Average Error: 0.1 → 0.1
Time: 25.5s
Precision: 64
\[0.954929658551372 \cdot x - 0.12900613773279798 \cdot \left(\left(x \cdot x\right) \cdot x\right)\]
↓
\[\left(0.954929658551372 - \left(x \cdot 0.12900613773279798\right) \cdot x\right) \cdot x\]
0.954929658551372 \cdot x - 0.12900613773279798 \cdot \left(\left(x \cdot x\right) \cdot x\right)
↓
\left(0.954929658551372 - \left(x \cdot 0.12900613773279798\right) \cdot x\right) \cdot x
double f(double x) {
        double r896730 = 0.954929658551372;
        double r896731 = x;
        double r896732 = r896730 * r896731;
        double r896733 = 0.12900613773279798;
        double r896734 = r896731 * r896731;
        double r896735 = r896734 * r896731;
        double r896736 = r896733 * r896735;
        double r896737 = r896732 - r896736;
        return r896737;
}
↓
double f(double x) {
        double r896738 = 0.954929658551372;
        double r896739 = x;
        double r896740 = 0.12900613773279798;
        double r896741 = r896739 * r896740;
        double r896742 = r896741 * r896739;
        double r896743 = r896738 - r896742;
        double r896744 = r896743 * r896739;
        return r896744;
}

Error

Bits error versus x

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.1

    \[0.954929658551372 \cdot x - 0.12900613773279798 \cdot \left(\left(x \cdot x\right) \cdot x\right)\]

  2. Simplified0.1

    \[\leadsto \color{blue}{x \cdot \left(0.954929658551372 - 0.12900613773279798 \cdot \left(x \cdot x\right)\right)}\]
  3. Using strategy rm

  4. Applied associate-*r*0.1

    \[\leadsto x \cdot \left(0.954929658551372 - \color{blue}{\left(0.12900613773279798 \cdot x\right) \cdot x}\right)\]

  5. Final simplification0.1

    \[\leadsto \left(0.954929658551372 - \left(x \cdot 0.12900613773279798\right) \cdot x\right) \cdot x\]

Reproduce

herbie shell --seed 2019104 
(FPCore (x)
  :name "Rosa's Benchmark"
  (- (* 0.954929658551372 x) (* 0.12900613773279798 (* (* x x) x))))