Average Error: 0.1 → 0.1
Time: 2.3s
Precision: 64
\[0.95492965855137202 \cdot x - 0.129006137732797982 \cdot \left(\left(x \cdot x\right) \cdot x\right)\]
↓
\[0.95492965855137202 \cdot x - 0.129006137732797982 \cdot {\left({x}^{3}\right)}^{1}\]
0.95492965855137202 \cdot x - 0.129006137732797982 \cdot \left(\left(x \cdot x\right) \cdot x\right)
↓
0.95492965855137202 \cdot x - 0.129006137732797982 \cdot {\left({x}^{3}\right)}^{1}
double f(double x) {
        double r20982 = 0.954929658551372;
        double r20983 = x;
        double r20984 = r20982 * r20983;
        double r20985 = 0.12900613773279798;
        double r20986 = r20983 * r20983;
        double r20987 = r20986 * r20983;
        double r20988 = r20985 * r20987;
        double r20989 = r20984 - r20988;
        return r20989;
}
↓
double f(double x) {
        double r20990 = 0.954929658551372;
        double r20991 = x;
        double r20992 = r20990 * r20991;
        double r20993 = 0.12900613773279798;
        double r20994 = 3.0;
        double r20995 = pow(r20991, r20994);
        double r20996 = 1.0;
        double r20997 = pow(r20995, r20996);
        double r20998 = r20993 * r20997;
        double r20999 = r20992 - r20998;
        return r20999;
}

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-down0.1

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

  7. Applied pow-prod-down0.1

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

  8. Simplified0.1

    \[\leadsto 0.95492965855137202 \cdot x - 0.129006137732797982 \cdot {\color{blue}{\left({x}^{3}\right)}}^{1}\]

  9. Final simplification0.1

    \[\leadsto 0.95492965855137202 \cdot x - 0.129006137732797982 \cdot {\left({x}^{3}\right)}^{1}\]

Reproduce

herbie shell --seed 2020024 
(FPCore (x)
  :name "Rosa's Benchmark"
  :precision binary64
  (- (* 0.954929658551372 x) (* 0.12900613773279798 (* (* x x) x))))