Average Error: 0.1 → 0.1
Time: 1.8s
Precision: 64
\[0.95492965855137202 \cdot x - 0.129006137732797982 \cdot \left(\left(x \cdot x\right) \cdot x\right)\]
↓
\[0.95492965855137202 \cdot x - \left(\left(0.129006137732797982 \cdot x\right) \cdot x\right) \cdot x\]
0.95492965855137202 \cdot x - 0.129006137732797982 \cdot \left(\left(x \cdot x\right) \cdot x\right)
↓
0.95492965855137202 \cdot x - \left(\left(0.129006137732797982 \cdot x\right) \cdot x\right) \cdot x
double f(double x) {
        double r14514 = 0.954929658551372;
        double r14515 = x;
        double r14516 = r14514 * r14515;
        double r14517 = 0.12900613773279798;
        double r14518 = r14515 * r14515;
        double r14519 = r14518 * r14515;
        double r14520 = r14517 * r14519;
        double r14521 = r14516 - r14520;
        return r14521;
}
↓
double f(double x) {
        double r14522 = 0.954929658551372;
        double r14523 = x;
        double r14524 = r14522 * r14523;
        double r14525 = 0.12900613773279798;
        double r14526 = r14525 * r14523;
        double r14527 = r14526 * r14523;
        double r14528 = r14527 * r14523;
        double r14529 = r14524 - r14528;
        return r14529;
}

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. Using strategy rm

  3. Applied pow10.1

    \[\leadsto 0.95492965855137202 \cdot x - 0.129006137732797982 \cdot \left(\left(x \cdot x\right) \cdot \color{blue}{{x}^{1}}\right)\]

  4. Applied pow10.1

    \[\leadsto 0.95492965855137202 \cdot x - 0.129006137732797982 \cdot \left(\left(x \cdot \color{blue}{{x}^{1}}\right) \cdot {x}^{1}\right)\]

  5. Applied pow10.1

    \[\leadsto 0.95492965855137202 \cdot x - 0.129006137732797982 \cdot \left(\left(\color{blue}{{x}^{1}} \cdot {x}^{1}\right) \cdot {x}^{1}\right)\]

  6. Applied pow-prod-up0.1

    \[\leadsto 0.95492965855137202 \cdot x - 0.129006137732797982 \cdot \left(\color{blue}{{x}^{\left(1 + 1\right)}} \cdot {x}^{1}\right)\]

  7. Applied pow-prod-up0.1

    \[\leadsto 0.95492965855137202 \cdot x - 0.129006137732797982 \cdot \color{blue}{{x}^{\left(\left(1 + 1\right) + 1\right)}}\]

  8. Simplified0.1

    \[\leadsto 0.95492965855137202 \cdot x - 0.129006137732797982 \cdot {x}^{\color{blue}{3}}\]
  9. Using strategy rm

  10. Applied cube-mult0.1

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

  11. Applied associate-*r*0.1

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

  13. Applied associate-*r*0.1

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

  14. Final simplification0.1

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

Reproduce

herbie shell --seed 2020021 
(FPCore (x)
  :name "Rosa's Benchmark"
  :precision binary64
  (- (* 0.954929658551372 x) (* 0.12900613773279798 (* (* x x) x))))