Average Error: 0.1 → 0.1
Time: 47.0s
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 r3698156 = a;
        double r3698157 = 1.0;
        double r3698158 = 3.0;
        double r3698159 = r3698157 / r3698158;
        double r3698160 = r3698156 - r3698159;
        double r3698161 = 9.0;
        double r3698162 = r3698161 * r3698160;
        double r3698163 = sqrt(r3698162);
        double r3698164 = r3698157 / r3698163;
        double r3698165 = rand;
        double r3698166 = r3698164 * r3698165;
        double r3698167 = r3698157 + r3698166;
        double r3698168 = r3698160 * r3698167;
        return r3698168;
}
↓
double f(double a, double rand) {
        double r3698169 = rand;
        double r3698170 = 1.0;
        double r3698171 = a;
        double r3698172 = 3.0;
        double r3698173 = r3698170 / r3698172;
        double r3698174 = r3698171 - r3698173;
        double r3698175 = 9.0;
        double r3698176 = r3698174 * r3698175;
        double r3698177 = sqrt(r3698176);
        double r3698178 = r3698170 / r3698177;
        double r3698179 = r3698169 * r3698178;
        double r3698180 = r3698179 + r3698170;
        double r3698181 = r3698180 * r3698174;
        return r3698181;
}

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))))