Average Error: 12.9 → 0.5
Time: 34.0s
Precision: 64
\[\left(\left(3 + \frac{2}{r \cdot r}\right) - \frac{\left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left(\left(\left(w \cdot w\right) \cdot r\right) \cdot r\right)}{1 - v}\right) - 4.5\]
↓
\[\left(\frac{2}{r \cdot r} + \left(3 - 4.5\right)\right) - \left(\left(\left(r \cdot w\right) \cdot \left(r \cdot w\right)\right) \cdot \left(\frac{\sqrt[3]{\sqrt{0.125}} \cdot \sqrt[3]{\sqrt{0.125}}}{\sqrt[3]{1 - v}} \cdot \frac{\sqrt[3]{\left(\sqrt[3]{0.125} \cdot \sqrt[3]{0.125}\right) \cdot \sqrt[3]{0.125}}}{\sqrt[3]{1 - v}}\right)\right) \cdot \left(\frac{\sqrt[3]{0.125}}{\sqrt[3]{1 - v}} \cdot \left(3 - v \cdot 2\right)\right)\]
\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(\frac{2}{r \cdot r} + \left(3 - 4.5\right)\right) - \left(\left(\left(r \cdot w\right) \cdot \left(r \cdot w\right)\right) \cdot \left(\frac{\sqrt[3]{\sqrt{0.125}} \cdot \sqrt[3]{\sqrt{0.125}}}{\sqrt[3]{1 - v}} \cdot \frac{\sqrt[3]{\left(\sqrt[3]{0.125} \cdot \sqrt[3]{0.125}\right) \cdot \sqrt[3]{0.125}}}{\sqrt[3]{1 - v}}\right)\right) \cdot \left(\frac{\sqrt[3]{0.125}}{\sqrt[3]{1 - v}} \cdot \left(3 - v \cdot 2\right)\right)
double f(double v, double w, double r) {
        double r2039019 = 3.0;
        double r2039020 = 2.0;
        double r2039021 = r;
        double r2039022 = r2039021 * r2039021;
        double r2039023 = r2039020 / r2039022;
        double r2039024 = r2039019 + r2039023;
        double r2039025 = 0.125;
        double r2039026 = v;
        double r2039027 = r2039020 * r2039026;
        double r2039028 = r2039019 - r2039027;
        double r2039029 = r2039025 * r2039028;
        double r2039030 = w;
        double r2039031 = r2039030 * r2039030;
        double r2039032 = r2039031 * r2039021;
        double r2039033 = r2039032 * r2039021;
        double r2039034 = r2039029 * r2039033;
        double r2039035 = 1.0;
        double r2039036 = r2039035 - r2039026;
        double r2039037 = r2039034 / r2039036;
        double r2039038 = r2039024 - r2039037;
        double r2039039 = 4.5;
        double r2039040 = r2039038 - r2039039;
        return r2039040;
}
↓
double f(double v, double w, double r) {
        double r2039041 = 2.0;
        double r2039042 = r;
        double r2039043 = r2039042 * r2039042;
        double r2039044 = r2039041 / r2039043;
        double r2039045 = 3.0;
        double r2039046 = 4.5;
        double r2039047 = r2039045 - r2039046;
        double r2039048 = r2039044 + r2039047;
        double r2039049 = w;
        double r2039050 = r2039042 * r2039049;
        double r2039051 = r2039050 * r2039050;
        double r2039052 = 0.125;
        double r2039053 = sqrt(r2039052);
        double r2039054 = cbrt(r2039053);
        double r2039055 = r2039054 * r2039054;
        double r2039056 = 1.0;
        double r2039057 = v;
        double r2039058 = r2039056 - r2039057;
        double r2039059 = cbrt(r2039058);
        double r2039060 = r2039055 / r2039059;
        double r2039061 = cbrt(r2039052);
        double r2039062 = r2039061 * r2039061;
        double r2039063 = r2039062 * r2039061;
        double r2039064 = cbrt(r2039063);
        double r2039065 = r2039064 / r2039059;
        double r2039066 = r2039060 * r2039065;
        double r2039067 = r2039051 * r2039066;
        double r2039068 = r2039061 / r2039059;
        double r2039069 = r2039057 * r2039041;
        double r2039070 = r2039045 - r2039069;
        double r2039071 = r2039068 * r2039070;
        double r2039072 = r2039067 * r2039071;
        double r2039073 = r2039048 - r2039072;
        return r2039073;
}

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. Simplified6.9

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

  4. Applied add-cube-cbrt7.0

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

  5. Applied add-cube-cbrt7.2

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

  6. Applied times-frac7.2

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

  7. Applied associate-*r*7.2

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

  8. Simplified2.9

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

  10. Applied associate-*l*0.8

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

  12. Applied add-sqr-sqrt0.8

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

  13. Applied cbrt-prod0.6

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

  15. Applied add-cbrt-cube0.5

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

  16. Final simplification0.5

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

Reproduce

herbie shell --seed 2019171 
(FPCore (v w r)
  :name "Rosa's TurbineBenchmark"
  (- (- (+ 3.0 (/ 2.0 (* r r))) (/ (* (* 0.125 (- 3.0 (* 2.0 v))) (* (* (* w w) r) r)) (- 1.0 v))) 4.5))