Average Error: 0.0 → 0.0
Time: 16.7s
Precision: 64
\[\left(\frac{\sqrt{2}}{4} \cdot \sqrt{1 - 3 \cdot \left(v \cdot v\right)}\right) \cdot \left(1 - v \cdot v\right)\]
↓
\[\frac{\frac{\sqrt{2}}{4} \cdot \left(\sqrt{1 - 3 \cdot \left(v \cdot v\right)} \cdot \left({1}^{3} - {v}^{6}\right)\right)}{1 \cdot 1 + \left(\left(v \cdot v\right) \cdot \left(v \cdot v\right) + 1 \cdot \left(v \cdot v\right)\right)}\]
\left(\frac{\sqrt{2}}{4} \cdot \sqrt{1 - 3 \cdot \left(v \cdot v\right)}\right) \cdot \left(1 - v \cdot v\right)
↓
\frac{\frac{\sqrt{2}}{4} \cdot \left(\sqrt{1 - 3 \cdot \left(v \cdot v\right)} \cdot \left({1}^{3} - {v}^{6}\right)\right)}{1 \cdot 1 + \left(\left(v \cdot v\right) \cdot \left(v \cdot v\right) + 1 \cdot \left(v \cdot v\right)\right)}
double f(double v) {
        double r173438 = 2.0;
        double r173439 = sqrt(r173438);
        double r173440 = 4.0;
        double r173441 = r173439 / r173440;
        double r173442 = 1.0;
        double r173443 = 3.0;
        double r173444 = v;
        double r173445 = r173444 * r173444;
        double r173446 = r173443 * r173445;
        double r173447 = r173442 - r173446;
        double r173448 = sqrt(r173447);
        double r173449 = r173441 * r173448;
        double r173450 = r173442 - r173445;
        double r173451 = r173449 * r173450;
        return r173451;
}
↓
double f(double v) {
        double r173452 = 2.0;
        double r173453 = sqrt(r173452);
        double r173454 = 4.0;
        double r173455 = r173453 / r173454;
        double r173456 = 1.0;
        double r173457 = 3.0;
        double r173458 = v;
        double r173459 = r173458 * r173458;
        double r173460 = r173457 * r173459;
        double r173461 = r173456 - r173460;
        double r173462 = sqrt(r173461);
        double r173463 = 3.0;
        double r173464 = pow(r173456, r173463);
        double r173465 = 6.0;
        double r173466 = pow(r173458, r173465);
        double r173467 = r173464 - r173466;
        double r173468 = r173462 * r173467;
        double r173469 = r173455 * r173468;
        double r173470 = r173456 * r173456;
        double r173471 = r173459 * r173459;
        double r173472 = r173456 * r173459;
        double r173473 = r173471 + r173472;
        double r173474 = r173470 + r173473;
        double r173475 = r173469 / r173474;
        return r173475;
}

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 flip3--0.0

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

  4. Applied associate-*r/0.0

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

  5. Simplified0.0

    \[\leadsto \frac{\color{blue}{\frac{\sqrt{2}}{4} \cdot \left(\sqrt{1 - 3 \cdot \left(v \cdot v\right)} \cdot \left({1}^{3} - {v}^{6}\right)\right)}}{1 \cdot 1 + \left(\left(v \cdot v\right) \cdot \left(v \cdot v\right) + 1 \cdot \left(v \cdot v\right)\right)}\]

  6. Final simplification0.0

    \[\leadsto \frac{\frac{\sqrt{2}}{4} \cdot \left(\sqrt{1 - 3 \cdot \left(v \cdot v\right)} \cdot \left({1}^{3} - {v}^{6}\right)\right)}{1 \cdot 1 + \left(\left(v \cdot v\right) \cdot \left(v \cdot v\right) + 1 \cdot \left(v \cdot v\right)\right)}\]

Reproduce

herbie shell --seed 2019305 
(FPCore (v)
  :name "Falkner and Boettcher, Appendix B, 2"
  :precision binary64
  (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- 1 (* v v))))