Average Error: 0.1 → 0.1
Time: 7.3s
Precision: 64
\[\left(a - \frac{1}{3}\right) \cdot \left(1 + \frac{1}{\sqrt{9 \cdot \left(a - \frac{1}{3}\right)}} \cdot rand\right)\]
↓
\[\left(a - \frac{1}{3}\right) \cdot \left(1 + \frac{\frac{1 \cdot rand}{\sqrt{9}}}{\sqrt{a - \frac{1}{3}}}\right)\]
\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 \left(1 + \frac{\frac{1 \cdot rand}{\sqrt{9}}}{\sqrt{a - \frac{1}{3}}}\right)
double f(double a, double rand) {
        double r89313 = a;
        double r89314 = 1.0;
        double r89315 = 3.0;
        double r89316 = r89314 / r89315;
        double r89317 = r89313 - r89316;
        double r89318 = 9.0;
        double r89319 = r89318 * r89317;
        double r89320 = sqrt(r89319);
        double r89321 = r89314 / r89320;
        double r89322 = rand;
        double r89323 = r89321 * r89322;
        double r89324 = r89314 + r89323;
        double r89325 = r89317 * r89324;
        return r89325;
}
↓
double f(double a, double rand) {
        double r89326 = a;
        double r89327 = 1.0;
        double r89328 = 3.0;
        double r89329 = r89327 / r89328;
        double r89330 = r89326 - r89329;
        double r89331 = rand;
        double r89332 = r89327 * r89331;
        double r89333 = 9.0;
        double r89334 = sqrt(r89333);
        double r89335 = r89332 / r89334;
        double r89336 = sqrt(r89330);
        double r89337 = r89335 / r89336;
        double r89338 = r89327 + r89337;
        double r89339 = r89330 * r89338;
        return r89339;
}

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 sqrt-prod0.1

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

  6. Applied associate-/r*0.1

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

  7. Final simplification0.1

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

Reproduce

herbie shell --seed 2019352 +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))))