Average Error: 12.7 → 0.4
Time: 9.4s
Precision: 64
\[\left(\left(3 + \frac{2}{r \cdot r}\right) - \frac{\left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left(\left(\left(w \cdot w\right) \cdot r\right) \cdot r\right)}{1 - v}\right) - 4.5\]
↓
\[\left(\left(3 + \frac{\frac{2}{r}}{r}\right) - \frac{1}{\sqrt{\frac{1 - v}{0.125 \cdot \left(3 - 2 \cdot v\right)}}} \cdot \frac{1}{\frac{\sqrt{\frac{1 - v}{0.125 \cdot \left(3 - 2 \cdot v\right)}}}{{\left(\left|w \cdot r\right|\right)}^{2}}}\right) - 4.5\]
\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}{\sqrt{\frac{1 - v}{0.125 \cdot \left(3 - 2 \cdot v\right)}}} \cdot \frac{1}{\frac{\sqrt{\frac{1 - v}{0.125 \cdot \left(3 - 2 \cdot v\right)}}}{{\left(\left|w \cdot r\right|\right)}^{2}}}\right) - 4.5
double f(double v, double w, double r) {
        double r34122 = 3.0;
        double r34123 = 2.0;
        double r34124 = r;
        double r34125 = r34124 * r34124;
        double r34126 = r34123 / r34125;
        double r34127 = r34122 + r34126;
        double r34128 = 0.125;
        double r34129 = v;
        double r34130 = r34123 * r34129;
        double r34131 = r34122 - r34130;
        double r34132 = r34128 * r34131;
        double r34133 = w;
        double r34134 = r34133 * r34133;
        double r34135 = r34134 * r34124;
        double r34136 = r34135 * r34124;
        double r34137 = r34132 * r34136;
        double r34138 = 1.0;
        double r34139 = r34138 - r34129;
        double r34140 = r34137 / r34139;
        double r34141 = r34127 - r34140;
        double r34142 = 4.5;
        double r34143 = r34141 - r34142;
        return r34143;
}
↓
double f(double v, double w, double r) {
        double r34144 = 3.0;
        double r34145 = 2.0;
        double r34146 = r;
        double r34147 = r34145 / r34146;
        double r34148 = r34147 / r34146;
        double r34149 = r34144 + r34148;
        double r34150 = 1.0;
        double r34151 = 1.0;
        double r34152 = v;
        double r34153 = r34151 - r34152;
        double r34154 = 0.125;
        double r34155 = r34145 * r34152;
        double r34156 = r34144 - r34155;
        double r34157 = r34154 * r34156;
        double r34158 = r34153 / r34157;
        double r34159 = sqrt(r34158);
        double r34160 = r34150 / r34159;
        double r34161 = w;
        double r34162 = r34161 * r34146;
        double r34163 = fabs(r34162);
        double r34164 = 2.0;
        double r34165 = pow(r34163, r34164);
        double r34166 = r34159 / r34165;
        double r34167 = r34150 / r34166;
        double r34168 = r34160 * r34167;
        double r34169 = r34149 - r34168;
        double r34170 = 4.5;
        double r34171 = r34169 - r34170;
        return r34171;
}

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 12.7

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

  3. Applied add-sqr-sqrt12.7

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

  4. Simplified12.7

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

  5. Simplified6.6

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

  7. Applied clear-num6.6

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

  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 *-un-lft-identity0.4

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

  11. Applied unpow-prod-down0.4

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

  12. Applied add-sqr-sqrt0.4

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

  13. Applied times-frac0.4

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

  14. Applied add-sqr-sqrt0.4

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

  15. Applied times-frac0.4

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

  16. Simplified0.4

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

  17. Simplified0.4

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

  19. Applied associate-/r*0.4

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

  20. Final simplification0.4

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

Reproduce

herbie shell --seed 2020001 
(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))