Average Error: 0.1 → 0.1
Time: 48.6s
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 r2515118 = 0.954929658551372;
        double r2515119 = x;
        double r2515120 = r2515118 * r2515119;
        double r2515121 = 0.12900613773279798;
        double r2515122 = r2515119 * r2515119;
        double r2515123 = r2515122 * r2515119;
        double r2515124 = r2515121 * r2515123;
        double r2515125 = r2515120 - r2515124;
        return r2515125;
}
↓
double f(double x) {
        double r2515126 = 0.954929658551372;
        double r2515127 = x;
        double r2515128 = 0.12900613773279798;
        double r2515129 = r2515127 * r2515128;
        double r2515130 = r2515129 * r2515127;
        double r2515131 = r2515126 - r2515130;
        double r2515132 = r2515131 * r2515127;
        return r2515132;
}

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. Simplified0.1

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

  3. Taylor expanded around inf 0.1

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

  4. Simplified0.1

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

  5. Final simplification0.1

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

Reproduce

herbie shell --seed 2019128 
(FPCore (x)
  :name "Rosa's Benchmark"
  (- (* 0.954929658551372 x) (* 0.12900613773279798 (* (* x x) x))))