Average Error: 0.1 → 0.2
Time: 8.8s
Precision: 64
\[\left(a - \frac{1}{3}\right) \cdot \left(1 + \frac{1}{\sqrt{9 \cdot \left(a - \frac{1}{3}\right)}} \cdot rand\right)\]
↓
\[\left(a - \frac{1}{3}\right) \cdot 1 + \left(\left(a - \frac{1}{3}\right) \cdot \frac{\sqrt{1}}{\sqrt{9}}\right) \cdot \left(\frac{\sqrt{1}}{\sqrt{a - \frac{1}{3}}} \cdot rand\right)\]
\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 1 + \left(\left(a - \frac{1}{3}\right) \cdot \frac{\sqrt{1}}{\sqrt{9}}\right) \cdot \left(\frac{\sqrt{1}}{\sqrt{a - \frac{1}{3}}} \cdot rand\right)
double f(double a, double rand) {
        double r84215 = a;
        double r84216 = 1.0;
        double r84217 = 3.0;
        double r84218 = r84216 / r84217;
        double r84219 = r84215 - r84218;
        double r84220 = 9.0;
        double r84221 = r84220 * r84219;
        double r84222 = sqrt(r84221);
        double r84223 = r84216 / r84222;
        double r84224 = rand;
        double r84225 = r84223 * r84224;
        double r84226 = r84216 + r84225;
        double r84227 = r84219 * r84226;
        return r84227;
}
↓
double f(double a, double rand) {
        double r84228 = a;
        double r84229 = 1.0;
        double r84230 = 3.0;
        double r84231 = r84229 / r84230;
        double r84232 = r84228 - r84231;
        double r84233 = r84232 * r84229;
        double r84234 = sqrt(r84229);
        double r84235 = 9.0;
        double r84236 = sqrt(r84235);
        double r84237 = r84234 / r84236;
        double r84238 = r84232 * r84237;
        double r84239 = sqrt(r84232);
        double r84240 = r84234 / r84239;
        double r84241 = rand;
        double r84242 = r84240 * r84241;
        double r84243 = r84238 * r84242;
        double r84244 = r84233 + r84243;
        return r84244;
}

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 distribute-lft-in0.1

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

  5. Applied sqrt-prod0.1

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

  6. Applied add-sqr-sqrt0.1

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

  7. Applied times-frac0.2

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

  8. Applied associate-*l*0.2

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

  10. Applied associate-*r*0.2

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

  11. Final simplification0.2

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

Reproduce

herbie shell --seed 2020046 
(FPCore (a rand)
  :name "Octave 3.8, oct_fill_randg"
  :precision binary64
  (* (- a (/ 1 3)) (+ 1 (* (/ 1 (sqrt (* 9 (- a (/ 1 3))))) rand))))