Average Error: 13.4 → 0.4
Time: 8.5s
Precision: 64
\[\left(\left(3 + \frac{2}{r \cdot r}\right) - \frac{\left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left(\left(\left(w \cdot w\right) \cdot r\right) \cdot r\right)}{1 - v}\right) - 4.5\]
↓
\[\left(\left(3 + \frac{\frac{2}{r}}{r}\right) - \frac{1}{\frac{\sqrt{\frac{1 - v}{0.125 \cdot \left(3 - 2 \cdot v\right)}}}{\sqrt{{\left(\left|w \cdot r\right|\right)}^{2}}} \cdot \frac{\sqrt{\frac{1 - v}{0.125 \cdot \left(3 - 2 \cdot v\right)}}}{\sqrt{{\left(\left|w \cdot r\right|\right)}^{2}}}}\right) - 4.5\]
\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) - \frac{1}{\frac{\sqrt{\frac{1 - v}{0.125 \cdot \left(3 - 2 \cdot v\right)}}}{\sqrt{{\left(\left|w \cdot r\right|\right)}^{2}}} \cdot \frac{\sqrt{\frac{1 - v}{0.125 \cdot \left(3 - 2 \cdot v\right)}}}{\sqrt{{\left(\left|w \cdot r\right|\right)}^{2}}}}\right) - 4.5
double f(double v, double w, double r) {
        double r27870 = 3.0;
        double r27871 = 2.0;
        double r27872 = r;
        double r27873 = r27872 * r27872;
        double r27874 = r27871 / r27873;
        double r27875 = r27870 + r27874;
        double r27876 = 0.125;
        double r27877 = v;
        double r27878 = r27871 * r27877;
        double r27879 = r27870 - r27878;
        double r27880 = r27876 * r27879;
        double r27881 = w;
        double r27882 = r27881 * r27881;
        double r27883 = r27882 * r27872;
        double r27884 = r27883 * r27872;
        double r27885 = r27880 * r27884;
        double r27886 = 1.0;
        double r27887 = r27886 - r27877;
        double r27888 = r27885 / r27887;
        double r27889 = r27875 - r27888;
        double r27890 = 4.5;
        double r27891 = r27889 - r27890;
        return r27891;
}
↓
double f(double v, double w, double r) {
        double r27892 = 3.0;
        double r27893 = 2.0;
        double r27894 = r;
        double r27895 = r27893 / r27894;
        double r27896 = r27895 / r27894;
        double r27897 = r27892 + r27896;
        double r27898 = 1.0;
        double r27899 = 1.0;
        double r27900 = v;
        double r27901 = r27899 - r27900;
        double r27902 = 0.125;
        double r27903 = r27893 * r27900;
        double r27904 = r27892 - r27903;
        double r27905 = r27902 * r27904;
        double r27906 = r27901 / r27905;
        double r27907 = sqrt(r27906);
        double r27908 = w;
        double r27909 = r27908 * r27894;
        double r27910 = fabs(r27909);
        double r27911 = 2.0;
        double r27912 = pow(r27910, r27911);
        double r27913 = sqrt(r27912);
        double r27914 = r27907 / r27913;
        double r27915 = r27914 * r27914;
        double r27916 = r27898 / r27915;
        double r27917 = r27897 - r27916;
        double r27918 = 4.5;
        double r27919 = r27917 - r27918;
        return r27919;
}

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 13.4

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

  3. Applied add-sqr-sqrt13.4

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

  4. Simplified13.4

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

  5. Simplified6.9

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

  7. Applied clear-num7.0

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

  8. Simplified0.4

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

  10. Applied associate-/r*0.4

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

  12. Applied add-sqr-sqrt0.4

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

  13. Applied add-sqr-sqrt0.4

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

  14. Applied times-frac0.4

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

  15. Final simplification0.4

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

Reproduce

herbie shell --seed 2020002 
(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))