Average Error: 12.9 → 0.4
Time: 19.3s
Precision: 64
\[\left(\left(3 + \frac{2}{r \cdot r}\right) - \frac{\left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left(\left(\left(w \cdot w\right) \cdot r\right) \cdot r\right)}{1 - v}\right) - 4.5\]
↓
\[\left(\left(3 + \frac{\frac{2}{r}}{r}\right) - 4.5\right) - \frac{3 - 2 \cdot v}{\frac{\frac{1 - v}{{\left(\left|w \cdot r\right|\right)}^{2}}}{0.125}}\]
\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{3 - 2 \cdot v}{\frac{\frac{1 - v}{{\left(\left|w \cdot r\right|\right)}^{2}}}{0.125}}
double f(double v, double w, double r) {
        double r23129 = 3.0;
        double r23130 = 2.0;
        double r23131 = r;
        double r23132 = r23131 * r23131;
        double r23133 = r23130 / r23132;
        double r23134 = r23129 + r23133;
        double r23135 = 0.125;
        double r23136 = v;
        double r23137 = r23130 * r23136;
        double r23138 = r23129 - r23137;
        double r23139 = r23135 * r23138;
        double r23140 = w;
        double r23141 = r23140 * r23140;
        double r23142 = r23141 * r23131;
        double r23143 = r23142 * r23131;
        double r23144 = r23139 * r23143;
        double r23145 = 1.0;
        double r23146 = r23145 - r23136;
        double r23147 = r23144 / r23146;
        double r23148 = r23134 - r23147;
        double r23149 = 4.5;
        double r23150 = r23148 - r23149;
        return r23150;
}
↓
double f(double v, double w, double r) {
        double r23151 = 3.0;
        double r23152 = 2.0;
        double r23153 = r;
        double r23154 = r23152 / r23153;
        double r23155 = r23154 / r23153;
        double r23156 = r23151 + r23155;
        double r23157 = 4.5;
        double r23158 = r23156 - r23157;
        double r23159 = v;
        double r23160 = r23152 * r23159;
        double r23161 = r23151 - r23160;
        double r23162 = 1.0;
        double r23163 = r23162 - r23159;
        double r23164 = w;
        double r23165 = r23164 * r23153;
        double r23166 = fabs(r23165);
        double r23167 = 2.0;
        double r23168 = pow(r23166, r23167);
        double r23169 = r23163 / r23168;
        double r23170 = 0.125;
        double r23171 = r23169 / r23170;
        double r23172 = r23161 / r23171;
        double r23173 = r23158 - r23172;
        return r23173;
}

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. Simplified6.9

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

  7. Applied associate-/l*0.4

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

  8. Simplified0.4

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

  10. Applied div-inv0.4

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

  12. Applied associate-/r*0.4

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

  13. Final simplification0.4

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

Reproduce

herbie shell --seed 2019294 
(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))