Average Error: 0.0 → 0.0
Time: 30.1s
Precision: 64
\[\left(\frac{\sqrt{2}}{4} \cdot \sqrt{1 - 3 \cdot \left(v \cdot v\right)}\right) \cdot \left(1 - v \cdot v\right)\]
↓
\[\left(\sqrt{\sqrt{1 - \left(v \cdot v\right) \cdot 3}} \cdot \left(\frac{\sqrt{2}}{4} \cdot \sqrt{\sqrt{1 - \left(v \cdot v\right) \cdot 3}}\right)\right) \cdot \left(1 - v \cdot v\right)\]
\left(\frac{\sqrt{2}}{4} \cdot \sqrt{1 - 3 \cdot \left(v \cdot v\right)}\right) \cdot \left(1 - v \cdot v\right)
↓
\left(\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) \cdot \left(1 - v \cdot v\right)
double f(double v) {
        double r7199700 = 2.0;
        double r7199701 = sqrt(r7199700);
        double r7199702 = 4.0;
        double r7199703 = r7199701 / r7199702;
        double r7199704 = 1.0;
        double r7199705 = 3.0;
        double r7199706 = v;
        double r7199707 = r7199706 * r7199706;
        double r7199708 = r7199705 * r7199707;
        double r7199709 = r7199704 - r7199708;
        double r7199710 = sqrt(r7199709);
        double r7199711 = r7199703 * r7199710;
        double r7199712 = r7199704 - r7199707;
        double r7199713 = r7199711 * r7199712;
        return r7199713;
}
↓
double f(double v) {
        double r7199714 = 1.0;
        double r7199715 = v;
        double r7199716 = r7199715 * r7199715;
        double r7199717 = 3.0;
        double r7199718 = r7199716 * r7199717;
        double r7199719 = r7199714 - r7199718;
        double r7199720 = sqrt(r7199719);
        double r7199721 = sqrt(r7199720);
        double r7199722 = 2.0;
        double r7199723 = sqrt(r7199722);
        double r7199724 = 4.0;
        double r7199725 = r7199723 / r7199724;
        double r7199726 = r7199725 * r7199721;
        double r7199727 = r7199721 * r7199726;
        double r7199728 = r7199714 - r7199716;
        double r7199729 = r7199727 * r7199728;
        return r7199729;
}

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

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

Reproduce

herbie shell --seed 2019200 
(FPCore (v)
  :name "Falkner and Boettcher, Appendix B, 2"
  (* (* (/ (sqrt 2.0) 4.0) (sqrt (- 1.0 (* 3.0 (* v v))))) (- 1.0 (* v v))))