Average Error: 0.1 → 0.2
Time: 6.8s
Precision: 64
\[\left(a - \frac{1}{3}\right) \cdot \left(1 + \frac{1}{\sqrt{9 \cdot \left(a - \frac{1}{3}\right)}} \cdot rand\right)\]
↓
\[\left(a - \frac{1}{3}\right) \cdot 1 + \sqrt{a - \frac{1}{3}} \cdot \left(\sqrt{a - \frac{1}{3}} \cdot \left(\frac{1}{\sqrt{9} \cdot \sqrt{a - \frac{1}{3}}} \cdot rand\right)\right)\]
\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 1 + \sqrt{a - \frac{1}{3}} \cdot \left(\sqrt{a - \frac{1}{3}} \cdot \left(\frac{1}{\sqrt{9} \cdot \sqrt{a - \frac{1}{3}}} \cdot rand\right)\right)
double f(double a, double rand) {
        double r145193 = a;
        double r145194 = 1.0;
        double r145195 = 3.0;
        double r145196 = r145194 / r145195;
        double r145197 = r145193 - r145196;
        double r145198 = 9.0;
        double r145199 = r145198 * r145197;
        double r145200 = sqrt(r145199);
        double r145201 = r145194 / r145200;
        double r145202 = rand;
        double r145203 = r145201 * r145202;
        double r145204 = r145194 + r145203;
        double r145205 = r145197 * r145204;
        return r145205;
}
↓
double f(double a, double rand) {
        double r145206 = a;
        double r145207 = 1.0;
        double r145208 = 3.0;
        double r145209 = r145207 / r145208;
        double r145210 = r145206 - r145209;
        double r145211 = r145210 * r145207;
        double r145212 = sqrt(r145210);
        double r145213 = 9.0;
        double r145214 = sqrt(r145213);
        double r145215 = r145214 * r145212;
        double r145216 = r145207 / r145215;
        double r145217 = rand;
        double r145218 = r145216 * r145217;
        double r145219 = r145212 * r145218;
        double r145220 = r145212 * r145219;
        double r145221 = r145211 + r145220;
        return r145221;
}

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. Using strategy rm

  7. Applied add-sqr-sqrt0.2

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

  8. Applied associate-*l*0.2

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

  9. Final simplification0.2

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

Reproduce

herbie shell --seed 2020024 
(FPCore (a rand)
  :name "Octave 3.8, oct_fill_randg"
  :precision binary64
  (* (- a (/ 1 3)) (+ 1 (* (/ 1 (sqrt (* 9 (- a (/ 1 3))))) rand))))