Average Error: 0.1 → 0.1
Time: 6.6s
Precision: 64
\[\left(a - \frac{1}{3}\right) \cdot \left(1 + \frac{1}{\sqrt{9 \cdot \left(a - \frac{1}{3}\right)}} \cdot rand\right)\]
↓
\[\left(a - \frac{1}{3}\right) \cdot 1 + \left(\left(a - \frac{1}{3}\right) \cdot \frac{1}{\sqrt{9 \cdot \left(a - \frac{1}{3}\right)}}\right) \cdot rand\]
\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(\left(a - \frac{1}{3}\right) \cdot \frac{1}{\sqrt{9 \cdot \left(a - \frac{1}{3}\right)}}\right) \cdot rand
double f(double a, double rand) {
        double r88371 = a;
        double r88372 = 1.0;
        double r88373 = 3.0;
        double r88374 = r88372 / r88373;
        double r88375 = r88371 - r88374;
        double r88376 = 9.0;
        double r88377 = r88376 * r88375;
        double r88378 = sqrt(r88377);
        double r88379 = r88372 / r88378;
        double r88380 = rand;
        double r88381 = r88379 * r88380;
        double r88382 = r88372 + r88381;
        double r88383 = r88375 * r88382;
        return r88383;
}
↓
double f(double a, double rand) {
        double r88384 = a;
        double r88385 = 1.0;
        double r88386 = 3.0;
        double r88387 = r88385 / r88386;
        double r88388 = r88384 - r88387;
        double r88389 = r88388 * r88385;
        double r88390 = 9.0;
        double r88391 = r88390 * r88388;
        double r88392 = sqrt(r88391);
        double r88393 = r88385 / r88392;
        double r88394 = r88388 * r88393;
        double r88395 = rand;
        double r88396 = r88394 * r88395;
        double r88397 = r88389 + r88396;
        return r88397;
}

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 associate-*r*0.1

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

  6. Final simplification0.1

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

Reproduce

herbie shell --seed 2020060 
(FPCore (a rand)
  :name "Octave 3.8, oct_fill_randg"
  :precision binary64
  (* (- a (/ 1 3)) (+ 1 (* (/ 1 (sqrt (* 9 (- a (/ 1 3))))) rand))))