Rectangular parallelepiped of dimension a×b×c

Average Error: 0 → 0

Time: 5.1m

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 r76604 = 2.0;
        double r76605 = 1.0;
        double r76606 = 9.0;
        double r76607 = r76605 / r76606;
        double r76608 = r76605 * r76607;
        double r76609 = r76607 * r76607;
        double r76610 = r76608 + r76609;
        double r76611 = r76607 * r76605;
        double r76612 = r76610 + r76611;
        double r76613 = r76604 * r76612;
        return r76613;
}

↓

double f() {
        double r76614 = 2.0;
        double r76615 = 1.0;
        double r76616 = 9.0;
        double r76617 = r76615 / r76616;
        double r76618 = r76615 * r76617;
        double r76619 = r76617 * r76617;
        double r76620 = r76618 + r76619;
        double r76621 = r76617 * r76615;
        double r76622 = r76620 + r76621;
        double r76623 = r76614 * r76622;
        return r76623;
}

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 2019235 +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))))