Average Error: 0.1 → 0.1
Time: 14.8s
Precision: 64
\[\left(a - \frac{1}{3}\right) \cdot \left(1 + \frac{1}{\sqrt{9 \cdot \left(a - \frac{1}{3}\right)}} \cdot rand\right)\]
↓
\[\left(a - \frac{1}{3}\right) \cdot 1 + \frac{\left(a - \frac{1}{3}\right) \cdot 1}{\sqrt{9 \cdot \left(a - \frac{1}{3}\right)}} \cdot rand\]
\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 + \frac{\left(a - \frac{1}{3}\right) \cdot 1}{\sqrt{9 \cdot \left(a - \frac{1}{3}\right)}} \cdot rand
double f(double a, double rand) {
        double r118059 = a;
        double r118060 = 1.0;
        double r118061 = 3.0;
        double r118062 = r118060 / r118061;
        double r118063 = r118059 - r118062;
        double r118064 = 9.0;
        double r118065 = r118064 * r118063;
        double r118066 = sqrt(r118065);
        double r118067 = r118060 / r118066;
        double r118068 = rand;
        double r118069 = r118067 * r118068;
        double r118070 = r118060 + r118069;
        double r118071 = r118063 * r118070;
        return r118071;
}
↓
double f(double a, double rand) {
        double r118072 = a;
        double r118073 = 1.0;
        double r118074 = 3.0;
        double r118075 = r118073 / r118074;
        double r118076 = r118072 - r118075;
        double r118077 = r118076 * r118073;
        double r118078 = 9.0;
        double r118079 = r118078 * r118076;
        double r118080 = sqrt(r118079);
        double r118081 = r118077 / r118080;
        double r118082 = rand;
        double r118083 = r118081 * r118082;
        double r118084 = r118077 + r118083;
        return r118084;
}

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 distribute-lft-in0.1

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

  5. Applied associate-*r*0.1

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

  7. Applied associate-*r/0.1

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

  8. Final simplification0.1

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

Reproduce

herbie shell --seed 2020047 
(FPCore (a rand)
  :name "Octave 3.8, oct_fill_randg"
  :precision binary64
  (* (- a (/ 1 3)) (+ 1 (* (/ 1 (sqrt (* 9 (- a (/ 1 3))))) rand))))