Rectangular parallelepiped of dimension a×b×c

Average Error: 0 → 0

Time: 3.3s

Precision: 64

Math

\[2 \cdot \left(\left(1 \cdot \frac{1}{9} + \frac{1}{9} \cdot \frac{1}{9}\right) + \frac{1}{9} \cdot 1\right)\]

↓

\[2 \cdot \left(\frac{1}{9} \cdot \left(1 + \left(1 + \frac{1}{9}\right)\right)\right)\]

C

double f() {
        double r88161 = 2.0;
        double r88162 = 1.0;
        double r88163 = 9.0;
        double r88164 = r88162 / r88163;
        double r88165 = r88162 * r88164;
        double r88166 = r88164 * r88164;
        double r88167 = r88165 + r88166;
        double r88168 = r88164 * r88162;
        double r88169 = r88167 + r88168;
        double r88170 = r88161 * r88169;
        return r88170;
}

↓

double f() {
        double r88171 = 2.0;
        double r88172 = 1.0;
        double r88173 = 9.0;
        double r88174 = r88172 / r88173;
        double r88175 = r88172 + r88174;
        double r88176 = r88172 + r88175;
        double r88177 = r88174 * r88176;
        double r88178 = r88171 * r88177;
        return r88178;
}

Target

Original	0
Target	0
Herbie	0

\[\left(\left(\frac{1}{9} \cdot 1\right) \cdot 2 + 2 \cdot \left(\frac{1}{9} \cdot \frac{1}{9}\right)\right) + 2 \cdot \left(1 \cdot \frac{1}{9}\right)\]

Derivation

1. Initial program 0

   \[2 \cdot \left(\left(1 \cdot \frac{1}{9} + \frac{1}{9} \cdot \frac{1}{9}\right) + \frac{1}{9} \cdot 1\right)\]

2. Simplified 0

   \[\leadsto \color{blue}{2 \cdot \left(\frac{1}{9} \cdot \left(1 + \left(1 + \frac{1}{9}\right)\right)\right)}\]

3. Final simplification 0

   \[\leadsto 2 \cdot \left(\frac{1}{9} \cdot \left(1 + \left(1 + \frac{1}{9}\right)\right)\right)\]

Reproduce

herbie shell --seed 2019303 
(FPCore ()
  :name "Rectangular parallelepiped of dimension a×b×c"
  :precision binary64

  :herbie-target
  (+ (+ (* (* (/ 1 9) 1) 2) (* 2 (* (/ 1 9) (/ 1 9)))) (* 2 (* 1 (/ 1 9))))

  (* 2 (+ (+ (* 1 (/ 1 9)) (* (/ 1 9) (/ 1 9))) (* (/ 1 9) 1))))