Rectangular parallelepiped of dimension a×b×c

Average Error: 0 → 0

Time: 1.6s

Precision: 64

• Falling back on racket egraph because egg-herbie package not installed

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 r77093 = 2.0;
        double r77094 = 1.0;
        double r77095 = 9.0;
        double r77096 = r77094 / r77095;
        double r77097 = r77094 * r77096;
        double r77098 = r77096 * r77096;
        double r77099 = r77097 + r77098;
        double r77100 = r77096 * r77094;
        double r77101 = r77099 + r77100;
        double r77102 = r77093 * r77101;
        return r77102;
}

↓

double f() {
        double r77103 = 2.0;
        double r77104 = 1.0;
        double r77105 = 9.0;
        double r77106 = r77104 / r77105;
        double r77107 = r77104 + r77106;
        double r77108 = r77107 + r77104;
        double r77109 = r77106 * r77108;
        double r77110 = r77103 * r77109;
        return r77110;
}

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 2020047 
(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))))