Average Error: 0.1 → 0.1
Time: 2.3s
Precision: 64
\[0.95492965855137202 \cdot x - 0.129006137732797982 \cdot \left(\left(x \cdot x\right) \cdot x\right)\]
↓
\[0.95492965855137202 \cdot x - 0.129006137732797982 \cdot {x}^{3}\]
0.95492965855137202 \cdot x - 0.129006137732797982 \cdot \left(\left(x \cdot x\right) \cdot x\right)
↓
0.95492965855137202 \cdot x - 0.129006137732797982 \cdot {x}^{3}
double f(double x) {
        double r31168 = 0.954929658551372;
        double r31169 = x;
        double r31170 = r31168 * r31169;
        double r31171 = 0.12900613773279798;
        double r31172 = r31169 * r31169;
        double r31173 = r31172 * r31169;
        double r31174 = r31171 * r31173;
        double r31175 = r31170 - r31174;
        return r31175;
}
↓
double f(double x) {
        double r31176 = 0.954929658551372;
        double r31177 = x;
        double r31178 = r31176 * r31177;
        double r31179 = 0.12900613773279798;
        double r31180 = 3.0;
        double r31181 = pow(r31177, r31180);
        double r31182 = r31179 * r31181;
        double r31183 = r31178 - r31182;
        return r31183;
}

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. Final simplification0.1

    \[\leadsto 0.95492965855137202 \cdot x - 0.129006137732797982 \cdot {x}^{3}\]

Reproduce

herbie shell --seed 2020057 
(FPCore (x)
  :name "Rosa's Benchmark"
  :precision binary64
  (- (* 0.954929658551372 x) (* 0.12900613773279798 (* (* x x) x))))