Average Error: 12.8 → 0.4
Time: 19.0s
Precision: 64
\[\left(\left(3 + \frac{2}{r \cdot r}\right) - \frac{\left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left(\left(\left(w \cdot w\right) \cdot r\right) \cdot r\right)}{1 - v}\right) - 4.5\]
↓
\[\left(\left(3 + \frac{\frac{2}{r}}{r}\right) - \left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \frac{\left|r \cdot w\right| \cdot \left|r \cdot w\right|}{1 - v}\right) - 4.5\]
\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{\frac{2}{r}}{r}\right) - \left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \frac{\left|r \cdot w\right| \cdot \left|r \cdot w\right|}{1 - v}\right) - 4.5
double f(double v, double w, double r) {
        double r23481 = 3.0;
        double r23482 = 2.0;
        double r23483 = r;
        double r23484 = r23483 * r23483;
        double r23485 = r23482 / r23484;
        double r23486 = r23481 + r23485;
        double r23487 = 0.125;
        double r23488 = v;
        double r23489 = r23482 * r23488;
        double r23490 = r23481 - r23489;
        double r23491 = r23487 * r23490;
        double r23492 = w;
        double r23493 = r23492 * r23492;
        double r23494 = r23493 * r23483;
        double r23495 = r23494 * r23483;
        double r23496 = r23491 * r23495;
        double r23497 = 1.0;
        double r23498 = r23497 - r23488;
        double r23499 = r23496 / r23498;
        double r23500 = r23486 - r23499;
        double r23501 = 4.5;
        double r23502 = r23500 - r23501;
        return r23502;
}
↓
double f(double v, double w, double r) {
        double r23503 = 3.0;
        double r23504 = 2.0;
        double r23505 = r;
        double r23506 = r23504 / r23505;
        double r23507 = r23506 / r23505;
        double r23508 = r23503 + r23507;
        double r23509 = 0.125;
        double r23510 = v;
        double r23511 = r23504 * r23510;
        double r23512 = r23503 - r23511;
        double r23513 = r23509 * r23512;
        double r23514 = w;
        double r23515 = r23505 * r23514;
        double r23516 = fabs(r23515);
        double r23517 = r23516 * r23516;
        double r23518 = 1.0;
        double r23519 = r23518 - r23510;
        double r23520 = r23517 / r23519;
        double r23521 = r23513 * r23520;
        double r23522 = r23508 - r23521;
        double r23523 = 4.5;
        double r23524 = r23522 - r23523;
        return r23524;
}

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 12.8

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

  3. Applied associate-*l*8.0

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

  5. Applied *-un-lft-identity8.0

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

  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-sqrt2.5

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

  10. Simplified2.5

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

  11. Simplified0.4

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

  13. Applied associate-/r*0.4

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

  14. Final simplification0.4

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

Reproduce

herbie shell --seed 2019212 
(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))