Average Error: 0.1 → 0.1
Time: 9.3s
Precision: 64
\[\left(a - \frac{1}{3}\right) \cdot \left(1 + \frac{1}{\sqrt{9 \cdot \left(a - \frac{1}{3}\right)}} \cdot rand\right)\]
↓
\[\left(a - \frac{1}{3}\right) \cdot 1 + \left(a - \frac{1}{3}\right) \cdot \left(\frac{1}{\sqrt{9} \cdot \sqrt{a - \frac{1}{3}}} \cdot rand\right)\]
\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 + \left(a - \frac{1}{3}\right) \cdot \left(\frac{1}{\sqrt{9} \cdot \sqrt{a - \frac{1}{3}}} \cdot rand\right)
double f(double a, double rand) {
        double r141488 = a;
        double r141489 = 1.0;
        double r141490 = 3.0;
        double r141491 = r141489 / r141490;
        double r141492 = r141488 - r141491;
        double r141493 = 9.0;
        double r141494 = r141493 * r141492;
        double r141495 = sqrt(r141494);
        double r141496 = r141489 / r141495;
        double r141497 = rand;
        double r141498 = r141496 * r141497;
        double r141499 = r141489 + r141498;
        double r141500 = r141492 * r141499;
        return r141500;
}
↓
double f(double a, double rand) {
        double r141501 = a;
        double r141502 = 1.0;
        double r141503 = 3.0;
        double r141504 = r141502 / r141503;
        double r141505 = r141501 - r141504;
        double r141506 = r141505 * r141502;
        double r141507 = 9.0;
        double r141508 = sqrt(r141507);
        double r141509 = sqrt(r141505);
        double r141510 = r141508 * r141509;
        double r141511 = r141502 / r141510;
        double r141512 = rand;
        double r141513 = r141511 * r141512;
        double r141514 = r141505 * r141513;
        double r141515 = r141506 + r141514;
        return r141515;
}

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. Final simplification0.1

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

Reproduce

herbie shell --seed 2020033 +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))))