Average Error: 13.1 → 0.3
Time: 26.4s
Precision: 64
\[\left(\left(3 + \frac{2}{r \cdot r}\right) - \frac{\left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left(\left(\left(w \cdot w\right) \cdot r\right) \cdot r\right)}{1 - v}\right) - 4.5\]
↓
\[\left(\left(3 + \frac{2}{r \cdot r}\right) - \left(w \cdot r\right) \cdot \left(\left(\frac{3 - 2 \cdot v}{1 - v} \cdot 0.125\right) \cdot \left(w \cdot r\right)\right)\right) - 4.5\]
\left(\left(3 + \frac{2}{r \cdot r}\right) - \frac{\left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left(\left(\left(w \cdot w\right) \cdot r\right) \cdot r\right)}{1 - v}\right) - 4.5
↓
\left(\left(3 + \frac{2}{r \cdot r}\right) - \left(w \cdot r\right) \cdot \left(\left(\frac{3 - 2 \cdot v}{1 - v} \cdot 0.125\right) \cdot \left(w \cdot r\right)\right)\right) - 4.5
double f(double v, double w, double r) {
        double r1368735 = 3.0;
        double r1368736 = 2.0;
        double r1368737 = r;
        double r1368738 = r1368737 * r1368737;
        double r1368739 = r1368736 / r1368738;
        double r1368740 = r1368735 + r1368739;
        double r1368741 = 0.125;
        double r1368742 = v;
        double r1368743 = r1368736 * r1368742;
        double r1368744 = r1368735 - r1368743;
        double r1368745 = r1368741 * r1368744;
        double r1368746 = w;
        double r1368747 = r1368746 * r1368746;
        double r1368748 = r1368747 * r1368737;
        double r1368749 = r1368748 * r1368737;
        double r1368750 = r1368745 * r1368749;
        double r1368751 = 1.0;
        double r1368752 = r1368751 - r1368742;
        double r1368753 = r1368750 / r1368752;
        double r1368754 = r1368740 - r1368753;
        double r1368755 = 4.5;
        double r1368756 = r1368754 - r1368755;
        return r1368756;
}
↓
double f(double v, double w, double r) {
        double r1368757 = 3.0;
        double r1368758 = 2.0;
        double r1368759 = r;
        double r1368760 = r1368759 * r1368759;
        double r1368761 = r1368758 / r1368760;
        double r1368762 = r1368757 + r1368761;
        double r1368763 = w;
        double r1368764 = r1368763 * r1368759;
        double r1368765 = v;
        double r1368766 = r1368758 * r1368765;
        double r1368767 = r1368757 - r1368766;
        double r1368768 = 1.0;
        double r1368769 = r1368768 - r1368765;
        double r1368770 = r1368767 / r1368769;
        double r1368771 = 0.125;
        double r1368772 = r1368770 * r1368771;
        double r1368773 = r1368772 * r1368764;
        double r1368774 = r1368764 * r1368773;
        double r1368775 = r1368762 - r1368774;
        double r1368776 = 4.5;
        double r1368777 = r1368775 - r1368776;
        return r1368777;
}

Error

Bits error versus v

Bits error versus w

Bits error versus r

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 13.1

    \[\left(\left(3 + \frac{2}{r \cdot r}\right) - \frac{\left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left(\left(\left(w \cdot w\right) \cdot r\right) \cdot r\right)}{1 - v}\right) - 4.5\]

  2. Simplified0.4

    \[\leadsto \color{blue}{\left(3 + \frac{2}{r \cdot r}\right) - \mathsf{fma}\left(\left(w \cdot r\right) \cdot \left(w \cdot r\right), \frac{0.125}{1 - v} \cdot \left(3 - 2 \cdot v\right), 4.5\right)}\]
  3. Using strategy rm

  4. Applied div-inv0.4

    \[\leadsto \left(3 + \frac{2}{r \cdot r}\right) - \mathsf{fma}\left(\left(w \cdot r\right) \cdot \left(w \cdot r\right), \color{blue}{\left(0.125 \cdot \frac{1}{1 - v}\right)} \cdot \left(3 - 2 \cdot v\right), 4.5\right)\]

  5. Applied associate-*l*0.4

    \[\leadsto \left(3 + \frac{2}{r \cdot r}\right) - \mathsf{fma}\left(\left(w \cdot r\right) \cdot \left(w \cdot r\right), \color{blue}{0.125 \cdot \left(\frac{1}{1 - v} \cdot \left(3 - 2 \cdot v\right)\right)}, 4.5\right)\]

  6. Simplified0.4

    \[\leadsto \left(3 + \frac{2}{r \cdot r}\right) - \mathsf{fma}\left(\left(w \cdot r\right) \cdot \left(w \cdot r\right), 0.125 \cdot \color{blue}{\frac{3 - 2 \cdot v}{1 - v}}, 4.5\right)\]
  7. Using strategy rm

  8. Applied fma-udef0.4

    \[\leadsto \left(3 + \frac{2}{r \cdot r}\right) - \color{blue}{\left(\left(\left(w \cdot r\right) \cdot \left(w \cdot r\right)\right) \cdot \left(0.125 \cdot \frac{3 - 2 \cdot v}{1 - v}\right) + 4.5\right)}\]

  9. Applied associate--r+0.4

    \[\leadsto \color{blue}{\left(\left(3 + \frac{2}{r \cdot r}\right) - \left(\left(w \cdot r\right) \cdot \left(w \cdot r\right)\right) \cdot \left(0.125 \cdot \frac{3 - 2 \cdot v}{1 - v}\right)\right) - 4.5}\]
  10. Using strategy rm

  11. Applied associate-*l*0.3

    \[\leadsto \left(\left(3 + \frac{2}{r \cdot r}\right) - \color{blue}{\left(w \cdot r\right) \cdot \left(\left(w \cdot r\right) \cdot \left(0.125 \cdot \frac{3 - 2 \cdot v}{1 - v}\right)\right)}\right) - 4.5\]

  12. Final simplification0.3

    \[\leadsto \left(\left(3 + \frac{2}{r \cdot r}\right) - \left(w \cdot r\right) \cdot \left(\left(\frac{3 - 2 \cdot v}{1 - v} \cdot 0.125\right) \cdot \left(w \cdot r\right)\right)\right) - 4.5\]

Reproduce

herbie shell --seed 2019174 +o rules:numerics
(FPCore (v w r)
  :name "Rosa's TurbineBenchmark"
  (- (- (+ 3.0 (/ 2.0 (* r r))) (/ (* (* 0.125 (- 3.0 (* 2.0 v))) (* (* (* w w) r) r)) (- 1.0 v))) 4.5))