Average Error: 12.4 → 0.4
Time: 5.1s
Precision: 64
\[\left(\left(3 + \frac{2}{r \cdot r}\right) - \frac{\left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left(\left(\left(w \cdot w\right) \cdot r\right) \cdot r\right)}{1 - v}\right) - 4.5\]
↓
\[\left(\left(3 + \frac{\frac{2}{r}}{r}\right) - \left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \frac{\left|w \cdot r\right|}{\frac{1 - v}{\left|w \cdot r\right|}}\right) - 4.5\]
\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{\frac{2}{r}}{r}\right) - \left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \frac{\left|w \cdot r\right|}{\frac{1 - v}{\left|w \cdot r\right|}}\right) - 4.5
double f(double v, double w, double r) {
        double r14779 = 3.0;
        double r14780 = 2.0;
        double r14781 = r;
        double r14782 = r14781 * r14781;
        double r14783 = r14780 / r14782;
        double r14784 = r14779 + r14783;
        double r14785 = 0.125;
        double r14786 = v;
        double r14787 = r14780 * r14786;
        double r14788 = r14779 - r14787;
        double r14789 = r14785 * r14788;
        double r14790 = w;
        double r14791 = r14790 * r14790;
        double r14792 = r14791 * r14781;
        double r14793 = r14792 * r14781;
        double r14794 = r14789 * r14793;
        double r14795 = 1.0;
        double r14796 = r14795 - r14786;
        double r14797 = r14794 / r14796;
        double r14798 = r14784 - r14797;
        double r14799 = 4.5;
        double r14800 = r14798 - r14799;
        return r14800;
}
↓
double f(double v, double w, double r) {
        double r14801 = 3.0;
        double r14802 = 2.0;
        double r14803 = r;
        double r14804 = r14802 / r14803;
        double r14805 = r14804 / r14803;
        double r14806 = r14801 + r14805;
        double r14807 = 0.125;
        double r14808 = v;
        double r14809 = r14802 * r14808;
        double r14810 = r14801 - r14809;
        double r14811 = r14807 * r14810;
        double r14812 = w;
        double r14813 = r14812 * r14803;
        double r14814 = fabs(r14813);
        double r14815 = 1.0;
        double r14816 = r14815 - r14808;
        double r14817 = r14816 / r14814;
        double r14818 = r14814 / r14817;
        double r14819 = r14811 * r14818;
        double r14820 = r14806 - r14819;
        double r14821 = 4.5;
        double r14822 = r14820 - r14821;
        return r14822;
}

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 12.4

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

  3. Applied *-un-lft-identity12.4

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

  4. Applied times-frac8.3

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

  5. Simplified8.3

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

  7. Applied add-sqr-sqrt8.4

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

  8. Simplified8.3

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

  9. Simplified0.4

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

  11. Applied associate-/r*0.4

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

  13. Applied associate-/l*0.4

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

  14. Final simplification0.4

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

Reproduce

herbie shell --seed 2020065 
(FPCore (v w r)
  :name "Rosa's TurbineBenchmark"
  :precision binary64
  (- (- (+ 3 (/ 2 (* r r))) (/ (* (* 0.125 (- 3 (* 2 v))) (* (* (* w w) r) r)) (- 1 v))) 4.5))