Average Error: 0.0 → 0.0
Time: 10.2s
Precision: 64
\[x \cdot \left(x - 1\right)\]
↓
\[x \cdot x - x \cdot 1\]
x \cdot \left(x - 1\right)
↓
x \cdot x - x \cdot 1
double f(double x) {
        double r15419821 = x;
        double r15419822 = 1.0;
        double r15419823 = r15419821 - r15419822;
        double r15419824 = r15419821 * r15419823;
        return r15419824;
}
↓
double f(double x) {
        double r15419825 = x;
        double r15419826 = r15419825 * r15419825;
        double r15419827 = 1.0;
        double r15419828 = r15419825 * r15419827;
        double r15419829 = r15419826 - r15419828;
        return r15419829;
}

Error

Bits error versus x

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Results

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Target

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

Derivation

  1. Initial program 0.0

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

  2. Taylor expanded around 0 0.0

    \[\leadsto \color{blue}{{x}^{2} - 1 \cdot x}\]

  3. Simplified0.0

    \[\leadsto \color{blue}{x \cdot x - x \cdot 1}\]

  4. Final simplification0.0

    \[\leadsto x \cdot x - x \cdot 1\]

Reproduce

herbie shell --seed 2019168 
(FPCore (x)
  :name "Statistics.Correlation.Kendall:numOfTiesBy from math-functions-0.1.5.2"

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

  (* x (- x 1.0)))