Average Error: 0.1 → 0.1
Time: 6.8s
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 r130632 = a;
        double r130633 = 1.0;
        double r130634 = 3.0;
        double r130635 = r130633 / r130634;
        double r130636 = r130632 - r130635;
        double r130637 = 9.0;
        double r130638 = r130637 * r130636;
        double r130639 = sqrt(r130638);
        double r130640 = r130633 / r130639;
        double r130641 = rand;
        double r130642 = r130640 * r130641;
        double r130643 = r130633 + r130642;
        double r130644 = r130636 * r130643;
        return r130644;
}
↓
double f(double a, double rand) {
        double r130645 = a;
        double r130646 = 1.0;
        double r130647 = 3.0;
        double r130648 = r130646 / r130647;
        double r130649 = r130645 - r130648;
        double r130650 = r130649 * r130646;
        double r130651 = 9.0;
        double r130652 = r130651 * r130649;
        double r130653 = sqrt(r130652);
        double r130654 = r130646 / r130653;
        double r130655 = r130649 * r130654;
        double r130656 = rand;
        double r130657 = r130655 * r130656;
        double r130658 = r130650 + r130657;
        return r130658;
}

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 +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))))