Average Error: 0.2 → 0.1
Time: 1.5m
Precision: 64
\[\left(a - \frac{1.0}{3.0}\right) \cdot \left(1 + \frac{1}{\sqrt{9 \cdot \left(a - \frac{1.0}{3.0}\right)}} \cdot rand\right)\]
↓
\[\frac{a - \frac{1.0}{3.0}}{\sqrt{\left(\left(\sqrt[3]{9} \cdot \sqrt[3]{9}\right) \cdot \left(a - \frac{1.0}{3.0}\right)\right) \cdot \sqrt[3]{9}}} \cdot rand + \left(a - \frac{1.0}{3.0}\right)\]
\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)
↓
\frac{a - \frac{1.0}{3.0}}{\sqrt{\left(\left(\sqrt[3]{9} \cdot \sqrt[3]{9}\right) \cdot \left(a - \frac{1.0}{3.0}\right)\right) \cdot \sqrt[3]{9}}} \cdot rand + \left(a - \frac{1.0}{3.0}\right)
double f(double a, double rand) {
        double r6394209 = a;
        double r6394210 = 1.0;
        double r6394211 = 3.0;
        double r6394212 = r6394210 / r6394211;
        double r6394213 = r6394209 - r6394212;
        double r6394214 = 1.0;
        double r6394215 = 9.0;
        double r6394216 = r6394215 * r6394213;
        double r6394217 = sqrt(r6394216);
        double r6394218 = r6394214 / r6394217;
        double r6394219 = rand;
        double r6394220 = r6394218 * r6394219;
        double r6394221 = r6394214 + r6394220;
        double r6394222 = r6394213 * r6394221;
        return r6394222;
}
↓
double f(double a, double rand) {
        double r6394223 = a;
        double r6394224 = 1.0;
        double r6394225 = 3.0;
        double r6394226 = r6394224 / r6394225;
        double r6394227 = r6394223 - r6394226;
        double r6394228 = 9.0;
        double r6394229 = cbrt(r6394228);
        double r6394230 = r6394229 * r6394229;
        double r6394231 = r6394230 * r6394227;
        double r6394232 = r6394231 * r6394229;
        double r6394233 = sqrt(r6394232);
        double r6394234 = r6394227 / r6394233;
        double r6394235 = rand;
        double r6394236 = r6394234 * r6394235;
        double r6394237 = r6394236 + r6394227;
        return r6394237;
}

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 0.2

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

  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 *-commutative0.1

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

  6. Applied add-cube-cbrt0.1

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

  7. Applied associate-*r*0.1

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

  8. Final simplification0.1

    \[\leadsto \frac{a - \frac{1.0}{3.0}}{\sqrt{\left(\left(\sqrt[3]{9} \cdot \sqrt[3]{9}\right) \cdot \left(a - \frac{1.0}{3.0}\right)\right) \cdot \sqrt[3]{9}}} \cdot rand + \left(a - \frac{1.0}{3.0}\right)\]

Reproduce

herbie shell --seed 2019107 
(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))))