Rectangular parallelepiped of dimension a×b×c

Average Error: 0 → 0

Time: 3.3s

Precision: 64

Math

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

↓

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

C

double f() {
        double r42262 = 2.0;
        double r42263 = 1.0;
        double r42264 = 9.0;
        double r42265 = r42263 / r42264;
        double r42266 = r42263 * r42265;
        double r42267 = r42265 * r42265;
        double r42268 = r42266 + r42267;
        double r42269 = r42265 * r42263;
        double r42270 = r42268 + r42269;
        double r42271 = r42262 * r42270;
        return r42271;
}

↓

double f() {
        double r42272 = 2.0;
        double r42273 = 1.0;
        double r42274 = 9.0;
        double r42275 = r42273 / r42274;
        double r42276 = r42273 * r42275;
        double r42277 = r42275 * r42275;
        double r42278 = r42276 + r42277;
        double r42279 = r42275 * r42273;
        double r42280 = r42278 + r42279;
        double r42281 = r42272 * r42280;
        return r42281;
}

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 2019326 
(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))))