Average Error: 0.0 → 0.0
Time: 10.0s
Precision: 64
\[\left(\frac{\sqrt{2}}{4} \cdot \sqrt{1 - 3 \cdot \left(v \cdot v\right)}\right) \cdot \left(1 - v \cdot v\right)\]
↓
\[\left(\frac{\sqrt{2}}{4} \cdot \sqrt{1 - \log \left(e^{3 \cdot \left(v \cdot v\right)}\right)}\right) \cdot \left(1 - v \cdot v\right)\]
\left(\frac{\sqrt{2}}{4} \cdot \sqrt{1 - 3 \cdot \left(v \cdot v\right)}\right) \cdot \left(1 - v \cdot v\right)
↓
\left(\frac{\sqrt{2}}{4} \cdot \sqrt{1 - \log \left(e^{3 \cdot \left(v \cdot v\right)}\right)}\right) \cdot \left(1 - v \cdot v\right)
double f(double v) {
        double r185508 = 2.0;
        double r185509 = sqrt(r185508);
        double r185510 = 4.0;
        double r185511 = r185509 / r185510;
        double r185512 = 1.0;
        double r185513 = 3.0;
        double r185514 = v;
        double r185515 = r185514 * r185514;
        double r185516 = r185513 * r185515;
        double r185517 = r185512 - r185516;
        double r185518 = sqrt(r185517);
        double r185519 = r185511 * r185518;
        double r185520 = r185512 - r185515;
        double r185521 = r185519 * r185520;
        return r185521;
}
↓
double f(double v) {
        double r185522 = 2.0;
        double r185523 = sqrt(r185522);
        double r185524 = 4.0;
        double r185525 = r185523 / r185524;
        double r185526 = 1.0;
        double r185527 = 3.0;
        double r185528 = v;
        double r185529 = r185528 * r185528;
        double r185530 = r185527 * r185529;
        double r185531 = exp(r185530);
        double r185532 = log(r185531);
        double r185533 = r185526 - r185532;
        double r185534 = sqrt(r185533);
        double r185535 = r185525 * r185534;
        double r185536 = r185526 - r185529;
        double r185537 = r185535 * r185536;
        return r185537;
}

Error

Bits error versus v

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.0

    \[\left(\frac{\sqrt{2}}{4} \cdot \sqrt{1 - 3 \cdot \left(v \cdot v\right)}\right) \cdot \left(1 - v \cdot v\right)\]
  2. Using strategy rm

  3. Applied add-log-exp0.0

    \[\leadsto \left(\frac{\sqrt{2}}{4} \cdot \sqrt{1 - \color{blue}{\log \left(e^{3 \cdot \left(v \cdot v\right)}\right)}}\right) \cdot \left(1 - v \cdot v\right)\]

  4. Final simplification0.0

    \[\leadsto \left(\frac{\sqrt{2}}{4} \cdot \sqrt{1 - \log \left(e^{3 \cdot \left(v \cdot v\right)}\right)}\right) \cdot \left(1 - v \cdot v\right)\]

Reproduce

herbie shell --seed 2020042 
(FPCore (v)
  :name "Falkner and Boettcher, Appendix B, 2"
  :precision binary64
  (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- 1 (* v v))))