Rectangular parallelepiped of dimension a×b×c

Average Error: 0 → 0

Time: 356.0ms

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 r69410 = 2.0;
        double r69411 = 1.0;
        double r69412 = 9.0;
        double r69413 = r69411 / r69412;
        double r69414 = r69411 * r69413;
        double r69415 = r69413 * r69413;
        double r69416 = r69414 + r69415;
        double r69417 = r69413 * r69411;
        double r69418 = r69416 + r69417;
        double r69419 = r69410 * r69418;
        return r69419;
}

↓

double f() {
        double r69420 = 2.0;
        double r69421 = 1.0;
        double r69422 = 9.0;
        double r69423 = r69421 / r69422;
        double r69424 = r69421 * r69423;
        double r69425 = r69423 * r69423;
        double r69426 = r69424 + r69425;
        double r69427 = r69423 * r69421;
        double r69428 = r69426 + r69427;
        double r69429 = r69420 * r69428;
        return r69429;
}

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 2020057 +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))))