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 r71080 = 2.0;
        double r71081 = 1.0;
        double r71082 = 9.0;
        double r71083 = r71081 / r71082;
        double r71084 = r71081 * r71083;
        double r71085 = r71083 * r71083;
        double r71086 = r71084 + r71085;
        double r71087 = r71083 * r71081;
        double r71088 = r71086 + r71087;
        double r71089 = r71080 * r71088;
        return r71089;
}

↓

double f() {
        double r71090 = 2.0;
        double r71091 = 1.0;
        double r71092 = 9.0;
        double r71093 = r71091 / r71092;
        double r71094 = r71091 * r71093;
        double r71095 = r71093 * r71093;
        double r71096 = r71094 + r71095;
        double r71097 = r71093 * r71091;
        double r71098 = r71096 + r71097;
        double r71099 = r71090 * r71098;
        return r71099;
}

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))))