Average Error: 0.1 → 0.1
Time: 27.2s
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 r2380111 = a;
        double r2380112 = 1.0;
        double r2380113 = 3.0;
        double r2380114 = r2380112 / r2380113;
        double r2380115 = r2380111 - r2380114;
        double r2380116 = 1.0;
        double r2380117 = 9.0;
        double r2380118 = r2380117 * r2380115;
        double r2380119 = sqrt(r2380118);
        double r2380120 = r2380116 / r2380119;
        double r2380121 = rand;
        double r2380122 = r2380120 * r2380121;
        double r2380123 = r2380116 + r2380122;
        double r2380124 = r2380115 * r2380123;
        return r2380124;
}
↓
double f(double a, double rand) {
        double r2380125 = a;
        double r2380126 = 1.0;
        double r2380127 = 3.0;
        double r2380128 = r2380126 / r2380127;
        double r2380129 = r2380125 - r2380128;
        double r2380130 = sqrt(r2380129);
        double r2380131 = rand;
        double r2380132 = 3.0;
        double r2380133 = r2380131 / r2380132;
        double r2380134 = r2380133 / r2380130;
        double r2380135 = r2380134 * r2380130;
        double r2380136 = r2380130 * r2380135;
        double r2380137 = r2380129 + r2380136;
        return r2380137;
}

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

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

  4. Applied sqrt-prod0.1

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

  5. Applied associate-/r*0.1

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

  6. Simplified0.1

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

  8. Applied add-sqr-sqrt0.1

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

  9. Applied associate-*l*0.1

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

  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 2019137 
(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))))