Rectangular parallelepiped of dimension a×b×c

Average Error: 0 → 0

Time: 369.0ms

Precision: 64

Math

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

↓

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

C

double f() {
        double r80157 = 2.0;
        double r80158 = 1.0;
        double r80159 = 9.0;
        double r80160 = r80158 / r80159;
        double r80161 = r80158 * r80160;
        double r80162 = r80160 * r80160;
        double r80163 = r80161 + r80162;
        double r80164 = r80160 * r80158;
        double r80165 = r80163 + r80164;
        double r80166 = r80157 * r80165;
        return r80166;
}

↓

double f() {
        double r80167 = 2.0;
        double r80168 = 1.0;
        double r80169 = 9.0;
        double r80170 = r80168 / r80169;
        double r80171 = r80168 * r80170;
        double r80172 = r80170 * r80170;
        double r80173 = r80171 + r80172;
        double r80174 = r80170 * r80168;
        double r80175 = r80173 + r80174;
        double r80176 = r80167 * r80175;
        return r80176;
}

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. Final simplification 0

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

Reproduce

herbie shell --seed 2020002 
(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))))