Average Error: 0.1 → 0.1
Time: 7.1s
Precision: 64
\[\left(a - \frac{1}{3}\right) \cdot \left(1 + \frac{1}{\sqrt{9 \cdot \left(a - \frac{1}{3}\right)}} \cdot rand\right)\]
↓
\[\left(a - \frac{1}{3}\right) \cdot \left(1 + \frac{1 \cdot rand}{\sqrt{9} \cdot \sqrt{a - \frac{1}{3}}}\right)\]
\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 \left(1 + \frac{1 \cdot rand}{\sqrt{9} \cdot \sqrt{a - \frac{1}{3}}}\right)
double f(double a, double rand) {
        double r64094 = a;
        double r64095 = 1.0;
        double r64096 = 3.0;
        double r64097 = r64095 / r64096;
        double r64098 = r64094 - r64097;
        double r64099 = 9.0;
        double r64100 = r64099 * r64098;
        double r64101 = sqrt(r64100);
        double r64102 = r64095 / r64101;
        double r64103 = rand;
        double r64104 = r64102 * r64103;
        double r64105 = r64095 + r64104;
        double r64106 = r64098 * r64105;
        return r64106;
}
↓
double f(double a, double rand) {
        double r64107 = a;
        double r64108 = 1.0;
        double r64109 = 3.0;
        double r64110 = r64108 / r64109;
        double r64111 = r64107 - r64110;
        double r64112 = rand;
        double r64113 = r64108 * r64112;
        double r64114 = 9.0;
        double r64115 = sqrt(r64114);
        double r64116 = sqrt(r64111);
        double r64117 = r64115 * r64116;
        double r64118 = r64113 / r64117;
        double r64119 = r64108 + r64118;
        double r64120 = r64111 * r64119;
        return r64120;
}

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 sqrt-prod0.1

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

  6. Final simplification0.1

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

Reproduce

herbie shell --seed 2020018 
(FPCore (a rand)
  :name "Octave 3.8, oct_fill_randg"
  :precision binary64
  (* (- a (/ 1 3)) (+ 1 (* (/ 1 (sqrt (* 9 (- a (/ 1 3))))) rand))))