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

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

↓

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

C

double f() {
        double r52816 = 2.0;
        double r52817 = 1.0;
        double r52818 = 9.0;
        double r52819 = r52817 / r52818;
        double r52820 = r52817 * r52819;
        double r52821 = r52819 * r52819;
        double r52822 = r52820 + r52821;
        double r52823 = r52819 * r52817;
        double r52824 = r52822 + r52823;
        double r52825 = r52816 * r52824;
        return r52825;
}

↓

double f() {
        double r52826 = 2.0;
        double r52827 = 1.0;
        double r52828 = 9.0;
        double r52829 = r52827 / r52828;
        double r52830 = r52827 * r52829;
        double r52831 = r52829 * r52829;
        double r52832 = r52830 + r52831;
        double r52833 = r52829 * r52827;
        double r52834 = r52832 + r52833;
        double r52835 = r52826 * r52834;
        return r52835;
}

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 2020045 
(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))))