Rectangular parallelepiped of dimension a×b×c

Average Error: 0 → 0

Time: 3.5m

Precision: 64

Math

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

↓

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

C

double f() {
        double r82078 = 2.0;
        double r82079 = 1.0;
        double r82080 = 9.0;
        double r82081 = r82079 / r82080;
        double r82082 = r82079 * r82081;
        double r82083 = r82081 * r82081;
        double r82084 = r82082 + r82083;
        double r82085 = r82081 * r82079;
        double r82086 = r82084 + r82085;
        double r82087 = r82078 * r82086;
        return r82087;
}

↓

double f() {
        double r82088 = 2.0;
        double r82089 = 1.0;
        double r82090 = 9.0;
        double r82091 = r82089 / r82090;
        double r82092 = r82089 + r82091;
        double r82093 = r82092 + r82089;
        double r82094 = r82091 * r82093;
        double r82095 = r82088 * r82094;
        return r82095;
}

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

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

3. Final simplification 0

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

Reproduce

herbie shell --seed 2019212 
(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))))