Average Error: 0.1 → 0.1
Time: 1.4m
Precision: 64
\[\left(a - \frac{1}{3}\right) \cdot \left(1 + \frac{1}{\sqrt{9 \cdot \left(a - \frac{1}{3}\right)}} \cdot rand\right)\]
↓
\[\left(rand \cdot \frac{1}{\sqrt{\left(a - \frac{1}{3}\right) \cdot 9}} + 1\right) \cdot \left(a - \frac{1}{3}\right)\]
\left(a - \frac{1}{3}\right) \cdot \left(1 + \frac{1}{\sqrt{9 \cdot \left(a - \frac{1}{3}\right)}} \cdot rand\right)
↓
\left(rand \cdot \frac{1}{\sqrt{\left(a - \frac{1}{3}\right) \cdot 9}} + 1\right) \cdot \left(a - \frac{1}{3}\right)
double f(double a, double rand) {
        double r5175369 = a;
        double r5175370 = 1.0;
        double r5175371 = 3.0;
        double r5175372 = r5175370 / r5175371;
        double r5175373 = r5175369 - r5175372;
        double r5175374 = 9.0;
        double r5175375 = r5175374 * r5175373;
        double r5175376 = sqrt(r5175375);
        double r5175377 = r5175370 / r5175376;
        double r5175378 = rand;
        double r5175379 = r5175377 * r5175378;
        double r5175380 = r5175370 + r5175379;
        double r5175381 = r5175373 * r5175380;
        return r5175381;
}
↓
double f(double a, double rand) {
        double r5175382 = rand;
        double r5175383 = 1.0;
        double r5175384 = a;
        double r5175385 = 3.0;
        double r5175386 = r5175383 / r5175385;
        double r5175387 = r5175384 - r5175386;
        double r5175388 = 9.0;
        double r5175389 = r5175387 * r5175388;
        double r5175390 = sqrt(r5175389);
        double r5175391 = r5175383 / r5175390;
        double r5175392 = r5175382 * r5175391;
        double r5175393 = r5175392 + r5175383;
        double r5175394 = r5175393 * r5175387;
        return r5175394;
}

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 *-commutative0.1

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

  4. Final simplification0.1

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

Reproduce

herbie shell --seed 2019200 +o rules:numerics
(FPCore (a rand)
  :name "Octave 3.8, oct_fill_randg"
  (* (- a (/ 1.0 3.0)) (+ 1.0 (* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand))))