Rectangular parallelepiped of dimension a×b×c

Average Error: 0 → 0

Time: 3.2s

Precision: 64

Math

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

↓

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

C

double f() {
        double r42331 = 2.0;
        double r42332 = 1.0;
        double r42333 = 9.0;
        double r42334 = r42332 / r42333;
        double r42335 = r42332 * r42334;
        double r42336 = r42334 * r42334;
        double r42337 = r42335 + r42336;
        double r42338 = r42334 * r42332;
        double r42339 = r42337 + r42338;
        double r42340 = r42331 * r42339;
        return r42340;
}

↓

double f() {
        double r42341 = 2.0;
        double r42342 = 1.0;
        double r42343 = 9.0;
        double r42344 = r42342 / r42343;
        double r42345 = r42341 * r42344;
        double r42346 = r42342 + r42344;
        double r42347 = r42346 + r42342;
        double r42348 = r42345 * r42347;
        return r42348;
}

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

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

3. Final simplification 0

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

Reproduce

herbie shell --seed 2019298 
(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))))