Average Error: 0.1 → 0.1
Time: 27.5s
Precision: 64
\[\left(a - \frac{1.0}{3.0}\right) \cdot \left(1 + \frac{1}{\sqrt{9 \cdot \left(a - \frac{1.0}{3.0}\right)}} \cdot rand\right)\]
↓
\[rand \cdot \frac{\sqrt{a - \frac{1.0}{3.0}}}{3} + \left(a - \frac{1.0}{3.0}\right)\]
\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)
↓
rand \cdot \frac{\sqrt{a - \frac{1.0}{3.0}}}{3} + \left(a - \frac{1.0}{3.0}\right)
double f(double a, double rand) {
        double r2050080 = a;
        double r2050081 = 1.0;
        double r2050082 = 3.0;
        double r2050083 = r2050081 / r2050082;
        double r2050084 = r2050080 - r2050083;
        double r2050085 = 1.0;
        double r2050086 = 9.0;
        double r2050087 = r2050086 * r2050084;
        double r2050088 = sqrt(r2050087);
        double r2050089 = r2050085 / r2050088;
        double r2050090 = rand;
        double r2050091 = r2050089 * r2050090;
        double r2050092 = r2050085 + r2050091;
        double r2050093 = r2050084 * r2050092;
        return r2050093;
}
↓
double f(double a, double rand) {
        double r2050094 = rand;
        double r2050095 = a;
        double r2050096 = 1.0;
        double r2050097 = 3.0;
        double r2050098 = r2050096 / r2050097;
        double r2050099 = r2050095 - r2050098;
        double r2050100 = sqrt(r2050099);
        double r2050101 = 3.0;
        double r2050102 = r2050100 / r2050101;
        double r2050103 = r2050094 * r2050102;
        double r2050104 = r2050103 + r2050099;
        return r2050104;
}

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

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

  4. Applied sqrt-prod0.1

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

  5. Applied add-sqr-sqrt0.2

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

  6. Applied times-frac0.1

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

  7. Applied associate-*l*0.1

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

  8. Simplified0.1

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

  9. Final simplification0.1

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

Reproduce

herbie shell --seed 2019139 
(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))))