Average Error: 12.8 → 0.5
Time: 27.4s
Precision: 64
\[\left(\left(3 + \frac{2}{r \cdot r}\right) - \frac{\left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left(\left(\left(w \cdot w\right) \cdot r\right) \cdot r\right)}{1 - v}\right) - 4.5\]
↓
\[\frac{2}{r \cdot r} - \left(\left(r \cdot w\right) \cdot \left(\frac{\sqrt{0.125} \cdot \left(3 - v \cdot 2\right)}{\frac{1 - v}{\sqrt{0.125}}} \cdot \left(r \cdot w\right)\right) - \left(3 - 4.5\right)\right)\]
\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
↓
\frac{2}{r \cdot r} - \left(\left(r \cdot w\right) \cdot \left(\frac{\sqrt{0.125} \cdot \left(3 - v \cdot 2\right)}{\frac{1 - v}{\sqrt{0.125}}} \cdot \left(r \cdot w\right)\right) - \left(3 - 4.5\right)\right)
double f(double v, double w, double r) {
        double r1471471 = 3.0;
        double r1471472 = 2.0;
        double r1471473 = r;
        double r1471474 = r1471473 * r1471473;
        double r1471475 = r1471472 / r1471474;
        double r1471476 = r1471471 + r1471475;
        double r1471477 = 0.125;
        double r1471478 = v;
        double r1471479 = r1471472 * r1471478;
        double r1471480 = r1471471 - r1471479;
        double r1471481 = r1471477 * r1471480;
        double r1471482 = w;
        double r1471483 = r1471482 * r1471482;
        double r1471484 = r1471483 * r1471473;
        double r1471485 = r1471484 * r1471473;
        double r1471486 = r1471481 * r1471485;
        double r1471487 = 1.0;
        double r1471488 = r1471487 - r1471478;
        double r1471489 = r1471486 / r1471488;
        double r1471490 = r1471476 - r1471489;
        double r1471491 = 4.5;
        double r1471492 = r1471490 - r1471491;
        return r1471492;
}
↓
double f(double v, double w, double r) {
        double r1471493 = 2.0;
        double r1471494 = r;
        double r1471495 = r1471494 * r1471494;
        double r1471496 = r1471493 / r1471495;
        double r1471497 = w;
        double r1471498 = r1471494 * r1471497;
        double r1471499 = 0.125;
        double r1471500 = sqrt(r1471499);
        double r1471501 = 3.0;
        double r1471502 = v;
        double r1471503 = r1471502 * r1471493;
        double r1471504 = r1471501 - r1471503;
        double r1471505 = r1471500 * r1471504;
        double r1471506 = 1.0;
        double r1471507 = r1471506 - r1471502;
        double r1471508 = r1471507 / r1471500;
        double r1471509 = r1471505 / r1471508;
        double r1471510 = r1471509 * r1471498;
        double r1471511 = r1471498 * r1471510;
        double r1471512 = 4.5;
        double r1471513 = r1471501 - r1471512;
        double r1471514 = r1471511 - r1471513;
        double r1471515 = r1471496 - r1471514;
        return r1471515;
}

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. Simplified0.4

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

  4. Applied add-sqr-sqrt0.6

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

  5. Applied *-un-lft-identity0.6

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

  6. Applied times-frac0.6

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

  7. Applied associate-/r*0.5

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

  8. Simplified0.5

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

  9. Final simplification0.5

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

Reproduce

herbie shell --seed 2019169 
(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))