Average Error: 0.1 → 0.1
Time: 7.3s
Precision: 64
\[\left(a - \frac{1}{3}\right) \cdot \left(1 + \frac{1}{\sqrt{9 \cdot \left(a - \frac{1}{3}\right)}} \cdot rand\right)\]
↓
\[\left(a - \frac{1}{3}\right) \cdot \left(1 + \frac{1 \cdot rand}{\sqrt{\left(\sqrt{9} \cdot \sqrt{a - \frac{1}{3}}\right) \cdot \left(\sqrt{9} \cdot \sqrt{a - \frac{1}{3}}\right)}}\right)\]
\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{1 \cdot rand}{\sqrt{\left(\sqrt{9} \cdot \sqrt{a - \frac{1}{3}}\right) \cdot \left(\sqrt{9} \cdot \sqrt{a - \frac{1}{3}}\right)}}\right)
double f(double a, double rand) {
        double r77202 = a;
        double r77203 = 1.0;
        double r77204 = 3.0;
        double r77205 = r77203 / r77204;
        double r77206 = r77202 - r77205;
        double r77207 = 9.0;
        double r77208 = r77207 * r77206;
        double r77209 = sqrt(r77208);
        double r77210 = r77203 / r77209;
        double r77211 = rand;
        double r77212 = r77210 * r77211;
        double r77213 = r77203 + r77212;
        double r77214 = r77206 * r77213;
        return r77214;
}
↓
double f(double a, double rand) {
        double r77215 = a;
        double r77216 = 1.0;
        double r77217 = 3.0;
        double r77218 = r77216 / r77217;
        double r77219 = r77215 - r77218;
        double r77220 = rand;
        double r77221 = r77216 * r77220;
        double r77222 = 9.0;
        double r77223 = sqrt(r77222);
        double r77224 = sqrt(r77219);
        double r77225 = r77223 * r77224;
        double r77226 = r77225 * r77225;
        double r77227 = sqrt(r77226);
        double r77228 = r77221 / r77227;
        double r77229 = r77216 + r77228;
        double r77230 = r77219 * r77229;
        return r77230;
}

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 add-sqr-sqrt0.1

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

  6. Applied add-sqr-sqrt0.1

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

  7. Applied unswap-sqr0.1

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

  8. Final simplification0.1

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

Reproduce

herbie shell --seed 2019356 
(FPCore (a rand)
  :name "Octave 3.8, oct_fill_randg"
  :precision binary64
  (* (- a (/ 1 3)) (+ 1 (* (/ 1 (sqrt (* 9 (- a (/ 1 3))))) rand))))