Average Error: 0.1 → 0.1
Time: 8.6s
Precision: 64
\[\left(a - \frac{1}{3}\right) \cdot \left(1 + \frac{1}{\sqrt{9 \cdot \left(a - \frac{1}{3}\right)}} \cdot rand\right)\]
↓
\[\left(a - \frac{1}{3}\right) \cdot \left(1 + \frac{1 \cdot rand}{\sqrt{\left(\sqrt[3]{9} \cdot \sqrt[3]{9}\right) \cdot \left(\left(\sqrt[3]{\sqrt[3]{9}} \cdot \sqrt[3]{\sqrt[3]{9}}\right) \cdot \left(\sqrt[3]{\sqrt[3]{9}} \cdot \left(a - \frac{1}{3}\right)\right)\right)}}\right)\]
\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[3]{9} \cdot \sqrt[3]{9}\right) \cdot \left(\left(\sqrt[3]{\sqrt[3]{9}} \cdot \sqrt[3]{\sqrt[3]{9}}\right) \cdot \left(\sqrt[3]{\sqrt[3]{9}} \cdot \left(a - \frac{1}{3}\right)\right)\right)}}\right)
double f(double a, double rand) {
        double r77299 = a;
        double r77300 = 1.0;
        double r77301 = 3.0;
        double r77302 = r77300 / r77301;
        double r77303 = r77299 - r77302;
        double r77304 = 9.0;
        double r77305 = r77304 * r77303;
        double r77306 = sqrt(r77305);
        double r77307 = r77300 / r77306;
        double r77308 = rand;
        double r77309 = r77307 * r77308;
        double r77310 = r77300 + r77309;
        double r77311 = r77303 * r77310;
        return r77311;
}
↓
double f(double a, double rand) {
        double r77312 = a;
        double r77313 = 1.0;
        double r77314 = 3.0;
        double r77315 = r77313 / r77314;
        double r77316 = r77312 - r77315;
        double r77317 = rand;
        double r77318 = r77313 * r77317;
        double r77319 = 9.0;
        double r77320 = cbrt(r77319);
        double r77321 = r77320 * r77320;
        double r77322 = cbrt(r77320);
        double r77323 = r77322 * r77322;
        double r77324 = r77322 * r77316;
        double r77325 = r77323 * r77324;
        double r77326 = r77321 * r77325;
        double r77327 = sqrt(r77326);
        double r77328 = r77318 / r77327;
        double r77329 = r77313 + r77328;
        double r77330 = r77316 * r77329;
        return r77330;
}

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-cube-cbrt0.1

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

  6. Applied associate-*l*0.1

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

  8. Applied add-cube-cbrt0.1

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

  9. Applied associate-*l*0.1

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

  10. Final simplification0.1

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

Reproduce

herbie shell --seed 2019353 +o rules:numerics
(FPCore (a rand)
  :name "Octave 3.8, oct_fill_randg"
  :precision binary64
  (* (- a (/ 1 3)) (+ 1 (* (/ 1 (sqrt (* 9 (- a (/ 1 3))))) rand))))