Average Error: 12.8 → 0.4
Time: 5.4s
Precision: 64
\[\left(\left(3 + \frac{2}{r \cdot r}\right) - \frac{\left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left(\left(\left(w \cdot w\right) \cdot r\right) \cdot r\right)}{1 - v}\right) - 4.5\]
↓
\[\left(\left(3 + \frac{2}{r \cdot r}\right) - \frac{1}{\frac{\frac{1 - v}{0.125 \cdot \left(3 - 2 \cdot v\right)}}{{\left(\left|w \cdot r\right|\right)}^{2}}}\right) - 4.5\]
\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) - \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
double f(double v, double w, double r) {
        double r16358 = 3.0;
        double r16359 = 2.0;
        double r16360 = r;
        double r16361 = r16360 * r16360;
        double r16362 = r16359 / r16361;
        double r16363 = r16358 + r16362;
        double r16364 = 0.125;
        double r16365 = v;
        double r16366 = r16359 * r16365;
        double r16367 = r16358 - r16366;
        double r16368 = r16364 * r16367;
        double r16369 = w;
        double r16370 = r16369 * r16369;
        double r16371 = r16370 * r16360;
        double r16372 = r16371 * r16360;
        double r16373 = r16368 * r16372;
        double r16374 = 1.0;
        double r16375 = r16374 - r16365;
        double r16376 = r16373 / r16375;
        double r16377 = r16363 - r16376;
        double r16378 = 4.5;
        double r16379 = r16377 - r16378;
        return r16379;
}
↓
double f(double v, double w, double r) {
        double r16380 = 3.0;
        double r16381 = 2.0;
        double r16382 = r;
        double r16383 = r16382 * r16382;
        double r16384 = r16381 / r16383;
        double r16385 = r16380 + r16384;
        double r16386 = 1.0;
        double r16387 = 1.0;
        double r16388 = v;
        double r16389 = r16387 - r16388;
        double r16390 = 0.125;
        double r16391 = r16381 * r16388;
        double r16392 = r16380 - r16391;
        double r16393 = r16390 * r16392;
        double r16394 = r16389 / r16393;
        double r16395 = w;
        double r16396 = r16395 * r16382;
        double r16397 = fabs(r16396);
        double r16398 = 2.0;
        double r16399 = pow(r16397, r16398);
        double r16400 = r16394 / r16399;
        double r16401 = r16386 / r16400;
        double r16402 = r16385 - r16401;
        double r16403 = 4.5;
        double r16404 = r16402 - r16403;
        return r16404;
}

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 add-sqr-sqrt12.8

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

  4. Simplified12.8

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

  5. Simplified6.7

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

  7. Applied clear-num6.7

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

  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. Final simplification0.4

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

Reproduce

herbie shell --seed 2020062 
(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))