Average Error: 0.1 → 0.1
Time: 8.2s
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 r152944 = a;
        double r152945 = 1.0;
        double r152946 = 3.0;
        double r152947 = r152945 / r152946;
        double r152948 = r152944 - r152947;
        double r152949 = 9.0;
        double r152950 = r152949 * r152948;
        double r152951 = sqrt(r152950);
        double r152952 = r152945 / r152951;
        double r152953 = rand;
        double r152954 = r152952 * r152953;
        double r152955 = r152945 + r152954;
        double r152956 = r152948 * r152955;
        return r152956;
}
↓
double f(double a, double rand) {
        double r152957 = a;
        double r152958 = 1.0;
        double r152959 = 3.0;
        double r152960 = r152958 / r152959;
        double r152961 = r152957 - r152960;
        double r152962 = rand;
        double r152963 = r152958 * r152962;
        double r152964 = 9.0;
        double r152965 = r152964 * r152961;
        double r152966 = sqrt(r152965);
        double r152967 = r152963 / r152966;
        double r152968 = r152958 + r152967;
        double r152969 = r152961 * r152968;
        return r152969;
}

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 2020003 +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))))