Average Error: 12.3 → 0.4
Time: 6.5m
Precision: 64
\[\left(\left(3 + \frac{2}{r \cdot r}\right) - \frac{\left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left(\left(\left(w \cdot w\right) \cdot r\right) \cdot r\right)}{1 - v}\right) - 4.5\]
↓
\[\left(\left(3 + \frac{\frac{2}{r}}{r}\right) - 4.5\right) - \frac{\frac{0.125}{\frac{\sqrt{\frac{1 - v}{3 - v \cdot 2}}}{r \cdot w}}}{\frac{\sqrt{\frac{1 - v}{3 - v \cdot 2}}}{r \cdot w}}\]
\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) - 4.5\right) - \frac{\frac{0.125}{\frac{\sqrt{\frac{1 - v}{3 - v \cdot 2}}}{r \cdot w}}}{\frac{\sqrt{\frac{1 - v}{3 - v \cdot 2}}}{r \cdot w}}
double f(double v, double w, double r) {
        double r41983150 = 3.0;
        double r41983151 = 2.0;
        double r41983152 = r;
        double r41983153 = r41983152 * r41983152;
        double r41983154 = r41983151 / r41983153;
        double r41983155 = r41983150 + r41983154;
        double r41983156 = 0.125;
        double r41983157 = v;
        double r41983158 = r41983151 * r41983157;
        double r41983159 = r41983150 - r41983158;
        double r41983160 = r41983156 * r41983159;
        double r41983161 = w;
        double r41983162 = r41983161 * r41983161;
        double r41983163 = r41983162 * r41983152;
        double r41983164 = r41983163 * r41983152;
        double r41983165 = r41983160 * r41983164;
        double r41983166 = 1.0;
        double r41983167 = r41983166 - r41983157;
        double r41983168 = r41983165 / r41983167;
        double r41983169 = r41983155 - r41983168;
        double r41983170 = 4.5;
        double r41983171 = r41983169 - r41983170;
        return r41983171;
}
↓
double f(double v, double w, double r) {
        double r41983172 = 3.0;
        double r41983173 = 2.0;
        double r41983174 = r;
        double r41983175 = r41983173 / r41983174;
        double r41983176 = r41983175 / r41983174;
        double r41983177 = r41983172 + r41983176;
        double r41983178 = 4.5;
        double r41983179 = r41983177 - r41983178;
        double r41983180 = 0.125;
        double r41983181 = 1.0;
        double r41983182 = v;
        double r41983183 = r41983181 - r41983182;
        double r41983184 = r41983182 * r41983173;
        double r41983185 = r41983172 - r41983184;
        double r41983186 = r41983183 / r41983185;
        double r41983187 = sqrt(r41983186);
        double r41983188 = w;
        double r41983189 = r41983174 * r41983188;
        double r41983190 = r41983187 / r41983189;
        double r41983191 = r41983180 / r41983190;
        double r41983192 = r41983191 / r41983190;
        double r41983193 = r41983179 - r41983192;
        return r41983193;
}

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 12.3

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

  2. Simplified0.4

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

  4. Applied associate-/r*0.4

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

  6. Applied add-sqr-sqrt0.5

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

  7. Applied times-frac0.4

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

  8. Applied associate-/r*0.4

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

  9. Final simplification0.4

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

Reproduce

herbie shell --seed 2019125 
(FPCore (v w r)
  :name "Rosa's TurbineBenchmark"
  (- (- (+ 3 (/ 2 (* r r))) (/ (* (* 0.125 (- 3 (* 2 v))) (* (* (* w w) r) r)) (- 1 v))) 4.5))