Average Error: 0.1 → 0.1
Time: 2.9s
Precision: 64
\[0.95492965855137202 \cdot x - 0.129006137732797982 \cdot \left(\left(x \cdot x\right) \cdot x\right)\]
↓
\[x \cdot 0.95492965855137202 + \left(-0.129006137732797982 \cdot {x}^{3}\right)\]
0.95492965855137202 \cdot x - 0.129006137732797982 \cdot \left(\left(x \cdot x\right) \cdot x\right)
↓
x \cdot 0.95492965855137202 + \left(-0.129006137732797982 \cdot {x}^{3}\right)
double f(double x) {
        double r22462 = 0.954929658551372;
        double r22463 = x;
        double r22464 = r22462 * r22463;
        double r22465 = 0.12900613773279798;
        double r22466 = r22463 * r22463;
        double r22467 = r22466 * r22463;
        double r22468 = r22465 * r22467;
        double r22469 = r22464 - r22468;
        return r22469;
}
↓
double f(double x) {
        double r22470 = x;
        double r22471 = 0.954929658551372;
        double r22472 = r22470 * r22471;
        double r22473 = 0.12900613773279798;
        double r22474 = 3.0;
        double r22475 = pow(r22470, r22474);
        double r22476 = r22473 * r22475;
        double r22477 = -r22476;
        double r22478 = r22472 + r22477;
        return r22478;
}

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

    \[0.95492965855137202 \cdot x - 0.129006137732797982 \cdot \left(\left(x \cdot x\right) \cdot x\right)\]

  2. Simplified0.1

    \[\leadsto \color{blue}{x \cdot \left(0.95492965855137202 - 0.129006137732797982 \cdot \left(x \cdot x\right)\right)}\]
  3. Using strategy rm

  4. Applied associate-*r*0.1

    \[\leadsto x \cdot \left(0.95492965855137202 - \color{blue}{\left(0.129006137732797982 \cdot x\right) \cdot x}\right)\]
  5. Using strategy rm

  6. Applied sub-neg0.1

    \[\leadsto x \cdot \color{blue}{\left(0.95492965855137202 + \left(-\left(0.129006137732797982 \cdot x\right) \cdot x\right)\right)}\]

  7. Applied distribute-lft-in0.1

    \[\leadsto \color{blue}{x \cdot 0.95492965855137202 + x \cdot \left(-\left(0.129006137732797982 \cdot x\right) \cdot x\right)}\]

  8. Simplified0.1

    \[\leadsto x \cdot 0.95492965855137202 + \color{blue}{\left(-0.129006137732797982 \cdot {x}^{3}\right)}\]

  9. Final simplification0.1

    \[\leadsto x \cdot 0.95492965855137202 + \left(-0.129006137732797982 \cdot {x}^{3}\right)\]

Reproduce

herbie shell --seed 2020035 
(FPCore (x)
  :name "Rosa's Benchmark"
  :precision binary64
  (- (* 0.954929658551372 x) (* 0.12900613773279798 (* (* x x) x))))