Average Error: 12.9 → 0.4
Time: 7.6s
Precision: 64
\[\left(\left(3 + \frac{2}{r \cdot r}\right) - \frac{\left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left(\left(\left(w \cdot w\right) \cdot r\right) \cdot r\right)}{1 - v}\right) - 4.5\]
↓
\[\left(\left(3 + \frac{2}{r \cdot r}\right) - \left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \frac{{\left(\sqrt{\left|w \cdot r\right|}\right)}^{2}}{\frac{1 - v}{\left|w \cdot r\right|}}\right) - 4.5\]
\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{2}{r \cdot r}\right) - \left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \frac{{\left(\sqrt{\left|w \cdot r\right|}\right)}^{2}}{\frac{1 - v}{\left|w \cdot r\right|}}\right) - 4.5
double f(double v, double w, double r) {
        double r22761 = 3.0;
        double r22762 = 2.0;
        double r22763 = r;
        double r22764 = r22763 * r22763;
        double r22765 = r22762 / r22764;
        double r22766 = r22761 + r22765;
        double r22767 = 0.125;
        double r22768 = v;
        double r22769 = r22762 * r22768;
        double r22770 = r22761 - r22769;
        double r22771 = r22767 * r22770;
        double r22772 = w;
        double r22773 = r22772 * r22772;
        double r22774 = r22773 * r22763;
        double r22775 = r22774 * r22763;
        double r22776 = r22771 * r22775;
        double r22777 = 1.0;
        double r22778 = r22777 - r22768;
        double r22779 = r22776 / r22778;
        double r22780 = r22766 - r22779;
        double r22781 = 4.5;
        double r22782 = r22780 - r22781;
        return r22782;
}
↓
double f(double v, double w, double r) {
        double r22783 = 3.0;
        double r22784 = 2.0;
        double r22785 = r;
        double r22786 = r22785 * r22785;
        double r22787 = r22784 / r22786;
        double r22788 = r22783 + r22787;
        double r22789 = 0.125;
        double r22790 = v;
        double r22791 = r22784 * r22790;
        double r22792 = r22783 - r22791;
        double r22793 = r22789 * r22792;
        double r22794 = w;
        double r22795 = r22794 * r22785;
        double r22796 = fabs(r22795);
        double r22797 = sqrt(r22796);
        double r22798 = 2.0;
        double r22799 = pow(r22797, r22798);
        double r22800 = 1.0;
        double r22801 = r22800 - r22790;
        double r22802 = r22801 / r22796;
        double r22803 = r22799 / r22802;
        double r22804 = r22793 * r22803;
        double r22805 = r22788 - r22804;
        double r22806 = 4.5;
        double r22807 = r22805 - r22806;
        return r22807;
}

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 12.9

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

  3. Applied add-sqr-sqrt12.9

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

  4. Simplified12.9

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

  5. Simplified6.5

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

  7. Applied *-un-lft-identity6.5

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

  8. Applied times-frac0.4

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

  9. Simplified0.4

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

  10. Simplified0.4

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

  12. Applied add-sqr-sqrt0.6

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

  13. Applied unpow-prod-down0.6

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

  14. Applied associate-/l*0.5

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

  15. Simplified0.4

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

  16. Final simplification0.4

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

Reproduce

herbie shell --seed 2019322 
(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))