Average Error: 0.1 → 0.1
Time: 1.3m
Precision: 64
\[\left(a - \frac{1}{3}\right) \cdot \left(1 + \frac{1}{\sqrt{9 \cdot \left(a - \frac{1}{3}\right)}} \cdot rand\right)\]
↓
\[\left(\frac{rand \cdot 1}{\sqrt{\left(a - \frac{1}{3}\right) \cdot 9}} + 1\right) \cdot \left(a - \frac{1}{3}\right)\]
\left(a - \frac{1}{3}\right) \cdot \left(1 + \frac{1}{\sqrt{9 \cdot \left(a - \frac{1}{3}\right)}} \cdot rand\right)
↓
\left(\frac{rand \cdot 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 r4461081 = a;
        double r4461082 = 1.0;
        double r4461083 = 3.0;
        double r4461084 = r4461082 / r4461083;
        double r4461085 = r4461081 - r4461084;
        double r4461086 = 9.0;
        double r4461087 = r4461086 * r4461085;
        double r4461088 = sqrt(r4461087);
        double r4461089 = r4461082 / r4461088;
        double r4461090 = rand;
        double r4461091 = r4461089 * r4461090;
        double r4461092 = r4461082 + r4461091;
        double r4461093 = r4461085 * r4461092;
        return r4461093;
}
↓
double f(double a, double rand) {
        double r4461094 = rand;
        double r4461095 = 1.0;
        double r4461096 = r4461094 * r4461095;
        double r4461097 = a;
        double r4461098 = 3.0;
        double r4461099 = r4461095 / r4461098;
        double r4461100 = r4461097 - r4461099;
        double r4461101 = 9.0;
        double r4461102 = r4461100 * r4461101;
        double r4461103 = sqrt(r4461102);
        double r4461104 = r4461096 / r4461103;
        double r4461105 = r4461104 + r4461095;
        double r4461106 = r4461105 * r4461100;
        return r4461106;
}

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

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

Reproduce

herbie shell --seed 2019200 
(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))))