Average Error: 0.1 → 0.1
Time: 11.5s
Precision: 64
\[0.954929658551372 \cdot x - 0.12900613773279798 \cdot \left(\left(x \cdot x\right) \cdot x\right)\]
↓
\[0.954929658551372 \cdot x - \left(0.12900613773279798 \cdot \left(x \cdot x\right)\right) \cdot x\]
0.954929658551372 \cdot x - 0.12900613773279798 \cdot \left(\left(x \cdot x\right) \cdot x\right)
↓
0.954929658551372 \cdot x - \left(0.12900613773279798 \cdot \left(x \cdot x\right)\right) \cdot x
double f(double x) {
        double r301712 = 0.954929658551372;
        double r301713 = x;
        double r301714 = r301712 * r301713;
        double r301715 = 0.12900613773279798;
        double r301716 = r301713 * r301713;
        double r301717 = r301716 * r301713;
        double r301718 = r301715 * r301717;
        double r301719 = r301714 - r301718;
        return r301719;
}
↓
double f(double x) {
        double r301720 = 0.954929658551372;
        double r301721 = x;
        double r301722 = r301720 * r301721;
        double r301723 = 0.12900613773279798;
        double r301724 = r301721 * r301721;
        double r301725 = r301723 * r301724;
        double r301726 = r301725 * r301721;
        double r301727 = r301722 - r301726;
        return r301727;
}

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 associate-*r*0.1

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

  4. Final simplification0.1

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

Reproduce

herbie shell --seed 2019151 +o rules:numerics
(FPCore (x)
  :name "Rosa's Benchmark"
  (- (* 0.954929658551372 x) (* 0.12900613773279798 (* (* x x) x))))