Average Error: 0.0 → 0.0
Time: 18.1s
Precision: 64
\[\left(\frac{\sqrt{2}}{4} \cdot \sqrt{1 - 3 \cdot \left(v \cdot v\right)}\right) \cdot \left(1 - v \cdot v\right)\]
↓
\[\left(\sqrt{1} - v\right) \cdot \left(\left(\sqrt{1 - \left(v \cdot v\right) \cdot 3} \cdot \frac{\sqrt{2}}{4}\right) \cdot \left(\sqrt{1} + v\right)\right)\]
\left(\frac{\sqrt{2}}{4} \cdot \sqrt{1 - 3 \cdot \left(v \cdot v\right)}\right) \cdot \left(1 - v \cdot v\right)
↓
\left(\sqrt{1} - v\right) \cdot \left(\left(\sqrt{1 - \left(v \cdot v\right) \cdot 3} \cdot \frac{\sqrt{2}}{4}\right) \cdot \left(\sqrt{1} + v\right)\right)
double f(double v) {
        double r8287782 = 2.0;
        double r8287783 = sqrt(r8287782);
        double r8287784 = 4.0;
        double r8287785 = r8287783 / r8287784;
        double r8287786 = 1.0;
        double r8287787 = 3.0;
        double r8287788 = v;
        double r8287789 = r8287788 * r8287788;
        double r8287790 = r8287787 * r8287789;
        double r8287791 = r8287786 - r8287790;
        double r8287792 = sqrt(r8287791);
        double r8287793 = r8287785 * r8287792;
        double r8287794 = r8287786 - r8287789;
        double r8287795 = r8287793 * r8287794;
        return r8287795;
}
↓
double f(double v) {
        double r8287796 = 1.0;
        double r8287797 = sqrt(r8287796);
        double r8287798 = v;
        double r8287799 = r8287797 - r8287798;
        double r8287800 = r8287798 * r8287798;
        double r8287801 = 3.0;
        double r8287802 = r8287800 * r8287801;
        double r8287803 = r8287796 - r8287802;
        double r8287804 = sqrt(r8287803);
        double r8287805 = 2.0;
        double r8287806 = sqrt(r8287805);
        double r8287807 = 4.0;
        double r8287808 = r8287806 / r8287807;
        double r8287809 = r8287804 * r8287808;
        double r8287810 = r8287797 + r8287798;
        double r8287811 = r8287809 * r8287810;
        double r8287812 = r8287799 * r8287811;
        return r8287812;
}

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-sqr-sqrt0.0

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

  4. Applied difference-of-squares0.0

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

  5. Applied associate-*r*0.0

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

  6. Final simplification0.0

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

Reproduce

herbie shell --seed 2019172 
(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))))