Average Error: 0.0 → 0
Time: 862.0ms
Precision: 64
\[x \cdot \left(x - 1\right)\]
↓
\[\mathsf{fma}\left({x}^{1}, {x}^{1}, x \cdot \left(-1\right)\right)\]
x \cdot \left(x - 1\right)
↓
\mathsf{fma}\left({x}^{1}, {x}^{1}, x \cdot \left(-1\right)\right)
double f(double x) {
        double r302586 = x;
        double r302587 = 1.0;
        double r302588 = r302586 - r302587;
        double r302589 = r302586 * r302588;
        return r302589;
}
↓
double f(double x) {
        double r302590 = x;
        double r302591 = 1.0;
        double r302592 = pow(r302590, r302591);
        double r302593 = 1.0;
        double r302594 = -r302593;
        double r302595 = r302590 * r302594;
        double r302596 = fma(r302592, r302592, r302595);
        return r302596;
}

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

    \[\leadsto \color{blue}{{x}^{2}} + x \cdot \left(-1\right)\]
  6. Using strategy rm

  7. Applied sqr-pow0.0

    \[\leadsto \color{blue}{{x}^{\left(\frac{2}{2}\right)} \cdot {x}^{\left(\frac{2}{2}\right)}} + x \cdot \left(-1\right)\]

  8. Applied fma-def0

    \[\leadsto \color{blue}{\mathsf{fma}\left({x}^{\left(\frac{2}{2}\right)}, {x}^{\left(\frac{2}{2}\right)}, x \cdot \left(-1\right)\right)}\]

  9. Final simplification0

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

Reproduce

herbie shell --seed 2019353 +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)))