Average Error: 0.1 → 0.1
Time: 7.7s
Precision: 64
\[\left(a - \frac{1}{3}\right) \cdot \left(1 + \frac{1}{\sqrt{9 \cdot \left(a - \frac{1}{3}\right)}} \cdot rand\right)\]
↓
\[\left(a - \frac{1}{3}\right) \cdot \left(1 + \frac{1 \cdot rand}{\sqrt{9 \cdot \left(a - \frac{1}{3}\right)}}\right)\]
\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 \left(a - \frac{1}{3}\right)}}\right)
double f(double a, double rand) {
        double r139912 = a;
        double r139913 = 1.0;
        double r139914 = 3.0;
        double r139915 = r139913 / r139914;
        double r139916 = r139912 - r139915;
        double r139917 = 9.0;
        double r139918 = r139917 * r139916;
        double r139919 = sqrt(r139918);
        double r139920 = r139913 / r139919;
        double r139921 = rand;
        double r139922 = r139920 * r139921;
        double r139923 = r139913 + r139922;
        double r139924 = r139916 * r139923;
        return r139924;
}
↓
double f(double a, double rand) {
        double r139925 = a;
        double r139926 = 1.0;
        double r139927 = 3.0;
        double r139928 = r139926 / r139927;
        double r139929 = r139925 - r139928;
        double r139930 = rand;
        double r139931 = r139926 * r139930;
        double r139932 = 9.0;
        double r139933 = r139932 * r139929;
        double r139934 = sqrt(r139933);
        double r139935 = r139931 / r139934;
        double r139936 = r139926 + r139935;
        double r139937 = r139929 * r139936;
        return r139937;
}

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. Final simplification0.1

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

Reproduce

herbie shell --seed 2019353 +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))))