Average Error: 0.1 → 0.1
Time: 8.7s
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 r82199 = a;
        double r82200 = 1.0;
        double r82201 = 3.0;
        double r82202 = r82200 / r82201;
        double r82203 = r82199 - r82202;
        double r82204 = 9.0;
        double r82205 = r82204 * r82203;
        double r82206 = sqrt(r82205);
        double r82207 = r82200 / r82206;
        double r82208 = rand;
        double r82209 = r82207 * r82208;
        double r82210 = r82200 + r82209;
        double r82211 = r82203 * r82210;
        return r82211;
}
↓
double f(double a, double rand) {
        double r82212 = a;
        double r82213 = 1.0;
        double r82214 = 3.0;
        double r82215 = r82213 / r82214;
        double r82216 = r82212 - r82215;
        double r82217 = rand;
        double r82218 = r82213 * r82217;
        double r82219 = 9.0;
        double r82220 = r82219 * r82216;
        double r82221 = sqrt(r82220);
        double r82222 = r82218 / r82221;
        double r82223 = r82213 + r82222;
        double r82224 = r82216 * r82223;
        return r82224;
}

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 2020027 +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))))