Rectangular parallelepiped of dimension a×b×c

Average Error: 0 → 0

Time: 382.0ms

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 r67652 = 2.0;
        double r67653 = 1.0;
        double r67654 = 9.0;
        double r67655 = r67653 / r67654;
        double r67656 = r67653 * r67655;
        double r67657 = r67655 * r67655;
        double r67658 = r67656 + r67657;
        double r67659 = r67655 * r67653;
        double r67660 = r67658 + r67659;
        double r67661 = r67652 * r67660;
        return r67661;
}

↓

double f() {
        double r67662 = 2.0;
        double r67663 = 1.0;
        double r67664 = 9.0;
        double r67665 = r67663 / r67664;
        double r67666 = r67663 * r67665;
        double r67667 = r67665 * r67665;
        double r67668 = r67666 + r67667;
        double r67669 = r67665 * r67663;
        double r67670 = r67668 + r67669;
        double r67671 = r67662 * r67670;
        return r67671;
}

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 2020003 +o rules:numerics
(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))))