Average Error: 0.1 → 0.2
Time: 22.6s
Precision: 64
\[\left(a - \frac{1}{3}\right) \cdot \left(1 + \frac{1}{\sqrt{9 \cdot \left(a - \frac{1}{3}\right)}} \cdot rand\right)\]
↓
\[\left(a - \frac{1}{3}\right) \cdot \left(1 + \frac{\frac{1}{\sqrt{9}}}{\sqrt{a - \frac{1}{3}}} \cdot rand\right)\]
\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 \left(1 + \frac{\frac{1}{\sqrt{9}}}{\sqrt{a - \frac{1}{3}}} \cdot rand\right)
double f(double a, double rand) {
        double r114477 = a;
        double r114478 = 1.0;
        double r114479 = 3.0;
        double r114480 = r114478 / r114479;
        double r114481 = r114477 - r114480;
        double r114482 = 9.0;
        double r114483 = r114482 * r114481;
        double r114484 = sqrt(r114483);
        double r114485 = r114478 / r114484;
        double r114486 = rand;
        double r114487 = r114485 * r114486;
        double r114488 = r114478 + r114487;
        double r114489 = r114481 * r114488;
        return r114489;
}
↓
double f(double a, double rand) {
        double r114490 = a;
        double r114491 = 1.0;
        double r114492 = 3.0;
        double r114493 = r114491 / r114492;
        double r114494 = r114490 - r114493;
        double r114495 = 9.0;
        double r114496 = sqrt(r114495);
        double r114497 = r114491 / r114496;
        double r114498 = sqrt(r114494);
        double r114499 = r114497 / r114498;
        double r114500 = rand;
        double r114501 = r114499 * r114500;
        double r114502 = r114491 + r114501;
        double r114503 = r114494 * r114502;
        return r114503;
}

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 sqrt-prod0.1

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

  4. Applied associate-/r*0.2

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

  5. Final simplification0.2

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

Reproduce

herbie shell --seed 2019350 +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))))