Average Error: 0.1 → 0.2
Time: 22.8s
Precision: 64
\[\left(a - \frac{1.0}{3.0}\right) \cdot \left(1 + \frac{1}{\sqrt{9 \cdot \left(a - \frac{1.0}{3.0}\right)}} \cdot rand\right)\]
↓
\[\left(rand \cdot \frac{\frac{1}{3}}{\sqrt{a - \frac{1.0}{3.0}}} + 1\right) \cdot \left(a - \frac{1.0}{3.0}\right)\]
\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(rand \cdot \frac{\frac{1}{3}}{\sqrt{a - \frac{1.0}{3.0}}} + 1\right) \cdot \left(a - \frac{1.0}{3.0}\right)
double f(double a, double rand) {
        double r2776743 = a;
        double r2776744 = 1.0;
        double r2776745 = 3.0;
        double r2776746 = r2776744 / r2776745;
        double r2776747 = r2776743 - r2776746;
        double r2776748 = 1.0;
        double r2776749 = 9.0;
        double r2776750 = r2776749 * r2776747;
        double r2776751 = sqrt(r2776750);
        double r2776752 = r2776748 / r2776751;
        double r2776753 = rand;
        double r2776754 = r2776752 * r2776753;
        double r2776755 = r2776748 + r2776754;
        double r2776756 = r2776747 * r2776755;
        return r2776756;
}
↓
double f(double a, double rand) {
        double r2776757 = rand;
        double r2776758 = 0.3333333333333333;
        double r2776759 = a;
        double r2776760 = 1.0;
        double r2776761 = 3.0;
        double r2776762 = r2776760 / r2776761;
        double r2776763 = r2776759 - r2776762;
        double r2776764 = sqrt(r2776763);
        double r2776765 = r2776758 / r2776764;
        double r2776766 = r2776757 * r2776765;
        double r2776767 = 1.0;
        double r2776768 = r2776766 + r2776767;
        double r2776769 = r2776768 * r2776763;
        return r2776769;
}

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. Using strategy rm

  3. Applied sqrt-prod0.2

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

  4. Applied add-cube-cbrt0.2

    \[\leadsto \left(a - \frac{1.0}{3.0}\right) \cdot \left(1 + \frac{\color{blue}{\left(\sqrt[3]{1} \cdot \sqrt[3]{1}\right) \cdot \sqrt[3]{1}}}{\sqrt{9} \cdot \sqrt{a - \frac{1.0}{3.0}}} \cdot rand\right)\]

  5. Applied times-frac0.2

    \[\leadsto \left(a - \frac{1.0}{3.0}\right) \cdot \left(1 + \color{blue}{\left(\frac{\sqrt[3]{1} \cdot \sqrt[3]{1}}{\sqrt{9}} \cdot \frac{\sqrt[3]{1}}{\sqrt{a - \frac{1.0}{3.0}}}\right)} \cdot rand\right)\]

  6. Simplified0.2

    \[\leadsto \left(a - \frac{1.0}{3.0}\right) \cdot \left(1 + \left(\color{blue}{\frac{1}{3}} \cdot \frac{\sqrt[3]{1}}{\sqrt{a - \frac{1.0}{3.0}}}\right) \cdot rand\right)\]

  7. Simplified0.2

    \[\leadsto \left(a - \frac{1.0}{3.0}\right) \cdot \left(1 + \left(\frac{1}{3} \cdot \color{blue}{\frac{1}{\sqrt{a - \frac{1.0}{3.0}}}}\right) \cdot rand\right)\]
  8. Using strategy rm

  9. Applied un-div-inv0.2

    \[\leadsto \left(a - \frac{1.0}{3.0}\right) \cdot \left(1 + \color{blue}{\frac{\frac{1}{3}}{\sqrt{a - \frac{1.0}{3.0}}}} \cdot rand\right)\]

  10. Final simplification0.2

    \[\leadsto \left(rand \cdot \frac{\frac{1}{3}}{\sqrt{a - \frac{1.0}{3.0}}} + 1\right) \cdot \left(a - \frac{1.0}{3.0}\right)\]

Reproduce

herbie shell --seed 2019165 
(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))))