Average Error: 0.1 → 0.2
Time: 29.6s
Precision: 64
\[\left(a - \frac{1}{3}\right) \cdot \left(1 + \frac{1}{\sqrt{9 \cdot \left(a - \frac{1}{3}\right)}} \cdot rand\right)\]
↓
\[\left(a - \frac{1}{3}\right) \cdot \left(1 + \left(\frac{\sqrt[3]{1} \cdot \sqrt[3]{1}}{\sqrt{9}} \cdot \frac{\sqrt[3]{1}}{\sqrt{a - \frac{1}{3}}}\right) \cdot rand\right)\]
\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 \left(1 + \left(\frac{\sqrt[3]{1} \cdot \sqrt[3]{1}}{\sqrt{9}} \cdot \frac{\sqrt[3]{1}}{\sqrt{a - \frac{1}{3}}}\right) \cdot rand\right)
double f(double a, double rand) {
        double r80095 = a;
        double r80096 = 1.0;
        double r80097 = 3.0;
        double r80098 = r80096 / r80097;
        double r80099 = r80095 - r80098;
        double r80100 = 9.0;
        double r80101 = r80100 * r80099;
        double r80102 = sqrt(r80101);
        double r80103 = r80096 / r80102;
        double r80104 = rand;
        double r80105 = r80103 * r80104;
        double r80106 = r80096 + r80105;
        double r80107 = r80099 * r80106;
        return r80107;
}
↓
double f(double a, double rand) {
        double r80108 = a;
        double r80109 = 1.0;
        double r80110 = 3.0;
        double r80111 = r80109 / r80110;
        double r80112 = r80108 - r80111;
        double r80113 = cbrt(r80109);
        double r80114 = r80113 * r80113;
        double r80115 = 9.0;
        double r80116 = sqrt(r80115);
        double r80117 = r80114 / r80116;
        double r80118 = sqrt(r80112);
        double r80119 = r80113 / r80118;
        double r80120 = r80117 * r80119;
        double r80121 = rand;
        double r80122 = r80120 * r80121;
        double r80123 = r80109 + r80122;
        double r80124 = r80112 * r80123;
        return r80124;
}

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 sqrt-prod0.1

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

  4. Applied add-cube-cbrt0.1

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

  5. Applied times-frac0.2

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

  6. Final simplification0.2

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

Reproduce

herbie shell --seed 2019326 
(FPCore (a rand)
  :name "Octave 3.8, oct_fill_randg"
  :precision binary64
  (* (- a (/ 1 3)) (+ 1 (* (/ 1 (sqrt (* 9 (- a (/ 1 3))))) rand))))