Average Error: 12.8 → 0.5
Time: 29.4s
Precision: 64
\[\left(\left(3 + \frac{2}{r \cdot r}\right) - \frac{\left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left(\left(\left(w \cdot w\right) \cdot r\right) \cdot r\right)}{1 - v}\right) - 4.5\]
↓
\[\left(\frac{\frac{2}{r}}{r} - \frac{3 + -2 \cdot v}{\frac{\sqrt[3]{1 - v}}{r \cdot w} \cdot \sqrt[3]{1 - v}} \cdot \frac{0.125}{\frac{\sqrt[3]{1 - v}}{r \cdot w}}\right) - \left(4.5 - 3\right)\]
\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{\frac{2}{r}}{r} - \frac{3 + -2 \cdot v}{\frac{\sqrt[3]{1 - v}}{r \cdot w} \cdot \sqrt[3]{1 - v}} \cdot \frac{0.125}{\frac{\sqrt[3]{1 - v}}{r \cdot w}}\right) - \left(4.5 - 3\right)
double f(double v, double w, double r) {
        double r1331534 = 3.0;
        double r1331535 = 2.0;
        double r1331536 = r;
        double r1331537 = r1331536 * r1331536;
        double r1331538 = r1331535 / r1331537;
        double r1331539 = r1331534 + r1331538;
        double r1331540 = 0.125;
        double r1331541 = v;
        double r1331542 = r1331535 * r1331541;
        double r1331543 = r1331534 - r1331542;
        double r1331544 = r1331540 * r1331543;
        double r1331545 = w;
        double r1331546 = r1331545 * r1331545;
        double r1331547 = r1331546 * r1331536;
        double r1331548 = r1331547 * r1331536;
        double r1331549 = r1331544 * r1331548;
        double r1331550 = 1.0;
        double r1331551 = r1331550 - r1331541;
        double r1331552 = r1331549 / r1331551;
        double r1331553 = r1331539 - r1331552;
        double r1331554 = 4.5;
        double r1331555 = r1331553 - r1331554;
        return r1331555;
}
↓
double f(double v, double w, double r) {
        double r1331556 = 2.0;
        double r1331557 = r;
        double r1331558 = r1331556 / r1331557;
        double r1331559 = r1331558 / r1331557;
        double r1331560 = 3.0;
        double r1331561 = -2.0;
        double r1331562 = v;
        double r1331563 = r1331561 * r1331562;
        double r1331564 = r1331560 + r1331563;
        double r1331565 = 1.0;
        double r1331566 = r1331565 - r1331562;
        double r1331567 = cbrt(r1331566);
        double r1331568 = w;
        double r1331569 = r1331557 * r1331568;
        double r1331570 = r1331567 / r1331569;
        double r1331571 = r1331570 * r1331567;
        double r1331572 = r1331564 / r1331571;
        double r1331573 = 0.125;
        double r1331574 = r1331573 / r1331570;
        double r1331575 = r1331572 * r1331574;
        double r1331576 = r1331559 - r1331575;
        double r1331577 = 4.5;
        double r1331578 = r1331577 - r1331560;
        double r1331579 = r1331576 - r1331578;
        return r1331579;
}

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. Simplified0.3

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

  3. Taylor expanded around 0 0.3

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

  4. Simplified0.3

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

  6. Applied add-cube-cbrt0.5

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

  7. Applied times-frac0.5

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

  8. Applied times-frac0.5

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

  9. Simplified0.5

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

  10. Final simplification0.5

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

Reproduce

herbie shell --seed 2019132 
(FPCore (v w r)
  :name "Rosa's TurbineBenchmark"
  (- (- (+ 3 (/ 2 (* r r))) (/ (* (* 0.125 (- 3 (* 2 v))) (* (* (* w w) r) r)) (- 1 v))) 4.5))