Rectangular parallelepiped of dimension a×b×c

Average Error: 0 → 0

Time: 1.9s

Precision: 64

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

Math

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

↓

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

C

double f() {
        double r79104 = 2.0;
        double r79105 = 1.0;
        double r79106 = 9.0;
        double r79107 = r79105 / r79106;
        double r79108 = r79105 * r79107;
        double r79109 = r79107 * r79107;
        double r79110 = r79108 + r79109;
        double r79111 = r79107 * r79105;
        double r79112 = r79110 + r79111;
        double r79113 = r79104 * r79112;
        return r79113;
}

↓

double f() {
        double r79114 = 2.0;
        double r79115 = 1.0;
        double r79116 = 9.0;
        double r79117 = r79115 / r79116;
        double r79118 = r79115 * r79117;
        double r79119 = r79117 * r79117;
        double r79120 = r79118 + r79119;
        double r79121 = r79117 * r79115;
        double r79122 = r79120 + r79121;
        double r79123 = r79114 * r79122;
        return r79123;
}

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 2019351 
(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))))