Average Error: 0.1 → 0.1
Time: 1.2m
Precision: 64
\[\left(a - \frac{1.0}{3.0}\right) \cdot \left(1 + \frac{1}{\sqrt{9 \cdot \left(a - \frac{1.0}{3.0}\right)}} \cdot rand\right)\]
↓
\[\left(a - \frac{1.0}{3.0}\right) + rand \cdot \frac{\sqrt{a - \frac{1.0}{3.0}}}{3}\]
\left(a - \frac{1.0}{3.0}\right) \cdot \left(1 + \frac{1}{\sqrt{9 \cdot \left(a - \frac{1.0}{3.0}\right)}} \cdot rand\right)
↓
\left(a - \frac{1.0}{3.0}\right) + rand \cdot \frac{\sqrt{a - \frac{1.0}{3.0}}}{3}
double f(double a, double rand) {
        double r13789255 = a;
        double r13789256 = 1.0;
        double r13789257 = 3.0;
        double r13789258 = r13789256 / r13789257;
        double r13789259 = r13789255 - r13789258;
        double r13789260 = 1.0;
        double r13789261 = 9.0;
        double r13789262 = r13789261 * r13789259;
        double r13789263 = sqrt(r13789262);
        double r13789264 = r13789260 / r13789263;
        double r13789265 = rand;
        double r13789266 = r13789264 * r13789265;
        double r13789267 = r13789260 + r13789266;
        double r13789268 = r13789259 * r13789267;
        return r13789268;
}
↓
double f(double a, double rand) {
        double r13789269 = a;
        double r13789270 = 1.0;
        double r13789271 = 3.0;
        double r13789272 = r13789270 / r13789271;
        double r13789273 = r13789269 - r13789272;
        double r13789274 = rand;
        double r13789275 = sqrt(r13789273);
        double r13789276 = 3.0;
        double r13789277 = r13789275 / r13789276;
        double r13789278 = r13789274 * r13789277;
        double r13789279 = r13789273 + r13789278;
        return r13789279;
}

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

    \[\left(a - \frac{1.0}{3.0}\right) \cdot \left(1 + \frac{1}{\sqrt{9 \cdot \left(a - \frac{1.0}{3.0}\right)}} \cdot rand\right)\]

  2. Simplified0.1

    \[\leadsto \color{blue}{rand \cdot \frac{a - \frac{1.0}{3.0}}{\sqrt{9 \cdot \left(a - \frac{1.0}{3.0}\right)}} + \left(a - \frac{1.0}{3.0}\right)}\]
  3. Using strategy rm

  4. Applied sqrt-prod0.1

    \[\leadsto rand \cdot \frac{a - \frac{1.0}{3.0}}{\color{blue}{\sqrt{9} \cdot \sqrt{a - \frac{1.0}{3.0}}}} + \left(a - \frac{1.0}{3.0}\right)\]

  5. Applied add-sqr-sqrt0.1

    \[\leadsto rand \cdot \frac{\color{blue}{\sqrt{a - \frac{1.0}{3.0}} \cdot \sqrt{a - \frac{1.0}{3.0}}}}{\sqrt{9} \cdot \sqrt{a - \frac{1.0}{3.0}}} + \left(a - \frac{1.0}{3.0}\right)\]

  6. Applied times-frac0.1

    \[\leadsto rand \cdot \color{blue}{\left(\frac{\sqrt{a - \frac{1.0}{3.0}}}{\sqrt{9}} \cdot \frac{\sqrt{a - \frac{1.0}{3.0}}}{\sqrt{a - \frac{1.0}{3.0}}}\right)} + \left(a - \frac{1.0}{3.0}\right)\]

  7. Simplified0.1

    \[\leadsto rand \cdot \left(\color{blue}{\frac{\sqrt{a - \frac{1.0}{3.0}}}{3}} \cdot \frac{\sqrt{a - \frac{1.0}{3.0}}}{\sqrt{a - \frac{1.0}{3.0}}}\right) + \left(a - \frac{1.0}{3.0}\right)\]

  8. Simplified0.1

    \[\leadsto rand \cdot \left(\frac{\sqrt{a - \frac{1.0}{3.0}}}{3} \cdot \color{blue}{1}\right) + \left(a - \frac{1.0}{3.0}\right)\]

  9. Final simplification0.1

    \[\leadsto \left(a - \frac{1.0}{3.0}\right) + rand \cdot \frac{\sqrt{a - \frac{1.0}{3.0}}}{3}\]

Reproduce

herbie shell --seed 2019104 
(FPCore (a rand)
  :name "Octave 3.8, oct_fill_randg"
  (* (- a (/ 1.0 3.0)) (+ 1 (* (/ 1 (sqrt (* 9 (- a (/ 1.0 3.0))))) rand))))