Average Error: 0.0 → 0.0
Time: 29.6s
Precision: 64
\[\left(\frac{\sqrt{2}}{4} \cdot \sqrt{1 - 3 \cdot \left(v \cdot v\right)}\right) \cdot \left(1 - v \cdot v\right)\]
↓
\[\left(1 - v \cdot v\right) \cdot \left(\log \left(e^{\sqrt{1 - \left(v \cdot v\right) \cdot 3}}\right) \cdot \frac{\sqrt{2}}{4}\right)\]
\left(\frac{\sqrt{2}}{4} \cdot \sqrt{1 - 3 \cdot \left(v \cdot v\right)}\right) \cdot \left(1 - v \cdot v\right)
↓
\left(1 - v \cdot v\right) \cdot \left(\log \left(e^{\sqrt{1 - \left(v \cdot v\right) \cdot 3}}\right) \cdot \frac{\sqrt{2}}{4}\right)
double f(double v) {
        double r8520761 = 2.0;
        double r8520762 = sqrt(r8520761);
        double r8520763 = 4.0;
        double r8520764 = r8520762 / r8520763;
        double r8520765 = 1.0;
        double r8520766 = 3.0;
        double r8520767 = v;
        double r8520768 = r8520767 * r8520767;
        double r8520769 = r8520766 * r8520768;
        double r8520770 = r8520765 - r8520769;
        double r8520771 = sqrt(r8520770);
        double r8520772 = r8520764 * r8520771;
        double r8520773 = r8520765 - r8520768;
        double r8520774 = r8520772 * r8520773;
        return r8520774;
}
↓
double f(double v) {
        double r8520775 = 1.0;
        double r8520776 = v;
        double r8520777 = r8520776 * r8520776;
        double r8520778 = r8520775 - r8520777;
        double r8520779 = 3.0;
        double r8520780 = r8520777 * r8520779;
        double r8520781 = r8520775 - r8520780;
        double r8520782 = sqrt(r8520781);
        double r8520783 = exp(r8520782);
        double r8520784 = log(r8520783);
        double r8520785 = 2.0;
        double r8520786 = sqrt(r8520785);
        double r8520787 = 4.0;
        double r8520788 = r8520786 / r8520787;
        double r8520789 = r8520784 * r8520788;
        double r8520790 = r8520778 * r8520789;
        return r8520790;
}

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

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

Reproduce

herbie shell --seed 2019168 +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))))