Average Error: 0.0 → 0.0
Time: 25.4s
Precision: 64
\[\left(\frac{\sqrt{2}}{4} \cdot \sqrt{1 - 3 \cdot \left(v \cdot v\right)}\right) \cdot \left(1 - v \cdot v\right)\]
↓
\[\left(\sqrt{\sqrt{1 - \left(v \cdot v\right) \cdot 3}} \cdot \left(\sqrt{\sqrt{1 - \sqrt[3]{\left(\left(\left(v \cdot v\right) \cdot 3\right) \cdot \left(\left(v \cdot v\right) \cdot 3\right)\right) \cdot \left(\left(v \cdot v\right) \cdot 3\right)}}} \cdot \frac{\sqrt{2}}{4}\right)\right) \cdot \left(1 - v \cdot v\right)\]
\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(\sqrt{\sqrt{1 - \sqrt[3]{\left(\left(\left(v \cdot v\right) \cdot 3\right) \cdot \left(\left(v \cdot v\right) \cdot 3\right)\right) \cdot \left(\left(v \cdot v\right) \cdot 3\right)}}} \cdot \frac{\sqrt{2}}{4}\right)\right) \cdot \left(1 - v \cdot v\right)
double f(double v) {
        double r71909047 = 2.0;
        double r71909048 = sqrt(r71909047);
        double r71909049 = 4.0;
        double r71909050 = r71909048 / r71909049;
        double r71909051 = 1.0;
        double r71909052 = 3.0;
        double r71909053 = v;
        double r71909054 = r71909053 * r71909053;
        double r71909055 = r71909052 * r71909054;
        double r71909056 = r71909051 - r71909055;
        double r71909057 = sqrt(r71909056);
        double r71909058 = r71909050 * r71909057;
        double r71909059 = r71909051 - r71909054;
        double r71909060 = r71909058 * r71909059;
        return r71909060;
}
↓
double f(double v) {
        double r71909061 = 1.0;
        double r71909062 = v;
        double r71909063 = r71909062 * r71909062;
        double r71909064 = 3.0;
        double r71909065 = r71909063 * r71909064;
        double r71909066 = r71909061 - r71909065;
        double r71909067 = sqrt(r71909066);
        double r71909068 = sqrt(r71909067);
        double r71909069 = r71909065 * r71909065;
        double r71909070 = r71909069 * r71909065;
        double r71909071 = cbrt(r71909070);
        double r71909072 = r71909061 - r71909071;
        double r71909073 = sqrt(r71909072);
        double r71909074 = sqrt(r71909073);
        double r71909075 = 2.0;
        double r71909076 = sqrt(r71909075);
        double r71909077 = 4.0;
        double r71909078 = r71909076 / r71909077;
        double r71909079 = r71909074 * r71909078;
        double r71909080 = r71909068 * r71909079;
        double r71909081 = r71909061 - r71909063;
        double r71909082 = r71909080 * r71909081;
        return r71909082;
}

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

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

  4. Applied associate-*r*0.0

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

  6. Applied add-cbrt-cube0.0

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

  7. Final simplification0.0

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

Reproduce

herbie shell --seed 2019107 
(FPCore (v)
  :name "Falkner and Boettcher, Appendix B, 2"
  (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- 1 (* v v))))