Average Error: 0.0 → 0.0
Time: 12.3s
Precision: 64
\[\left(\frac{\sqrt{2}}{4} \cdot \sqrt{1 - 3 \cdot \left(v \cdot v\right)}\right) \cdot \left(1 - v \cdot v\right)\]
↓
\[\left(1 - v \cdot v\right) \cdot \left(\sqrt{\sqrt{1 - \left(v \cdot v\right) \cdot 3}} \cdot \left(\frac{\sqrt{2}}{4} \cdot \sqrt{\sqrt{1 - \left(v \cdot v\right) \cdot 3}}\right)\right)\]
\left(\frac{\sqrt{2}}{4} \cdot \sqrt{1 - 3 \cdot \left(v \cdot v\right)}\right) \cdot \left(1 - v \cdot v\right)
↓
\left(1 - v \cdot v\right) \cdot \left(\sqrt{\sqrt{1 - \left(v \cdot v\right) \cdot 3}} \cdot \left(\frac{\sqrt{2}}{4} \cdot \sqrt{\sqrt{1 - \left(v \cdot v\right) \cdot 3}}\right)\right)
double f(double v) {
        double r2101492 = 2.0;
        double r2101493 = sqrt(r2101492);
        double r2101494 = 4.0;
        double r2101495 = r2101493 / r2101494;
        double r2101496 = 1.0;
        double r2101497 = 3.0;
        double r2101498 = v;
        double r2101499 = r2101498 * r2101498;
        double r2101500 = r2101497 * r2101499;
        double r2101501 = r2101496 - r2101500;
        double r2101502 = sqrt(r2101501);
        double r2101503 = r2101495 * r2101502;
        double r2101504 = r2101496 - r2101499;
        double r2101505 = r2101503 * r2101504;
        return r2101505;
}
↓
double f(double v) {
        double r2101506 = 1.0;
        double r2101507 = v;
        double r2101508 = r2101507 * r2101507;
        double r2101509 = r2101506 - r2101508;
        double r2101510 = 3.0;
        double r2101511 = r2101508 * r2101510;
        double r2101512 = r2101506 - r2101511;
        double r2101513 = sqrt(r2101512);
        double r2101514 = sqrt(r2101513);
        double r2101515 = 2.0;
        double r2101516 = sqrt(r2101515);
        double r2101517 = 4.0;
        double r2101518 = r2101516 / r2101517;
        double r2101519 = r2101518 * r2101514;
        double r2101520 = r2101514 * r2101519;
        double r2101521 = r2101509 * r2101520;
        return r2101521;
}

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-sqr-sqrt0.0

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

  4. Applied sqrt-prod0.0

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

  5. Applied associate-*r*0.0

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

  6. Final simplification0.0

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

Reproduce

herbie shell --seed 2019155 
(FPCore (v)
  :name "Falkner and Boettcher, Appendix B, 2"
  (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- 1 (* v v))))