Average Error: 12.6 → 0.4
Time: 8.9s
Precision: 64
\[\left(\left(3 + \frac{2}{r \cdot r}\right) - \frac{\left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left(\left(\left(w \cdot w\right) \cdot r\right) \cdot r\right)}{1 - v}\right) - 4.5\]
↓
\[\left(\left(3 + \frac{\frac{2}{r}}{r}\right) - \frac{1}{\frac{\sqrt{\frac{1 - v}{0.125 \cdot \left(3 - 2 \cdot v\right)}}}{\frac{{\left(\left|w \cdot r\right|\right)}^{2}}{\sqrt{\frac{1 - v}{0.125 \cdot \left(3 - 2 \cdot v\right)}}}}}\right) - 4.5\]
\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}{\frac{\sqrt{\frac{1 - v}{0.125 \cdot \left(3 - 2 \cdot v\right)}}}{\frac{{\left(\left|w \cdot r\right|\right)}^{2}}{\sqrt{\frac{1 - v}{0.125 \cdot \left(3 - 2 \cdot v\right)}}}}}\right) - 4.5
double f(double v, double w, double r) {
        double r29076 = 3.0;
        double r29077 = 2.0;
        double r29078 = r;
        double r29079 = r29078 * r29078;
        double r29080 = r29077 / r29079;
        double r29081 = r29076 + r29080;
        double r29082 = 0.125;
        double r29083 = v;
        double r29084 = r29077 * r29083;
        double r29085 = r29076 - r29084;
        double r29086 = r29082 * r29085;
        double r29087 = w;
        double r29088 = r29087 * r29087;
        double r29089 = r29088 * r29078;
        double r29090 = r29089 * r29078;
        double r29091 = r29086 * r29090;
        double r29092 = 1.0;
        double r29093 = r29092 - r29083;
        double r29094 = r29091 / r29093;
        double r29095 = r29081 - r29094;
        double r29096 = 4.5;
        double r29097 = r29095 - r29096;
        return r29097;
}
↓
double f(double v, double w, double r) {
        double r29098 = 3.0;
        double r29099 = 2.0;
        double r29100 = r;
        double r29101 = r29099 / r29100;
        double r29102 = r29101 / r29100;
        double r29103 = r29098 + r29102;
        double r29104 = 1.0;
        double r29105 = 1.0;
        double r29106 = v;
        double r29107 = r29105 - r29106;
        double r29108 = 0.125;
        double r29109 = r29099 * r29106;
        double r29110 = r29098 - r29109;
        double r29111 = r29108 * r29110;
        double r29112 = r29107 / r29111;
        double r29113 = sqrt(r29112);
        double r29114 = w;
        double r29115 = r29114 * r29100;
        double r29116 = fabs(r29115);
        double r29117 = 2.0;
        double r29118 = pow(r29116, r29117);
        double r29119 = r29118 / r29113;
        double r29120 = r29113 / r29119;
        double r29121 = r29104 / r29120;
        double r29122 = r29103 - r29121;
        double r29123 = 4.5;
        double r29124 = r29122 - r29123;
        return r29124;
}

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 12.6

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

  3. Applied add-sqr-sqrt12.6

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

  4. Simplified12.6

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

  5. Simplified6.4

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

  7. Applied clear-num6.4

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

  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 associate-/r*0.4

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

  12. Applied add-sqr-sqrt0.4

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

  13. Applied associate-/l*0.4

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

  14. Final simplification0.4

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

Reproduce

herbie shell --seed 2019354 
(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))