Average Error: 0.1 → 0.1
Time: 7.4s
Precision: 64
\[\left(a - \frac{1}{3}\right) \cdot \left(1 + \frac{1}{\sqrt{9 \cdot \left(a - \frac{1}{3}\right)}} \cdot rand\right)\]
↓
\[\left(a - \frac{1}{3}\right) \cdot \left(1 + \frac{1 \cdot rand}{\sqrt{\left(\sqrt[3]{9} \cdot \sqrt[3]{9}\right) \cdot \left(\sqrt[3]{9} \cdot \left(a - \frac{1}{3}\right)\right)}}\right)\]
\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(\sqrt[3]{9} \cdot \left(a - \frac{1}{3}\right)\right)}}\right)
double f(double a, double rand) {
        double r86485 = a;
        double r86486 = 1.0;
        double r86487 = 3.0;
        double r86488 = r86486 / r86487;
        double r86489 = r86485 - r86488;
        double r86490 = 9.0;
        double r86491 = r86490 * r86489;
        double r86492 = sqrt(r86491);
        double r86493 = r86486 / r86492;
        double r86494 = rand;
        double r86495 = r86493 * r86494;
        double r86496 = r86486 + r86495;
        double r86497 = r86489 * r86496;
        return r86497;
}
↓
double f(double a, double rand) {
        double r86498 = a;
        double r86499 = 1.0;
        double r86500 = 3.0;
        double r86501 = r86499 / r86500;
        double r86502 = r86498 - r86501;
        double r86503 = rand;
        double r86504 = r86499 * r86503;
        double r86505 = 9.0;
        double r86506 = cbrt(r86505);
        double r86507 = r86506 * r86506;
        double r86508 = r86506 * r86502;
        double r86509 = r86507 * r86508;
        double r86510 = sqrt(r86509);
        double r86511 = r86504 / r86510;
        double r86512 = r86499 + r86511;
        double r86513 = r86502 * r86512;
        return r86513;
}

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. Final simplification0.1

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

Reproduce

herbie shell --seed 2020001 +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))))