Average Error: 0.1 → 0.1
Time: 7.0s
Precision: 64
\[\left(a - \frac{1}{3}\right) \cdot \left(1 + \frac{1}{\sqrt{9 \cdot \left(a - \frac{1}{3}\right)}} \cdot rand\right)\]
↓
\[\left(a - \frac{1}{3}\right) \cdot 1 + \frac{\frac{\left(a - \frac{1}{3}\right) \cdot 1}{\sqrt{9}}}{\sqrt{a - \frac{1}{3}}} \cdot rand\]
\left(a - \frac{1}{3}\right) \cdot \left(1 + \frac{1}{\sqrt{9 \cdot \left(a - \frac{1}{3}\right)}} \cdot rand\right)
↓
\left(a - \frac{1}{3}\right) \cdot 1 + \frac{\frac{\left(a - \frac{1}{3}\right) \cdot 1}{\sqrt{9}}}{\sqrt{a - \frac{1}{3}}} \cdot rand
double f(double a, double rand) {
        double r80109 = a;
        double r80110 = 1.0;
        double r80111 = 3.0;
        double r80112 = r80110 / r80111;
        double r80113 = r80109 - r80112;
        double r80114 = 9.0;
        double r80115 = r80114 * r80113;
        double r80116 = sqrt(r80115);
        double r80117 = r80110 / r80116;
        double r80118 = rand;
        double r80119 = r80117 * r80118;
        double r80120 = r80110 + r80119;
        double r80121 = r80113 * r80120;
        return r80121;
}
↓
double f(double a, double rand) {
        double r80122 = a;
        double r80123 = 1.0;
        double r80124 = 3.0;
        double r80125 = r80123 / r80124;
        double r80126 = r80122 - r80125;
        double r80127 = r80126 * r80123;
        double r80128 = 9.0;
        double r80129 = sqrt(r80128);
        double r80130 = r80127 / r80129;
        double r80131 = sqrt(r80126);
        double r80132 = r80130 / r80131;
        double r80133 = rand;
        double r80134 = r80132 * r80133;
        double r80135 = r80127 + r80134;
        return r80135;
}

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

    \[\left(a - \frac{1}{3}\right) \cdot \left(1 + \frac{1}{\sqrt{9 \cdot \left(a - \frac{1}{3}\right)}} \cdot rand\right)\]
  2. Using strategy rm

  3. Applied distribute-lft-in0.1

    \[\leadsto \color{blue}{\left(a - \frac{1}{3}\right) \cdot 1 + \left(a - \frac{1}{3}\right) \cdot \left(\frac{1}{\sqrt{9 \cdot \left(a - \frac{1}{3}\right)}} \cdot rand\right)}\]
  4. Using strategy rm

  5. Applied associate-*r*0.1

    \[\leadsto \left(a - \frac{1}{3}\right) \cdot 1 + \color{blue}{\left(\left(a - \frac{1}{3}\right) \cdot \frac{1}{\sqrt{9 \cdot \left(a - \frac{1}{3}\right)}}\right) \cdot rand}\]
  6. Using strategy rm

  7. Applied associate-*r/0.1

    \[\leadsto \left(a - \frac{1}{3}\right) \cdot 1 + \color{blue}{\frac{\left(a - \frac{1}{3}\right) \cdot 1}{\sqrt{9 \cdot \left(a - \frac{1}{3}\right)}}} \cdot rand\]
  8. Using strategy rm

  9. Applied sqrt-prod0.1

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

  10. Applied associate-/r*0.1

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

  11. Final simplification0.1

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

Reproduce

herbie shell --seed 2019344 
(FPCore (a rand)
  :name "Octave 3.8, oct_fill_randg"
  :precision binary64
  (* (- a (/ 1 3)) (+ 1 (* (/ 1 (sqrt (* 9 (- a (/ 1 3))))) rand))))