Average Error: 0.1 → 0.1
Time: 27.9s
Precision: 64
\[\left(a - \frac{1.0}{3.0}\right) \cdot \left(1 + \frac{1}{\sqrt{9 \cdot \left(a - \frac{1.0}{3.0}\right)}} \cdot rand\right)\]
↓
\[\left(a - \frac{1.0}{3.0}\right) + rand \cdot \frac{\sqrt{a - \frac{1.0}{3.0}}}{3}\]
\left(a - \frac{1.0}{3.0}\right) \cdot \left(1 + \frac{1}{\sqrt{9 \cdot \left(a - \frac{1.0}{3.0}\right)}} \cdot rand\right)
↓
\left(a - \frac{1.0}{3.0}\right) + rand \cdot \frac{\sqrt{a - \frac{1.0}{3.0}}}{3}
double f(double a, double rand) {
        double r2805657 = a;
        double r2805658 = 1.0;
        double r2805659 = 3.0;
        double r2805660 = r2805658 / r2805659;
        double r2805661 = r2805657 - r2805660;
        double r2805662 = 1.0;
        double r2805663 = 9.0;
        double r2805664 = r2805663 * r2805661;
        double r2805665 = sqrt(r2805664);
        double r2805666 = r2805662 / r2805665;
        double r2805667 = rand;
        double r2805668 = r2805666 * r2805667;
        double r2805669 = r2805662 + r2805668;
        double r2805670 = r2805661 * r2805669;
        return r2805670;
}
↓
double f(double a, double rand) {
        double r2805671 = a;
        double r2805672 = 1.0;
        double r2805673 = 3.0;
        double r2805674 = r2805672 / r2805673;
        double r2805675 = r2805671 - r2805674;
        double r2805676 = rand;
        double r2805677 = sqrt(r2805675);
        double r2805678 = 3.0;
        double r2805679 = r2805677 / r2805678;
        double r2805680 = r2805676 * r2805679;
        double r2805681 = r2805675 + r2805680;
        return r2805681;
}

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

    \[\left(a - \frac{1.0}{3.0}\right) \cdot \left(1 + \frac{1}{\sqrt{9 \cdot \left(a - \frac{1.0}{3.0}\right)}} \cdot rand\right)\]

  2. Simplified0.1

    \[\leadsto \color{blue}{\left(a - \frac{1.0}{3.0}\right) + rand \cdot \frac{a - \frac{1.0}{3.0}}{\sqrt{9 \cdot \left(a - \frac{1.0}{3.0}\right)}}}\]
  3. Using strategy rm

  4. Applied sqrt-prod0.1

    \[\leadsto \left(a - \frac{1.0}{3.0}\right) + rand \cdot \frac{a - \frac{1.0}{3.0}}{\color{blue}{\sqrt{9} \cdot \sqrt{a - \frac{1.0}{3.0}}}}\]

  5. Applied add-sqr-sqrt0.1

    \[\leadsto \left(a - \frac{1.0}{3.0}\right) + rand \cdot \frac{\color{blue}{\sqrt{a - \frac{1.0}{3.0}} \cdot \sqrt{a - \frac{1.0}{3.0}}}}{\sqrt{9} \cdot \sqrt{a - \frac{1.0}{3.0}}}\]

  6. Applied times-frac0.1

    \[\leadsto \left(a - \frac{1.0}{3.0}\right) + rand \cdot \color{blue}{\left(\frac{\sqrt{a - \frac{1.0}{3.0}}}{\sqrt{9}} \cdot \frac{\sqrt{a - \frac{1.0}{3.0}}}{\sqrt{a - \frac{1.0}{3.0}}}\right)}\]

  7. Simplified0.1

    \[\leadsto \left(a - \frac{1.0}{3.0}\right) + rand \cdot \left(\color{blue}{\frac{\sqrt{a - \frac{1.0}{3.0}}}{3}} \cdot \frac{\sqrt{a - \frac{1.0}{3.0}}}{\sqrt{a - \frac{1.0}{3.0}}}\right)\]

  8. Simplified0.1

    \[\leadsto \left(a - \frac{1.0}{3.0}\right) + rand \cdot \left(\frac{\sqrt{a - \frac{1.0}{3.0}}}{3} \cdot \color{blue}{1}\right)\]

  9. Final simplification0.1

    \[\leadsto \left(a - \frac{1.0}{3.0}\right) + rand \cdot \frac{\sqrt{a - \frac{1.0}{3.0}}}{3}\]

Reproduce

herbie shell --seed 2019149 
(FPCore (a rand)
  :name "Octave 3.8, oct_fill_randg"
  (* (- a (/ 1.0 3.0)) (+ 1 (* (/ 1 (sqrt (* 9 (- a (/ 1.0 3.0))))) rand))))