Rectangular parallelepiped of dimension a×b×c

Average Error: 0 → 0

Time: 383.0ms

Precision: 64

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 r73491 = 2.0;
        double r73492 = 1.0;
        double r73493 = 9.0;
        double r73494 = r73492 / r73493;
        double r73495 = r73492 * r73494;
        double r73496 = r73494 * r73494;
        double r73497 = r73495 + r73496;
        double r73498 = r73494 * r73492;
        double r73499 = r73497 + r73498;
        double r73500 = r73491 * r73499;
        return r73500;
}

↓

double f() {
        double r73501 = 2.0;
        double r73502 = 1.0;
        double r73503 = 9.0;
        double r73504 = r73502 / r73503;
        double r73505 = r73502 * r73504;
        double r73506 = r73504 * r73504;
        double r73507 = r73505 + r73506;
        double r73508 = r73504 * r73502;
        double r73509 = r73507 + r73508;
        double r73510 = r73501 * r73509;
        return r73510;
}

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 2020027 
(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))))