Average Error: 0.1 → 0.1
Time: 2.6s
Precision: 64
\[0.95492965855137202 \cdot x - 0.129006137732797982 \cdot \left(\left(x \cdot x\right) \cdot x\right)\]
↓
\[x \cdot \left(0.95492965855137202 - \left(0.129006137732797982 \cdot x\right) \cdot x\right)\]
0.95492965855137202 \cdot x - 0.129006137732797982 \cdot \left(\left(x \cdot x\right) \cdot x\right)
↓
x \cdot \left(0.95492965855137202 - \left(0.129006137732797982 \cdot x\right) \cdot x\right)
double f(double x) {
        double r29642 = 0.954929658551372;
        double r29643 = x;
        double r29644 = r29642 * r29643;
        double r29645 = 0.12900613773279798;
        double r29646 = r29643 * r29643;
        double r29647 = r29646 * r29643;
        double r29648 = r29645 * r29647;
        double r29649 = r29644 - r29648;
        return r29649;
}
↓
double f(double x) {
        double r29650 = x;
        double r29651 = 0.954929658551372;
        double r29652 = 0.12900613773279798;
        double r29653 = r29652 * r29650;
        double r29654 = r29653 * r29650;
        double r29655 = r29651 - r29654;
        double r29656 = r29650 * r29655;
        return r29656;
}

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. Final simplification0.1

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

Reproduce

herbie shell --seed 2020039 
(FPCore (x)
  :name "Rosa's Benchmark"
  :precision binary64
  (- (* 0.954929658551372 x) (* 0.12900613773279798 (* (* x x) x))))