Average Error: 13.2 → 0.4
Time: 9.0s
Precision: 64
\[\left(\left(3 + \frac{2}{r \cdot r}\right) - \frac{\left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left(\left(\left(w \cdot w\right) \cdot r\right) \cdot r\right)}{1 - v}\right) - 4.5\]
↓
\[\left(\left(3 + \frac{2}{r \cdot r}\right) - \frac{\frac{1}{\sqrt{\frac{1 - v}{0.125 \cdot \left(3 - 2 \cdot v\right)}}} \cdot \left|\left|w \cdot r\right|\right|}{\frac{\sqrt{\frac{1 - v}{0.125 \cdot \left(3 - 2 \cdot v\right)}}}{\sqrt{{\left(\left|w \cdot r\right|\right)}^{2}}}}\right) - 4.5\]
\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{2}{r \cdot r}\right) - \frac{\frac{1}{\sqrt{\frac{1 - v}{0.125 \cdot \left(3 - 2 \cdot v\right)}}} \cdot \left|\left|w \cdot r\right|\right|}{\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 r27669 = 3.0;
        double r27670 = 2.0;
        double r27671 = r;
        double r27672 = r27671 * r27671;
        double r27673 = r27670 / r27672;
        double r27674 = r27669 + r27673;
        double r27675 = 0.125;
        double r27676 = v;
        double r27677 = r27670 * r27676;
        double r27678 = r27669 - r27677;
        double r27679 = r27675 * r27678;
        double r27680 = w;
        double r27681 = r27680 * r27680;
        double r27682 = r27681 * r27671;
        double r27683 = r27682 * r27671;
        double r27684 = r27679 * r27683;
        double r27685 = 1.0;
        double r27686 = r27685 - r27676;
        double r27687 = r27684 / r27686;
        double r27688 = r27674 - r27687;
        double r27689 = 4.5;
        double r27690 = r27688 - r27689;
        return r27690;
}
↓
double f(double v, double w, double r) {
        double r27691 = 3.0;
        double r27692 = 2.0;
        double r27693 = r;
        double r27694 = r27693 * r27693;
        double r27695 = r27692 / r27694;
        double r27696 = r27691 + r27695;
        double r27697 = 1.0;
        double r27698 = 1.0;
        double r27699 = v;
        double r27700 = r27698 - r27699;
        double r27701 = 0.125;
        double r27702 = r27692 * r27699;
        double r27703 = r27691 - r27702;
        double r27704 = r27701 * r27703;
        double r27705 = r27700 / r27704;
        double r27706 = sqrt(r27705);
        double r27707 = r27697 / r27706;
        double r27708 = w;
        double r27709 = r27708 * r27693;
        double r27710 = fabs(r27709);
        double r27711 = fabs(r27710);
        double r27712 = r27707 * r27711;
        double r27713 = 2.0;
        double r27714 = pow(r27710, r27713);
        double r27715 = sqrt(r27714);
        double r27716 = r27706 / r27715;
        double r27717 = r27712 / r27716;
        double r27718 = r27696 - r27717;
        double r27719 = 4.5;
        double r27720 = r27718 - r27719;
        return r27720;
}

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 13.2

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

  3. Applied add-sqr-sqrt13.2

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

  4. Simplified13.2

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

  5. Simplified6.8

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

  7. Applied clear-num6.8

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

  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 add-sqr-sqrt0.4

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

  11. Applied add-sqr-sqrt0.4

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

  12. Applied times-frac0.5

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

  13. Applied associate-/r*0.4

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

  14. Simplified0.4

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

  15. Final simplification0.4

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

Reproduce

herbie shell --seed 2020033 
(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))