Average Error: 0.1 → 0.1
Time: 9.6s
Precision: 64
\[\left(a - \frac{1}{3}\right) \cdot \left(1 + \frac{1}{\sqrt{9 \cdot \left(a - \frac{1}{3}\right)}} \cdot rand\right)\]
↓
\[\left(a - \frac{1}{3}\right) \cdot 1 + \left(a - \frac{1}{3}\right) \cdot \frac{1 \cdot rand}{\sqrt{9 \cdot \left(a - \frac{1}{3}\right)}}\]
\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 1 + \left(a - \frac{1}{3}\right) \cdot \frac{1 \cdot rand}{\sqrt{9 \cdot \left(a - \frac{1}{3}\right)}}
double f(double a, double rand) {
        double r136142 = a;
        double r136143 = 1.0;
        double r136144 = 3.0;
        double r136145 = r136143 / r136144;
        double r136146 = r136142 - r136145;
        double r136147 = 9.0;
        double r136148 = r136147 * r136146;
        double r136149 = sqrt(r136148);
        double r136150 = r136143 / r136149;
        double r136151 = rand;
        double r136152 = r136150 * r136151;
        double r136153 = r136143 + r136152;
        double r136154 = r136146 * r136153;
        return r136154;
}
↓
double f(double a, double rand) {
        double r136155 = a;
        double r136156 = 1.0;
        double r136157 = 3.0;
        double r136158 = r136156 / r136157;
        double r136159 = r136155 - r136158;
        double r136160 = r136159 * r136156;
        double r136161 = rand;
        double r136162 = r136156 * r136161;
        double r136163 = 9.0;
        double r136164 = r136163 * r136159;
        double r136165 = sqrt(r136164);
        double r136166 = r136162 / r136165;
        double r136167 = r136159 * r136166;
        double r136168 = r136160 + r136167;
        return r136168;
}

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 associate-*l/0.1

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

  5. Applied distribute-lft-in0.1

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

  6. Final simplification0.1

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

Reproduce

herbie shell --seed 2019318 
(FPCore (a rand)
  :name "Octave 3.8, oct_fill_randg"
  :precision binary64
  (* (- a (/ 1 3)) (+ 1 (* (/ 1 (sqrt (* 9 (- a (/ 1 3))))) rand))))