Average Error: 0.5 → 0.3
Time: 1.3m
Precision: 64
\[\frac{1 - 5 \cdot \left(v \cdot v\right)}{\left(\left(\pi \cdot t\right) \cdot \sqrt{2 \cdot \left(1 - 3 \cdot \left(v \cdot v\right)\right)}\right) \cdot \left(1 - v \cdot v\right)}\]
↓
\[\frac{\frac{\frac{\frac{1 - \left(v \cdot v\right) \cdot 5}{1 - v \cdot v}}{\pi}}{t}}{\sqrt{\left(v \cdot v\right) \cdot -6 + 2}}\]
\frac{1 - 5 \cdot \left(v \cdot v\right)}{\left(\left(\pi \cdot t\right) \cdot \sqrt{2 \cdot \left(1 - 3 \cdot \left(v \cdot v\right)\right)}\right) \cdot \left(1 - v \cdot v\right)}
↓
\frac{\frac{\frac{\frac{1 - \left(v \cdot v\right) \cdot 5}{1 - v \cdot v}}{\pi}}{t}}{\sqrt{\left(v \cdot v\right) \cdot -6 + 2}}
double f(double v, double t) {
        double r7870540 = 1.0;
        double r7870541 = 5.0;
        double r7870542 = v;
        double r7870543 = r7870542 * r7870542;
        double r7870544 = r7870541 * r7870543;
        double r7870545 = r7870540 - r7870544;
        double r7870546 = atan2(1.0, 0.0);
        double r7870547 = t;
        double r7870548 = r7870546 * r7870547;
        double r7870549 = 2.0;
        double r7870550 = 3.0;
        double r7870551 = r7870550 * r7870543;
        double r7870552 = r7870540 - r7870551;
        double r7870553 = r7870549 * r7870552;
        double r7870554 = sqrt(r7870553);
        double r7870555 = r7870548 * r7870554;
        double r7870556 = r7870540 - r7870543;
        double r7870557 = r7870555 * r7870556;
        double r7870558 = r7870545 / r7870557;
        return r7870558;
}
↓
double f(double v, double t) {
        double r7870559 = 1.0;
        double r7870560 = v;
        double r7870561 = r7870560 * r7870560;
        double r7870562 = 5.0;
        double r7870563 = r7870561 * r7870562;
        double r7870564 = r7870559 - r7870563;
        double r7870565 = r7870559 - r7870561;
        double r7870566 = r7870564 / r7870565;
        double r7870567 = atan2(1.0, 0.0);
        double r7870568 = r7870566 / r7870567;
        double r7870569 = t;
        double r7870570 = r7870568 / r7870569;
        double r7870571 = -6.0;
        double r7870572 = r7870561 * r7870571;
        double r7870573 = 2.0;
        double r7870574 = r7870572 + r7870573;
        double r7870575 = sqrt(r7870574);
        double r7870576 = r7870570 / r7870575;
        return r7870576;
}

Error

Bits error versus v

Bits error versus t

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.5

    \[\frac{1 - 5 \cdot \left(v \cdot v\right)}{\left(\left(\pi \cdot t\right) \cdot \sqrt{2 \cdot \left(1 - 3 \cdot \left(v \cdot v\right)\right)}\right) \cdot \left(1 - v \cdot v\right)}\]

  2. Simplified0.3

    \[\leadsto \color{blue}{\frac{\frac{\frac{1 - \left(v \cdot v\right) \cdot 5}{1 - v \cdot v}}{\pi}}{t \cdot \sqrt{-6 \cdot \left(v \cdot v\right) + 2}}}\]
  3. Using strategy rm

  4. Applied associate-/r*0.3

    \[\leadsto \color{blue}{\frac{\frac{\frac{\frac{1 - \left(v \cdot v\right) \cdot 5}{1 - v \cdot v}}{\pi}}{t}}{\sqrt{-6 \cdot \left(v \cdot v\right) + 2}}}\]

  5. Final simplification0.3

    \[\leadsto \frac{\frac{\frac{\frac{1 - \left(v \cdot v\right) \cdot 5}{1 - v \cdot v}}{\pi}}{t}}{\sqrt{\left(v \cdot v\right) \cdot -6 + 2}}\]

Reproduce

herbie shell --seed 2019144 
(FPCore (v t)
  :name "Falkner and Boettcher, Equation (20:1,3)"
  (/ (- 1 (* 5 (* v v))) (* (* (* PI t) (sqrt (* 2 (- 1 (* 3 (* v v)))))) (- 1 (* v v)))))