Average Error: 12.6 → 0.4
Time: 33.2s
Precision: 64
\[\left(\left(3 + \frac{2}{r \cdot r}\right) - \frac{\left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left(\left(\left(w \cdot w\right) \cdot r\right) \cdot r\right)}{1 - v}\right) - 4.5\]
↓
\[\left(\frac{2}{r \cdot r} - \frac{1}{\frac{1}{\frac{0.125 \cdot \left(3 - 2 \cdot v\right)}{\frac{1 - v}{\left(r \cdot w\right) \cdot \left(r \cdot w\right)}}}}\right) - \left(4.5 - 3\right)\]
\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(\frac{2}{r \cdot r} - \frac{1}{\frac{1}{\frac{0.125 \cdot \left(3 - 2 \cdot v\right)}{\frac{1 - v}{\left(r \cdot w\right) \cdot \left(r \cdot w\right)}}}}\right) - \left(4.5 - 3\right)
double f(double v, double w, double r) {
        double r742762 = 3.0;
        double r742763 = 2.0;
        double r742764 = r;
        double r742765 = r742764 * r742764;
        double r742766 = r742763 / r742765;
        double r742767 = r742762 + r742766;
        double r742768 = 0.125;
        double r742769 = v;
        double r742770 = r742763 * r742769;
        double r742771 = r742762 - r742770;
        double r742772 = r742768 * r742771;
        double r742773 = w;
        double r742774 = r742773 * r742773;
        double r742775 = r742774 * r742764;
        double r742776 = r742775 * r742764;
        double r742777 = r742772 * r742776;
        double r742778 = 1.0;
        double r742779 = r742778 - r742769;
        double r742780 = r742777 / r742779;
        double r742781 = r742767 - r742780;
        double r742782 = 4.5;
        double r742783 = r742781 - r742782;
        return r742783;
}
↓
double f(double v, double w, double r) {
        double r742784 = 2.0;
        double r742785 = r;
        double r742786 = r742785 * r742785;
        double r742787 = r742784 / r742786;
        double r742788 = 1.0;
        double r742789 = 0.125;
        double r742790 = 3.0;
        double r742791 = v;
        double r742792 = r742784 * r742791;
        double r742793 = r742790 - r742792;
        double r742794 = r742789 * r742793;
        double r742795 = r742788 - r742791;
        double r742796 = w;
        double r742797 = r742785 * r742796;
        double r742798 = r742797 * r742797;
        double r742799 = r742795 / r742798;
        double r742800 = r742794 / r742799;
        double r742801 = r742788 / r742800;
        double r742802 = r742788 / r742801;
        double r742803 = r742787 - r742802;
        double r742804 = 4.5;
        double r742805 = r742804 - r742790;
        double r742806 = r742803 - r742805;
        return r742806;
}

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 12.6

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

  2. Simplified0.4

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

  4. Applied clear-num0.4

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

  6. Applied *-un-lft-identity0.4

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

  7. Applied associate-/l*0.4

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

  8. Final simplification0.4

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

Reproduce

herbie shell --seed 2019128 
(FPCore (v w r)
  :name "Rosa's TurbineBenchmark"
  (- (- (+ 3 (/ 2 (* r r))) (/ (* (* 0.125 (- 3 (* 2 v))) (* (* (* w w) r) r)) (- 1 v))) 4.5))