Average Error: 12.3 → 0.4
Time: 32.5s
Precision: 64
\[\left(\left(3 + \frac{2}{r \cdot r}\right) - \frac{\left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left(\left(\left(w \cdot w\right) \cdot r\right) \cdot r\right)}{1 - v}\right) - 4.5\]
↓
\[\frac{2}{r \cdot r} + \left(3 - \left(\frac{\frac{0.125 \cdot \left(3 - 2 \cdot v\right)}{1 - v}}{\frac{1}{\left(w \cdot r\right) \cdot \left(w \cdot r\right)}} + 4.5\right)\right)\]
\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(3 - \left(\frac{\frac{0.125 \cdot \left(3 - 2 \cdot v\right)}{1 - v}}{\frac{1}{\left(w \cdot r\right) \cdot \left(w \cdot r\right)}} + 4.5\right)\right)
double f(double v, double w, double r) {
        double r4564533 = 3.0;
        double r4564534 = 2.0;
        double r4564535 = r;
        double r4564536 = r4564535 * r4564535;
        double r4564537 = r4564534 / r4564536;
        double r4564538 = r4564533 + r4564537;
        double r4564539 = 0.125;
        double r4564540 = v;
        double r4564541 = r4564534 * r4564540;
        double r4564542 = r4564533 - r4564541;
        double r4564543 = r4564539 * r4564542;
        double r4564544 = w;
        double r4564545 = r4564544 * r4564544;
        double r4564546 = r4564545 * r4564535;
        double r4564547 = r4564546 * r4564535;
        double r4564548 = r4564543 * r4564547;
        double r4564549 = 1.0;
        double r4564550 = r4564549 - r4564540;
        double r4564551 = r4564548 / r4564550;
        double r4564552 = r4564538 - r4564551;
        double r4564553 = 4.5;
        double r4564554 = r4564552 - r4564553;
        return r4564554;
}
↓
double f(double v, double w, double r) {
        double r4564555 = 2.0;
        double r4564556 = r;
        double r4564557 = r4564556 * r4564556;
        double r4564558 = r4564555 / r4564557;
        double r4564559 = 3.0;
        double r4564560 = 0.125;
        double r4564561 = v;
        double r4564562 = r4564555 * r4564561;
        double r4564563 = r4564559 - r4564562;
        double r4564564 = r4564560 * r4564563;
        double r4564565 = 1.0;
        double r4564566 = r4564565 - r4564561;
        double r4564567 = r4564564 / r4564566;
        double r4564568 = 1.0;
        double r4564569 = w;
        double r4564570 = r4564569 * r4564556;
        double r4564571 = r4564570 * r4564570;
        double r4564572 = r4564568 / r4564571;
        double r4564573 = r4564567 / r4564572;
        double r4564574 = 4.5;
        double r4564575 = r4564573 + r4564574;
        double r4564576 = r4564559 - r4564575;
        double r4564577 = r4564558 + r4564576;
        return r4564577;
}

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. Simplified0.4

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

  4. Applied div-inv0.4

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

  5. Applied associate-/r*0.4

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

  6. Final simplification0.4

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

Reproduce

herbie shell --seed 2019173 
(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))