x) {
        double r330663 = x;
        double r330664 = 1.0;
        double r330665 = -r330664;
        double r330666 = r330665 * r330663;
        double r330667 = fma(r330663, r330663, r330666);
        return r330667;
}

Error

Bits error versus x

Target

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

Derivation

  1. Initial program 0.0

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

  3. Applied sub-neg0.0

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

  4. Applied distribute-lft-in0.0

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

  5. Simplified0.0

    \[\leadsto x \cdot x + \color{blue}{\left(-1\right) \cdot x}\]
  6. Using strategy rm

  7. Applied fma-def0

    \[\leadsto \color{blue}{\mathsf{fma}\left(x, x, \left(-1\right) \cdot x\right)}\]

  8. Final simplification0

    \[\leadsto \mathsf{fma}\left(x, x, \left(-1\right) \cdot x\right)\]

Reproduce

herbie shell --seed 2019350 +o rules:numerics
(FPCore (x)
  :name "Statistics.Correlation.Kendall:numOfTiesBy from math-functions-0.1.5.2"
  :precision binary64

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

  (* x (- x 1)))