Average Error: 0.1 → 0.2
Time: 8.0s
Precision: 64
\[\left(a - \frac{1}{3}\right) \cdot \left(1 + \frac{1}{\sqrt{9 \cdot \left(a - \frac{1}{3}\right)}} \cdot rand\right)\]
↓
\[\left(a - \frac{1}{3}\right) \cdot \left(1 + \frac{\frac{1}{\sqrt{9}}}{\sqrt{a - \frac{1}{3}}} \cdot rand\right)\]
\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{\frac{1}{\sqrt{9}}}{\sqrt{a - \frac{1}{3}}} \cdot rand\right)
double f(double a, double rand) {
        double r85248 = a;
        double r85249 = 1.0;
        double r85250 = 3.0;
        double r85251 = r85249 / r85250;
        double r85252 = r85248 - r85251;
        double r85253 = 9.0;
        double r85254 = r85253 * r85252;
        double r85255 = sqrt(r85254);
        double r85256 = r85249 / r85255;
        double r85257 = rand;
        double r85258 = r85256 * r85257;
        double r85259 = r85249 + r85258;
        double r85260 = r85252 * r85259;
        return r85260;
}
↓
double f(double a, double rand) {
        double r85261 = a;
        double r85262 = 1.0;
        double r85263 = 3.0;
        double r85264 = r85262 / r85263;
        double r85265 = r85261 - r85264;
        double r85266 = 9.0;
        double r85267 = sqrt(r85266);
        double r85268 = r85262 / r85267;
        double r85269 = sqrt(r85265);
        double r85270 = r85268 / r85269;
        double r85271 = rand;
        double r85272 = r85270 * r85271;
        double r85273 = r85262 + r85272;
        double r85274 = r85265 * r85273;
        return r85274;
}

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 sqrt-prod0.2

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

  4. Applied associate-/r*0.2

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

  5. Final simplification0.2

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

Reproduce

herbie shell --seed 2019362 
(FPCore (a rand)
  :name "Octave 3.8, oct_fill_randg"
  :precision binary64
  (* (- a (/ 1 3)) (+ 1 (* (/ 1 (sqrt (* 9 (- a (/ 1 3))))) rand))))