Average Error: 0.1 → 0.1
Time: 23.9s
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 r1021578 = 0.954929658551372;
        double r1021579 = x;
        double r1021580 = r1021578 * r1021579;
        double r1021581 = 0.12900613773279798;
        double r1021582 = r1021579 * r1021579;
        double r1021583 = r1021582 * r1021579;
        double r1021584 = r1021581 * r1021583;
        double r1021585 = r1021580 - r1021584;
        return r1021585;
}
↓
double f(double x) {
        double r1021586 = 0.954929658551372;
        double r1021587 = x;
        double r1021588 = 0.12900613773279798;
        double r1021589 = r1021587 * r1021588;
        double r1021590 = r1021589 * r1021587;
        double r1021591 = r1021586 - r1021590;
        double r1021592 = r1021591 * r1021587;
        return r1021592;
}

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 2019107 
(FPCore (x)
  :name "Rosa's Benchmark"
  (- (* 0.954929658551372 x) (* 0.12900613773279798 (* (* x x) x))))