Average Error: 0.1 → 0.1
Time: 7.5s
Precision: 64
\[\left(a - \frac{1}{3}\right) \cdot \left(1 + \frac{1}{\sqrt{9 \cdot \left(a - \frac{1}{3}\right)}} \cdot rand\right)\]
↓
\[\left(a - \frac{1}{3}\right) \cdot \left(1 + \frac{1}{\sqrt{9 \cdot \left(a - \frac{1}{3}\right)}} \cdot rand\right)\]
\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 + \frac{1}{\sqrt{9 \cdot \left(a - \frac{1}{3}\right)}} \cdot rand\right)
double f(double a, double rand) {
        double r130088 = a;
        double r130089 = 1.0;
        double r130090 = 3.0;
        double r130091 = r130089 / r130090;
        double r130092 = r130088 - r130091;
        double r130093 = 9.0;
        double r130094 = r130093 * r130092;
        double r130095 = sqrt(r130094);
        double r130096 = r130089 / r130095;
        double r130097 = rand;
        double r130098 = r130096 * r130097;
        double r130099 = r130089 + r130098;
        double r130100 = r130092 * r130099;
        return r130100;
}
↓
double f(double a, double rand) {
        double r130101 = a;
        double r130102 = 1.0;
        double r130103 = 3.0;
        double r130104 = r130102 / r130103;
        double r130105 = r130101 - r130104;
        double r130106 = 9.0;
        double r130107 = r130106 * r130105;
        double r130108 = sqrt(r130107);
        double r130109 = r130102 / r130108;
        double r130110 = rand;
        double r130111 = r130109 * r130110;
        double r130112 = r130102 + r130111;
        double r130113 = r130105 * r130112;
        return r130113;
}

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. Final simplification0.1

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

Reproduce

herbie shell --seed 2020036 +o rules:numerics
(FPCore (a rand)
  :name "Octave 3.8, oct_fill_randg"
  :precision binary64
  (* (- a (/ 1 3)) (+ 1 (* (/ 1 (sqrt (* 9 (- a (/ 1 3))))) rand))))