Average Error: 0.0 → 0.0
Time: 25.9s
Precision: 64
\[\left(\frac{\sqrt{2}}{4} \cdot \sqrt{1 - 3 \cdot \left(v \cdot v\right)}\right) \cdot \left(1 - v \cdot v\right)\]
↓
\[\sqrt[3]{\left(\left(\frac{\sqrt{2}}{4} \cdot \sqrt{1 - 3 \cdot \left(v \cdot v\right)}\right) \cdot \left(\frac{\sqrt{2}}{4} \cdot \sqrt{1 - 3 \cdot \left(v \cdot v\right)}\right)\right) \cdot \left(\frac{\sqrt{2}}{4} \cdot \sqrt{1 - 3 \cdot \left(v \cdot v\right)}\right)} \cdot \left(1 - v \cdot v\right)\]
\left(\frac{\sqrt{2}}{4} \cdot \sqrt{1 - 3 \cdot \left(v \cdot v\right)}\right) \cdot \left(1 - v \cdot v\right)
↓
\sqrt[3]{\left(\left(\frac{\sqrt{2}}{4} \cdot \sqrt{1 - 3 \cdot \left(v \cdot v\right)}\right) \cdot \left(\frac{\sqrt{2}}{4} \cdot \sqrt{1 - 3 \cdot \left(v \cdot v\right)}\right)\right) \cdot \left(\frac{\sqrt{2}}{4} \cdot \sqrt{1 - 3 \cdot \left(v \cdot v\right)}\right)} \cdot \left(1 - v \cdot v\right)
double f(double v) {
        double r10774106 = 2.0;
        double r10774107 = sqrt(r10774106);
        double r10774108 = 4.0;
        double r10774109 = r10774107 / r10774108;
        double r10774110 = 1.0;
        double r10774111 = 3.0;
        double r10774112 = v;
        double r10774113 = r10774112 * r10774112;
        double r10774114 = r10774111 * r10774113;
        double r10774115 = r10774110 - r10774114;
        double r10774116 = sqrt(r10774115);
        double r10774117 = r10774109 * r10774116;
        double r10774118 = r10774110 - r10774113;
        double r10774119 = r10774117 * r10774118;
        return r10774119;
}
↓
double f(double v) {
        double r10774120 = 2.0;
        double r10774121 = sqrt(r10774120);
        double r10774122 = 4.0;
        double r10774123 = r10774121 / r10774122;
        double r10774124 = 1.0;
        double r10774125 = 3.0;
        double r10774126 = v;
        double r10774127 = r10774126 * r10774126;
        double r10774128 = r10774125 * r10774127;
        double r10774129 = r10774124 - r10774128;
        double r10774130 = sqrt(r10774129);
        double r10774131 = r10774123 * r10774130;
        double r10774132 = r10774131 * r10774131;
        double r10774133 = r10774132 * r10774131;
        double r10774134 = cbrt(r10774133);
        double r10774135 = r10774124 - r10774127;
        double r10774136 = r10774134 * r10774135;
        return r10774136;
}

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

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

  4. Final simplification0.0

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

Reproduce

herbie shell --seed 2019174 +o rules:numerics
(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))))