Average Error: 0.0 → 0.0
Time: 7.3s
Precision: 64
\[\left(\frac{\sqrt{2}}{4} \cdot \sqrt{1 - 3 \cdot \left(v \cdot v\right)}\right) \cdot \left(1 - v \cdot v\right)\]
↓
\[\frac{\sqrt{2}}{4} \cdot \left(\left(1 - v \cdot v\right) \cdot \sqrt{1 - 3 \cdot \left(v \cdot v\right)}\right)\]
\left(\frac{\sqrt{2}}{4} \cdot \sqrt{1 - 3 \cdot \left(v \cdot v\right)}\right) \cdot \left(1 - v \cdot v\right)
↓
\frac{\sqrt{2}}{4} \cdot \left(\left(1 - v \cdot v\right) \cdot \sqrt{1 - 3 \cdot \left(v \cdot v\right)}\right)
double f(double v) {
        double r172508 = 2.0;
        double r172509 = sqrt(r172508);
        double r172510 = 4.0;
        double r172511 = r172509 / r172510;
        double r172512 = 1.0;
        double r172513 = 3.0;
        double r172514 = v;
        double r172515 = r172514 * r172514;
        double r172516 = r172513 * r172515;
        double r172517 = r172512 - r172516;
        double r172518 = sqrt(r172517);
        double r172519 = r172511 * r172518;
        double r172520 = r172512 - r172515;
        double r172521 = r172519 * r172520;
        return r172521;
}
↓
double f(double v) {
        double r172522 = 2.0;
        double r172523 = sqrt(r172522);
        double r172524 = 4.0;
        double r172525 = r172523 / r172524;
        double r172526 = 1.0;
        double r172527 = v;
        double r172528 = r172527 * r172527;
        double r172529 = r172526 - r172528;
        double r172530 = 3.0;
        double r172531 = r172530 * r172528;
        double r172532 = r172526 - r172531;
        double r172533 = sqrt(r172532);
        double r172534 = r172529 * r172533;
        double r172535 = r172525 * r172534;
        return r172535;
}

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 associate-*l*0.0

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

  4. Simplified0.0

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

  5. Final simplification0.0

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

Reproduce

herbie shell --seed 2019351 
(FPCore (v)
  :name "Falkner and Boettcher, Appendix B, 2"
  :precision binary64
  (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- 1 (* v v))))