Average Error: 0.1 → 0.1
Time: 46.1s
Precision: 64
\[\left(a - \frac{1.0}{3.0}\right) \cdot \left(1 + \frac{1}{\sqrt{9 \cdot \left(a - \frac{1.0}{3.0}\right)}} \cdot rand\right)\]
↓
\[\left(a - \frac{1.0}{3.0}\right) + \sqrt{a - \frac{1.0}{3.0}} \cdot \left(\frac{\frac{rand}{3}}{\sqrt{a - \frac{1.0}{3.0}}} \cdot \sqrt{a - \frac{1.0}{3.0}}\right)\]
\left(a - \frac{1.0}{3.0}\right) \cdot \left(1 + \frac{1}{\sqrt{9 \cdot \left(a - \frac{1.0}{3.0}\right)}} \cdot rand\right)
↓
\left(a - \frac{1.0}{3.0}\right) + \sqrt{a - \frac{1.0}{3.0}} \cdot \left(\frac{\frac{rand}{3}}{\sqrt{a - \frac{1.0}{3.0}}} \cdot \sqrt{a - \frac{1.0}{3.0}}\right)
double f(double a, double rand) {
        double r2594763 = a;
        double r2594764 = 1.0;
        double r2594765 = 3.0;
        double r2594766 = r2594764 / r2594765;
        double r2594767 = r2594763 - r2594766;
        double r2594768 = 1.0;
        double r2594769 = 9.0;
        double r2594770 = r2594769 * r2594767;
        double r2594771 = sqrt(r2594770);
        double r2594772 = r2594768 / r2594771;
        double r2594773 = rand;
        double r2594774 = r2594772 * r2594773;
        double r2594775 = r2594768 + r2594774;
        double r2594776 = r2594767 * r2594775;
        return r2594776;
}
↓
double f(double a, double rand) {
        double r2594777 = a;
        double r2594778 = 1.0;
        double r2594779 = 3.0;
        double r2594780 = r2594778 / r2594779;
        double r2594781 = r2594777 - r2594780;
        double r2594782 = sqrt(r2594781);
        double r2594783 = rand;
        double r2594784 = 3.0;
        double r2594785 = r2594783 / r2594784;
        double r2594786 = r2594785 / r2594782;
        double r2594787 = r2594786 * r2594782;
        double r2594788 = r2594782 * r2594787;
        double r2594789 = r2594781 + r2594788;
        return r2594789;
}

Error

Bits error versus a

Bits error versus rand

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.1

    \[\left(a - \frac{1.0}{3.0}\right) \cdot \left(1 + \frac{1}{\sqrt{9 \cdot \left(a - \frac{1.0}{3.0}\right)}} \cdot rand\right)\]

  2. Simplified0.1

    \[\leadsto \color{blue}{\left(a - \frac{1.0}{3.0}\right) + \left(a - \frac{1.0}{3.0}\right) \cdot \frac{rand}{\sqrt{9 \cdot \left(a - \frac{1.0}{3.0}\right)}}}\]
  3. Using strategy rm

  4. Applied sqrt-prod0.1

    \[\leadsto \left(a - \frac{1.0}{3.0}\right) + \left(a - \frac{1.0}{3.0}\right) \cdot \frac{rand}{\color{blue}{\sqrt{9} \cdot \sqrt{a - \frac{1.0}{3.0}}}}\]

  5. Applied associate-/r*0.1

    \[\leadsto \left(a - \frac{1.0}{3.0}\right) + \left(a - \frac{1.0}{3.0}\right) \cdot \color{blue}{\frac{\frac{rand}{\sqrt{9}}}{\sqrt{a - \frac{1.0}{3.0}}}}\]

  6. Simplified0.1

    \[\leadsto \left(a - \frac{1.0}{3.0}\right) + \left(a - \frac{1.0}{3.0}\right) \cdot \frac{\color{blue}{\frac{rand}{3}}}{\sqrt{a - \frac{1.0}{3.0}}}\]
  7. Using strategy rm

  8. Applied add-sqr-sqrt0.1

    \[\leadsto \left(a - \frac{1.0}{3.0}\right) + \color{blue}{\left(\sqrt{a - \frac{1.0}{3.0}} \cdot \sqrt{a - \frac{1.0}{3.0}}\right)} \cdot \frac{\frac{rand}{3}}{\sqrt{a - \frac{1.0}{3.0}}}\]

  9. Applied associate-*l*0.1

    \[\leadsto \left(a - \frac{1.0}{3.0}\right) + \color{blue}{\sqrt{a - \frac{1.0}{3.0}} \cdot \left(\sqrt{a - \frac{1.0}{3.0}} \cdot \frac{\frac{rand}{3}}{\sqrt{a - \frac{1.0}{3.0}}}\right)}\]

  10. Final simplification0.1

    \[\leadsto \left(a - \frac{1.0}{3.0}\right) + \sqrt{a - \frac{1.0}{3.0}} \cdot \left(\frac{\frac{rand}{3}}{\sqrt{a - \frac{1.0}{3.0}}} \cdot \sqrt{a - \frac{1.0}{3.0}}\right)\]

Reproduce

herbie shell --seed 2019153 
(FPCore (a rand)
  :name "Octave 3.8, oct_fill_randg"
  (* (- a (/ 1.0 3.0)) (+ 1 (* (/ 1 (sqrt (* 9 (- a (/ 1.0 3.0))))) rand))))