Rectangular parallelepiped of dimension a×b×c

Average Error: 0 → 0

Time: 861.0ms

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 r80575 = 2.0;
        double r80576 = 1.0;
        double r80577 = 9.0;
        double r80578 = r80576 / r80577;
        double r80579 = r80576 * r80578;
        double r80580 = r80578 * r80578;
        double r80581 = r80579 + r80580;
        double r80582 = r80578 * r80576;
        double r80583 = r80581 + r80582;
        double r80584 = r80575 * r80583;
        return r80584;
}

↓

double f() {
        double r80585 = 2.0;
        double r80586 = 1.0;
        double r80587 = 9.0;
        double r80588 = r80586 / r80587;
        double r80589 = r80586 * r80588;
        double r80590 = r80588 * r80588;
        double r80591 = r80589 + r80590;
        double r80592 = r80588 * r80586;
        double r80593 = r80591 + r80592;
        double r80594 = r80585 * r80593;
        return r80594;
}

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 2019322 
(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))))