Average Error: 0.1 → 0.1
Time: 8.6s
Precision: 64
\[\left(a - \frac{1}{3}\right) \cdot \left(1 + \frac{1}{\sqrt{9 \cdot \left(a - \frac{1}{3}\right)}} \cdot rand\right)\]
↓
\[\left(a - \frac{1}{3}\right) \cdot \left(1 + \frac{1 \cdot rand}{\sqrt{9 \cdot \left(a - \frac{1}{3}\right)}}\right)\]
\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{1 \cdot rand}{\sqrt{9 \cdot \left(a - \frac{1}{3}\right)}}\right)
double f(double a, double rand) {
        double r76540 = a;
        double r76541 = 1.0;
        double r76542 = 3.0;
        double r76543 = r76541 / r76542;
        double r76544 = r76540 - r76543;
        double r76545 = 9.0;
        double r76546 = r76545 * r76544;
        double r76547 = sqrt(r76546);
        double r76548 = r76541 / r76547;
        double r76549 = rand;
        double r76550 = r76548 * r76549;
        double r76551 = r76541 + r76550;
        double r76552 = r76544 * r76551;
        return r76552;
}
↓
double f(double a, double rand) {
        double r76553 = a;
        double r76554 = 1.0;
        double r76555 = 3.0;
        double r76556 = r76554 / r76555;
        double r76557 = r76553 - r76556;
        double r76558 = rand;
        double r76559 = r76554 * r76558;
        double r76560 = 9.0;
        double r76561 = r76560 * r76557;
        double r76562 = sqrt(r76561);
        double r76563 = r76559 / r76562;
        double r76564 = r76554 + r76563;
        double r76565 = r76557 * r76564;
        return r76565;
}

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 associate-*l/0.1

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

  4. Final simplification0.1

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

Reproduce

herbie shell --seed 2020034 +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))))