Average Error: 0.0 → 0.0
Time: 9.0s
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 r267185 = 2.0;
        double r267186 = sqrt(r267185);
        double r267187 = 4.0;
        double r267188 = r267186 / r267187;
        double r267189 = 1.0;
        double r267190 = 3.0;
        double r267191 = v;
        double r267192 = r267191 * r267191;
        double r267193 = r267190 * r267192;
        double r267194 = r267189 - r267193;
        double r267195 = sqrt(r267194);
        double r267196 = r267188 * r267195;
        double r267197 = r267189 - r267192;
        double r267198 = r267196 * r267197;
        return r267198;
}
↓
double f(double v) {
        double r267199 = 2.0;
        double r267200 = sqrt(r267199);
        double r267201 = 4.0;
        double r267202 = r267200 / r267201;
        double r267203 = 1.0;
        double r267204 = 3.0;
        double r267205 = v;
        double r267206 = r267205 * r267205;
        double r267207 = r267204 * r267206;
        double r267208 = r267203 - r267207;
        double r267209 = sqrt(r267208);
        double r267210 = 3.0;
        double r267211 = pow(r267209, r267210);
        double r267212 = cbrt(r267211);
        double r267213 = r267202 * r267212;
        double r267214 = r267203 - r267206;
        double r267215 = r267213 * r267214;
        return r267215;
}

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))))