Average Error: 0.0 → 0.0
Time: 8.1s
Precision: 64
\[\left(\frac{\sqrt{2}}{4} \cdot \sqrt{1 - 3 \cdot \left(v \cdot v\right)}\right) \cdot \left(1 - v \cdot v\right)\]
↓
\[\left(\frac{\sqrt{2}}{4} \cdot \log \left(e^{\sqrt{1 - 3 \cdot \left(v \cdot v\right)}}\right)\right) \cdot \left(1 - v \cdot v\right)\]
\left(\frac{\sqrt{2}}{4} \cdot \sqrt{1 - 3 \cdot \left(v \cdot v\right)}\right) \cdot \left(1 - v \cdot v\right)
↓
\left(\frac{\sqrt{2}}{4} \cdot \log \left(e^{\sqrt{1 - 3 \cdot \left(v \cdot v\right)}}\right)\right) \cdot \left(1 - v \cdot v\right)
double f(double v) {
        double r249778 = 2.0;
        double r249779 = sqrt(r249778);
        double r249780 = 4.0;
        double r249781 = r249779 / r249780;
        double r249782 = 1.0;
        double r249783 = 3.0;
        double r249784 = v;
        double r249785 = r249784 * r249784;
        double r249786 = r249783 * r249785;
        double r249787 = r249782 - r249786;
        double r249788 = sqrt(r249787);
        double r249789 = r249781 * r249788;
        double r249790 = r249782 - r249785;
        double r249791 = r249789 * r249790;
        return r249791;
}
↓
double f(double v) {
        double r249792 = 2.0;
        double r249793 = sqrt(r249792);
        double r249794 = 4.0;
        double r249795 = r249793 / r249794;
        double r249796 = 1.0;
        double r249797 = 3.0;
        double r249798 = v;
        double r249799 = r249798 * r249798;
        double r249800 = r249797 * r249799;
        double r249801 = r249796 - r249800;
        double r249802 = sqrt(r249801);
        double r249803 = exp(r249802);
        double r249804 = log(r249803);
        double r249805 = r249795 * r249804;
        double r249806 = r249796 - r249799;
        double r249807 = r249805 * r249806;
        return r249807;
}

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-log-exp0.0

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

  4. Final simplification0.0

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

Reproduce

herbie shell --seed 2020046 
(FPCore (v)
  :name "Falkner and Boettcher, Appendix B, 2"
  :precision binary64
  (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- 1 (* v v))))