Average Error: 12.8 → 0.3
Time: 5.0s
Precision: 64
\[\left(\left(3 + \frac{2}{r \cdot r}\right) - \frac{\left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left(\left(\left(w \cdot w\right) \cdot r\right) \cdot r\right)}{1 - v}\right) - 4.5\]
↓
\[\left(\left(3 + \frac{\frac{2}{r}}{r}\right) - \left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \frac{\left(w \cdot r\right) \cdot \left(w \cdot r\right)}{1 - v}\right) - 4.5\]
\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) - \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
double f(double v, double w, double r) {
        double r14731 = 3.0;
        double r14732 = 2.0;
        double r14733 = r;
        double r14734 = r14733 * r14733;
        double r14735 = r14732 / r14734;
        double r14736 = r14731 + r14735;
        double r14737 = 0.125;
        double r14738 = v;
        double r14739 = r14732 * r14738;
        double r14740 = r14731 - r14739;
        double r14741 = r14737 * r14740;
        double r14742 = w;
        double r14743 = r14742 * r14742;
        double r14744 = r14743 * r14733;
        double r14745 = r14744 * r14733;
        double r14746 = r14741 * r14745;
        double r14747 = 1.0;
        double r14748 = r14747 - r14738;
        double r14749 = r14746 / r14748;
        double r14750 = r14736 - r14749;
        double r14751 = 4.5;
        double r14752 = r14750 - r14751;
        return r14752;
}
↓
double f(double v, double w, double r) {
        double r14753 = 3.0;
        double r14754 = 2.0;
        double r14755 = r;
        double r14756 = r14754 / r14755;
        double r14757 = r14756 / r14755;
        double r14758 = r14753 + r14757;
        double r14759 = 0.125;
        double r14760 = v;
        double r14761 = r14754 * r14760;
        double r14762 = r14753 - r14761;
        double r14763 = r14759 * r14762;
        double r14764 = w;
        double r14765 = r14764 * r14755;
        double r14766 = r14765 * r14765;
        double r14767 = 1.0;
        double r14768 = r14767 - r14760;
        double r14769 = r14766 / r14768;
        double r14770 = r14763 * r14769;
        double r14771 = r14758 - r14770;
        double r14772 = 4.5;
        double r14773 = r14771 - r14772;
        return r14773;
}

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*8.1

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

  5. Applied associate-/l*2.6

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

  7. Applied div-inv2.6

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

  8. Simplified0.3

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

  10. Applied associate-/r*0.3

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

  11. Final simplification0.3

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

Reproduce

herbie shell --seed 2020047 
(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))