Average Error: 12.3 → 0.4
Time: 11.2s
Precision: 64
\[\left(\left(3 + \frac{2}{r \cdot r}\right) - \frac{\left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left(\left(\left(w \cdot w\right) \cdot r\right) \cdot r\right)}{1 - v}\right) - 4.5\]
↓
\[\left(\left(3 + \frac{2}{r \cdot r}\right) - \left(\left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \frac{\left|w \cdot r\right|}{\sqrt[3]{1 - v} \cdot \sqrt[3]{1 - v}}\right) \cdot \frac{\left|w \cdot r\right|}{\sqrt[3]{1 - v}}\right) - 4.5\]
\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) - \left(\left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \frac{\left|w \cdot r\right|}{\sqrt[3]{1 - v} \cdot \sqrt[3]{1 - v}}\right) \cdot \frac{\left|w \cdot r\right|}{\sqrt[3]{1 - v}}\right) - 4.5
double f(double v, double w, double r) {
        double r15028 = 3.0;
        double r15029 = 2.0;
        double r15030 = r;
        double r15031 = r15030 * r15030;
        double r15032 = r15029 / r15031;
        double r15033 = r15028 + r15032;
        double r15034 = 0.125;
        double r15035 = v;
        double r15036 = r15029 * r15035;
        double r15037 = r15028 - r15036;
        double r15038 = r15034 * r15037;
        double r15039 = w;
        double r15040 = r15039 * r15039;
        double r15041 = r15040 * r15030;
        double r15042 = r15041 * r15030;
        double r15043 = r15038 * r15042;
        double r15044 = 1.0;
        double r15045 = r15044 - r15035;
        double r15046 = r15043 / r15045;
        double r15047 = r15033 - r15046;
        double r15048 = 4.5;
        double r15049 = r15047 - r15048;
        return r15049;
}
↓
double f(double v, double w, double r) {
        double r15050 = 3.0;
        double r15051 = 2.0;
        double r15052 = r;
        double r15053 = r15052 * r15052;
        double r15054 = r15051 / r15053;
        double r15055 = r15050 + r15054;
        double r15056 = 0.125;
        double r15057 = v;
        double r15058 = r15051 * r15057;
        double r15059 = r15050 - r15058;
        double r15060 = r15056 * r15059;
        double r15061 = w;
        double r15062 = r15061 * r15052;
        double r15063 = fabs(r15062);
        double r15064 = 1.0;
        double r15065 = r15064 - r15057;
        double r15066 = cbrt(r15065);
        double r15067 = r15066 * r15066;
        double r15068 = r15063 / r15067;
        double r15069 = r15060 * r15068;
        double r15070 = r15063 / r15066;
        double r15071 = r15069 * r15070;
        double r15072 = r15055 - r15071;
        double r15073 = 4.5;
        double r15074 = r15072 - r15073;
        return r15074;
}

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 12.3

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

  3. Applied associate-*l*7.9

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

  5. Applied *-un-lft-identity7.9

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

  6. Applied times-frac2.5

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

  7. Simplified2.5

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

  9. Applied add-sqr-sqrt2.6

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

  10. Simplified2.6

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

  11. Simplified0.3

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

  13. Applied add-cube-cbrt0.5

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

  14. Applied times-frac0.5

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

  15. Applied associate-*r*0.4

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

  16. Final simplification0.4

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

Reproduce

herbie shell --seed 2020042 
(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))