Average Error: 0.1 → 0.1
Time: 16.7s
Precision: 64
\[0.954929658551372 \cdot x - 0.12900613773279798 \cdot \left(\left(x \cdot x\right) \cdot x\right)\]
↓
\[0.954929658551372 \cdot x - 0.12900613773279798 \cdot {x}^{3}\]
0.954929658551372 \cdot x - 0.12900613773279798 \cdot \left(\left(x \cdot x\right) \cdot x\right)
↓
0.954929658551372 \cdot x - 0.12900613773279798 \cdot {x}^{3}
double f(double x) {
        double r660860 = 0.954929658551372;
        double r660861 = x;
        double r660862 = r660860 * r660861;
        double r660863 = 0.12900613773279798;
        double r660864 = r660861 * r660861;
        double r660865 = r660864 * r660861;
        double r660866 = r660863 * r660865;
        double r660867 = r660862 - r660866;
        return r660867;
}
↓
double f(double x) {
        double r660868 = 0.954929658551372;
        double r660869 = x;
        double r660870 = r660868 * r660869;
        double r660871 = 0.12900613773279798;
        double r660872 = 3.0;
        double r660873 = pow(r660869, r660872);
        double r660874 = r660871 * r660873;
        double r660875 = r660870 - r660874;
        return r660875;
}

Error

Bits error versus x

Try it out

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. Using strategy rm

  3. Applied pow10.1

    \[\leadsto 0.954929658551372 \cdot x - 0.12900613773279798 \cdot \left(\left(\color{blue}{{x}^{1}} \cdot x\right) \cdot x\right)\]

  4. Applied pow-plus0.1

    \[\leadsto 0.954929658551372 \cdot x - 0.12900613773279798 \cdot \left(\color{blue}{{x}^{\left(1 + 1\right)}} \cdot x\right)\]

  5. Applied pow-plus0.1

    \[\leadsto 0.954929658551372 \cdot x - 0.12900613773279798 \cdot \color{blue}{{x}^{\left(\left(1 + 1\right) + 1\right)}}\]

  6. Simplified0.1

    \[\leadsto 0.954929658551372 \cdot x - 0.12900613773279798 \cdot {x}^{\color{blue}{3}}\]

  7. Final simplification0.1

    \[\leadsto 0.954929658551372 \cdot x - 0.12900613773279798 \cdot {x}^{3}\]

Reproduce

herbie shell --seed 2019133 +o rules:numerics
(FPCore (x)
  :name "Rosa's Benchmark"
  (- (* 0.954929658551372 x) (* 0.12900613773279798 (* (* x x) x))))