Average Error: 12.8 → 0.4
Time: 18.3s
Precision: 64
\[\left(\left(3 + \frac{2}{r \cdot r}\right) - \frac{\left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left(\left(\left(w \cdot w\right) \cdot r\right) \cdot r\right)}{1 - v}\right) - 4.5\]
↓
\[\left(\left(3 + \frac{2}{r \cdot r}\right) - \sqrt{\frac{{\left(\left|r \cdot w\right|\right)}^{2}}{1 - v} \cdot \left(0.125 \cdot \left(3 - 2 \cdot v\right)\right)} \cdot \sqrt{\frac{{\left(\left|r \cdot w\right|\right)}^{2}}{1 - v} \cdot \left(0.125 \cdot \left(3 - 2 \cdot v\right)\right)}\right) - 4.5\]
\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) - \sqrt{\frac{{\left(\left|r \cdot w\right|\right)}^{2}}{1 - v} \cdot \left(0.125 \cdot \left(3 - 2 \cdot v\right)\right)} \cdot \sqrt{\frac{{\left(\left|r \cdot w\right|\right)}^{2}}{1 - v} \cdot \left(0.125 \cdot \left(3 - 2 \cdot v\right)\right)}\right) - 4.5
double f(double v, double w, double r) {
        double r23772 = 3.0;
        double r23773 = 2.0;
        double r23774 = r;
        double r23775 = r23774 * r23774;
        double r23776 = r23773 / r23775;
        double r23777 = r23772 + r23776;
        double r23778 = 0.125;
        double r23779 = v;
        double r23780 = r23773 * r23779;
        double r23781 = r23772 - r23780;
        double r23782 = r23778 * r23781;
        double r23783 = w;
        double r23784 = r23783 * r23783;
        double r23785 = r23784 * r23774;
        double r23786 = r23785 * r23774;
        double r23787 = r23782 * r23786;
        double r23788 = 1.0;
        double r23789 = r23788 - r23779;
        double r23790 = r23787 / r23789;
        double r23791 = r23777 - r23790;
        double r23792 = 4.5;
        double r23793 = r23791 - r23792;
        return r23793;
}
↓
double f(double v, double w, double r) {
        double r23794 = 3.0;
        double r23795 = 2.0;
        double r23796 = r;
        double r23797 = r23796 * r23796;
        double r23798 = r23795 / r23797;
        double r23799 = r23794 + r23798;
        double r23800 = w;
        double r23801 = r23796 * r23800;
        double r23802 = fabs(r23801);
        double r23803 = 2.0;
        double r23804 = pow(r23802, r23803);
        double r23805 = 1.0;
        double r23806 = v;
        double r23807 = r23805 - r23806;
        double r23808 = r23804 / r23807;
        double r23809 = 0.125;
        double r23810 = r23795 * r23806;
        double r23811 = r23794 - r23810;
        double r23812 = r23809 * r23811;
        double r23813 = r23808 * r23812;
        double r23814 = sqrt(r23813);
        double r23815 = r23814 * r23814;
        double r23816 = r23799 - r23815;
        double r23817 = 4.5;
        double r23818 = r23816 - r23817;
        return r23818;
}

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 12.8

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

  3. Applied associate-*l*7.7

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

  5. Applied *-un-lft-identity7.7

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

  6. Applied times-frac2.3

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

  7. Simplified2.3

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

  9. Applied add-sqr-sqrt2.3

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

  10. Simplified2.3

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

  11. Simplified0.3

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

  13. Applied add-sqr-sqrt0.4

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

  14. Simplified0.4

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

  15. Simplified0.4

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

  16. Final simplification0.4

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

Reproduce

herbie shell --seed 2019195 
(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))