Average Error: 0.1 → 0.1
Time: 7.2s
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 r73639 = a;
        double r73640 = 1.0;
        double r73641 = 3.0;
        double r73642 = r73640 / r73641;
        double r73643 = r73639 - r73642;
        double r73644 = 9.0;
        double r73645 = r73644 * r73643;
        double r73646 = sqrt(r73645);
        double r73647 = r73640 / r73646;
        double r73648 = rand;
        double r73649 = r73647 * r73648;
        double r73650 = r73640 + r73649;
        double r73651 = r73643 * r73650;
        return r73651;
}
↓
double f(double a, double rand) {
        double r73652 = a;
        double r73653 = 1.0;
        double r73654 = 3.0;
        double r73655 = r73653 / r73654;
        double r73656 = r73652 - r73655;
        double r73657 = rand;
        double r73658 = r73653 * r73657;
        double r73659 = 9.0;
        double r73660 = cbrt(r73659);
        double r73661 = r73660 * r73660;
        double r73662 = cbrt(r73660);
        double r73663 = r73662 * r73662;
        double r73664 = r73662 * r73656;
        double r73665 = r73663 * r73664;
        double r73666 = r73661 * r73665;
        double r73667 = sqrt(r73666);
        double r73668 = r73658 / r73667;
        double r73669 = r73653 + r73668;
        double r73670 = r73656 * r73669;
        return r73670;
}

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