Average Error: 12.7 → 0.4
Time: 20.9s
Precision: 64
\[\left(\left(3 + \frac{2}{r \cdot r}\right) - \frac{\left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left(\left(\left(w \cdot w\right) \cdot r\right) \cdot r\right)}{1 - v}\right) - 4.5\]
↓
\[\left(\left(3 + \frac{2}{r \cdot r}\right) - \sqrt{\frac{0.125}{\frac{\frac{1 - v}{{\left(\left|w \cdot r\right|\right)}^{2}}}{3 - 2 \cdot v}}} \cdot \left(\sqrt{\frac{0.125 \cdot \left(3 - 2 \cdot v\right)}{1 - v}} \cdot \left|\left|w \cdot r\right|\right|\right)\right) - 4.5\]
\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{2}{r \cdot r}\right) - \sqrt{\frac{0.125}{\frac{\frac{1 - v}{{\left(\left|w \cdot r\right|\right)}^{2}}}{3 - 2 \cdot v}}} \cdot \left(\sqrt{\frac{0.125 \cdot \left(3 - 2 \cdot v\right)}{1 - v}} \cdot \left|\left|w \cdot r\right|\right|\right)\right) - 4.5
double f(double v, double w, double r) {
        double r37090 = 3.0;
        double r37091 = 2.0;
        double r37092 = r;
        double r37093 = r37092 * r37092;
        double r37094 = r37091 / r37093;
        double r37095 = r37090 + r37094;
        double r37096 = 0.125;
        double r37097 = v;
        double r37098 = r37091 * r37097;
        double r37099 = r37090 - r37098;
        double r37100 = r37096 * r37099;
        double r37101 = w;
        double r37102 = r37101 * r37101;
        double r37103 = r37102 * r37092;
        double r37104 = r37103 * r37092;
        double r37105 = r37100 * r37104;
        double r37106 = 1.0;
        double r37107 = r37106 - r37097;
        double r37108 = r37105 / r37107;
        double r37109 = r37095 - r37108;
        double r37110 = 4.5;
        double r37111 = r37109 - r37110;
        return r37111;
}
↓
double f(double v, double w, double r) {
        double r37112 = 3.0;
        double r37113 = 2.0;
        double r37114 = r;
        double r37115 = r37114 * r37114;
        double r37116 = r37113 / r37115;
        double r37117 = r37112 + r37116;
        double r37118 = 0.125;
        double r37119 = 1.0;
        double r37120 = v;
        double r37121 = r37119 - r37120;
        double r37122 = w;
        double r37123 = r37122 * r37114;
        double r37124 = fabs(r37123);
        double r37125 = 2.0;
        double r37126 = pow(r37124, r37125);
        double r37127 = r37121 / r37126;
        double r37128 = r37113 * r37120;
        double r37129 = r37112 - r37128;
        double r37130 = r37127 / r37129;
        double r37131 = r37118 / r37130;
        double r37132 = sqrt(r37131);
        double r37133 = r37118 * r37129;
        double r37134 = r37133 / r37121;
        double r37135 = sqrt(r37134);
        double r37136 = fabs(r37124);
        double r37137 = r37135 * r37136;
        double r37138 = r37132 * r37137;
        double r37139 = r37117 - r37138;
        double r37140 = 4.5;
        double r37141 = r37139 - r37140;
        return r37141;
}

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 add-sqr-sqrt6.7

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

  8. Simplified6.7

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

  9. Simplified0.4

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

  11. Applied associate-/r/0.4

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

  12. Applied sqrt-prod0.4

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

  13. Simplified0.4

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

  15. Applied associate-/l*0.4

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

  16. Final simplification0.4

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

Reproduce

herbie shell --seed 2019347 
(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))