Average Error: 0.1 → 0.1
Time: 31.4s
Precision: 64
\[\left(a - \frac{1}{3}\right) \cdot \left(1 + \frac{1}{\sqrt{9 \cdot \left(a - \frac{1}{3}\right)}} \cdot rand\right)\]
↓
\[\left(a - \frac{1}{3}\right) \cdot 1 + \left(a - \frac{1}{3}\right) \cdot \frac{1 \cdot rand}{\sqrt{9 \cdot \left(a - \frac{1}{3}\right)}}\]
\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 1 + \left(a - \frac{1}{3}\right) \cdot \frac{1 \cdot rand}{\sqrt{9 \cdot \left(a - \frac{1}{3}\right)}}
double f(double a, double rand) {
        double r66221 = a;
        double r66222 = 1.0;
        double r66223 = 3.0;
        double r66224 = r66222 / r66223;
        double r66225 = r66221 - r66224;
        double r66226 = 9.0;
        double r66227 = r66226 * r66225;
        double r66228 = sqrt(r66227);
        double r66229 = r66222 / r66228;
        double r66230 = rand;
        double r66231 = r66229 * r66230;
        double r66232 = r66222 + r66231;
        double r66233 = r66225 * r66232;
        return r66233;
}
↓
double f(double a, double rand) {
        double r66234 = a;
        double r66235 = 1.0;
        double r66236 = 3.0;
        double r66237 = r66235 / r66236;
        double r66238 = r66234 - r66237;
        double r66239 = r66238 * r66235;
        double r66240 = rand;
        double r66241 = r66235 * r66240;
        double r66242 = 9.0;
        double r66243 = r66242 * r66238;
        double r66244 = sqrt(r66243);
        double r66245 = r66241 / r66244;
        double r66246 = r66238 * r66245;
        double r66247 = r66239 + r66246;
        return r66247;
}

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. Using strategy rm

  5. Applied distribute-lft-in0.1

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

  6. Final simplification0.1

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

Reproduce

herbie shell --seed 2019303 
(FPCore (a rand)
  :name "Octave 3.8, oct_fill_randg"
  :precision binary64
  (* (- a (/ 1 3)) (+ 1 (* (/ 1 (sqrt (* 9 (- a (/ 1 3))))) rand))))