Average Error: 0.1 → 0.1
Time: 21.9s
Precision: 64
\[0.954929658551372 \cdot x - 0.12900613773279798 \cdot \left(\left(x \cdot x\right) \cdot x\right)\]
↓
\[0.954929658551372 \cdot x - 0.12900613773279798 \cdot {x}^{3}\]
0.954929658551372 \cdot x - 0.12900613773279798 \cdot \left(\left(x \cdot x\right) \cdot x\right)
↓
0.954929658551372 \cdot x - 0.12900613773279798 \cdot {x}^{3}
double f(double x) {
        double r990488 = 0.954929658551372;
        double r990489 = x;
        double r990490 = r990488 * r990489;
        double r990491 = 0.12900613773279798;
        double r990492 = r990489 * r990489;
        double r990493 = r990492 * r990489;
        double r990494 = r990491 * r990493;
        double r990495 = r990490 - r990494;
        return r990495;
}
↓
double f(double x) {
        double r990496 = 0.954929658551372;
        double r990497 = x;
        double r990498 = r990496 * r990497;
        double r990499 = 0.12900613773279798;
        double r990500 = 3.0;
        double r990501 = pow(r990497, r990500);
        double r990502 = r990499 * r990501;
        double r990503 = r990498 - r990502;
        return r990503;
}

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 pow10.1

    \[\leadsto 0.954929658551372 \cdot x - 0.12900613773279798 \cdot \left(\left(x \cdot x\right) \cdot \color{blue}{{x}^{1}}\right)\]

  4. Applied pow10.1

    \[\leadsto 0.954929658551372 \cdot x - 0.12900613773279798 \cdot \left(\left(x \cdot \color{blue}{{x}^{1}}\right) \cdot {x}^{1}\right)\]

  5. Applied pow10.1

    \[\leadsto 0.954929658551372 \cdot x - 0.12900613773279798 \cdot \left(\left(\color{blue}{{x}^{1}} \cdot {x}^{1}\right) \cdot {x}^{1}\right)\]

  6. Applied pow-prod-up0.1

    \[\leadsto 0.954929658551372 \cdot x - 0.12900613773279798 \cdot \left(\color{blue}{{x}^{\left(1 + 1\right)}} \cdot {x}^{1}\right)\]

  7. Applied pow-prod-up0.1

    \[\leadsto 0.954929658551372 \cdot x - 0.12900613773279798 \cdot \color{blue}{{x}^{\left(\left(1 + 1\right) + 1\right)}}\]

  8. Simplified0.1

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

  9. Final simplification0.1

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

Reproduce

herbie shell --seed 2019120 +o rules:numerics
(FPCore (x)
  :name "Rosa's Benchmark"
  (- (* 0.954929658551372 x) (* 0.12900613773279798 (* (* x x) x))))