Average Error: 0.1 → 0.1
Time: 2.3s
Precision: 64
\[0.95492965855137202 \cdot x - 0.129006137732797982 \cdot \left(\left(x \cdot x\right) \cdot x\right)\]
↓
\[0.95492965855137202 \cdot x - {\left({x}^{3} \cdot 0.129006137732797982\right)}^{1}\]
0.95492965855137202 \cdot x - 0.129006137732797982 \cdot \left(\left(x \cdot x\right) \cdot x\right)
↓
0.95492965855137202 \cdot x - {\left({x}^{3} \cdot 0.129006137732797982\right)}^{1}
double f(double x) {
        double r22008 = 0.954929658551372;
        double r22009 = x;
        double r22010 = r22008 * r22009;
        double r22011 = 0.12900613773279798;
        double r22012 = r22009 * r22009;
        double r22013 = r22012 * r22009;
        double r22014 = r22011 * r22013;
        double r22015 = r22010 - r22014;
        return r22015;
}
↓
double f(double x) {
        double r22016 = 0.954929658551372;
        double r22017 = x;
        double r22018 = r22016 * r22017;
        double r22019 = 3.0;
        double r22020 = pow(r22017, r22019);
        double r22021 = 0.12900613773279798;
        double r22022 = r22020 * r22021;
        double r22023 = 1.0;
        double r22024 = pow(r22022, r22023);
        double r22025 = r22018 - r22024;
        return r22025;
}

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. Applied pow10.1

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

  9. Applied pow-prod-down0.1

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

  10. Simplified0.1

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

  11. Final simplification0.1

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

Reproduce

herbie shell --seed 2020062 
(FPCore (x)
  :name "Rosa's Benchmark"
  :precision binary64
  (- (* 0.954929658551372 x) (* 0.12900613773279798 (* (* x x) x))))