Average Error: 0.0 → 0.0
Time: 7.9s
Precision: 64
\[\left(\frac{\sqrt{2}}{4} \cdot \sqrt{1 - 3 \cdot \left(v \cdot v\right)}\right) \cdot \left(1 - v \cdot v\right)\]
↓
\[\left(\frac{\sqrt{2}}{4} \cdot \sqrt[3]{{\left(\sqrt{1 - 3 \cdot \left(v \cdot v\right)}\right)}^{3}}\right) \cdot \left(1 - v \cdot v\right)\]
\left(\frac{\sqrt{2}}{4} \cdot \sqrt{1 - 3 \cdot \left(v \cdot v\right)}\right) \cdot \left(1 - v \cdot v\right)
↓
\left(\frac{\sqrt{2}}{4} \cdot \sqrt[3]{{\left(\sqrt{1 - 3 \cdot \left(v \cdot v\right)}\right)}^{3}}\right) \cdot \left(1 - v \cdot v\right)
double f(double v) {
        double r94971 = 2.0;
        double r94972 = sqrt(r94971);
        double r94973 = 4.0;
        double r94974 = r94972 / r94973;
        double r94975 = 1.0;
        double r94976 = 3.0;
        double r94977 = v;
        double r94978 = r94977 * r94977;
        double r94979 = r94976 * r94978;
        double r94980 = r94975 - r94979;
        double r94981 = sqrt(r94980);
        double r94982 = r94974 * r94981;
        double r94983 = r94975 - r94978;
        double r94984 = r94982 * r94983;
        return r94984;
}
↓
double f(double v) {
        double r94985 = 2.0;
        double r94986 = sqrt(r94985);
        double r94987 = 4.0;
        double r94988 = r94986 / r94987;
        double r94989 = 1.0;
        double r94990 = 3.0;
        double r94991 = v;
        double r94992 = r94991 * r94991;
        double r94993 = r94990 * r94992;
        double r94994 = r94989 - r94993;
        double r94995 = sqrt(r94994);
        double r94996 = 3.0;
        double r94997 = pow(r94995, r94996);
        double r94998 = cbrt(r94997);
        double r94999 = r94988 * r94998;
        double r95000 = r94989 - r94992;
        double r95001 = r94999 * r95000;
        return r95001;
}

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-cbrt-cube0.0

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

  4. Simplified0.0

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

  5. Final simplification0.0

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

Reproduce

herbie shell --seed 2020045 
(FPCore (v)
  :name "Falkner and Boettcher, Appendix B, 2"
  :precision binary64
  (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- 1 (* v v))))