Average Error: 0.1 → 0.1
Time: 22.2s
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 r825209 = 0.954929658551372;
        double r825210 = x;
        double r825211 = r825209 * r825210;
        double r825212 = 0.12900613773279798;
        double r825213 = r825210 * r825210;
        double r825214 = r825213 * r825210;
        double r825215 = r825212 * r825214;
        double r825216 = r825211 - r825215;
        return r825216;
}
↓
double f(double x) {
        double r825217 = 0.954929658551372;
        double r825218 = x;
        double r825219 = 0.12900613773279798;
        double r825220 = r825218 * r825219;
        double r825221 = r825220 * r825218;
        double r825222 = r825217 - r825221;
        double r825223 = r825222 * r825218;
        return r825223;
}

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 2019163 
(FPCore (x)
  :name "Rosa's Benchmark"
  (- (* 0.954929658551372 x) (* 0.12900613773279798 (* (* x x) x))))