Average Error: 0.1 → 0.1
Time: 18.6s
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 r866392 = 0.954929658551372;
        double r866393 = x;
        double r866394 = r866392 * r866393;
        double r866395 = 0.12900613773279798;
        double r866396 = r866393 * r866393;
        double r866397 = r866396 * r866393;
        double r866398 = r866395 * r866397;
        double r866399 = r866394 - r866398;
        return r866399;
}
↓
double f(double x) {
        double r866400 = 0.954929658551372;
        double r866401 = x;
        double r866402 = 0.12900613773279798;
        double r866403 = r866401 * r866402;
        double r866404 = r866403 * r866401;
        double r866405 = r866400 - r866404;
        double r866406 = r866405 * r866401;
        return r866406;
}

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 2019120 
(FPCore (x)
  :name "Rosa's Benchmark"
  (- (* 0.954929658551372 x) (* 0.12900613773279798 (* (* x x) x))))