Rectangular parallelepiped of dimension a×b×c

Average Error: 0 → 0

Time: 1.8s

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 r74918 = 2.0;
        double r74919 = 1.0;
        double r74920 = 9.0;
        double r74921 = r74919 / r74920;
        double r74922 = r74919 * r74921;
        double r74923 = r74921 * r74921;
        double r74924 = r74922 + r74923;
        double r74925 = r74921 * r74919;
        double r74926 = r74924 + r74925;
        double r74927 = r74918 * r74926;
        return r74927;
}

↓

double f() {
        double r74928 = 2.0;
        double r74929 = 1.0;
        double r74930 = 9.0;
        double r74931 = r74929 / r74930;
        double r74932 = r74929 * r74931;
        double r74933 = r74931 * r74931;
        double r74934 = r74932 + r74933;
        double r74935 = r74931 * r74929;
        double r74936 = r74934 + r74935;
        double r74937 = r74928 * r74936;
        return r74937;
}

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 2020042 
(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))))