Rectangular parallelepiped of dimension a×b×c

Average Error: 0 → 0

Time: 581.0ms

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 r94457 = 2.0;
        double r94458 = 1.0;
        double r94459 = 9.0;
        double r94460 = r94458 / r94459;
        double r94461 = r94458 * r94460;
        double r94462 = r94460 * r94460;
        double r94463 = r94461 + r94462;
        double r94464 = r94460 * r94458;
        double r94465 = r94463 + r94464;
        double r94466 = r94457 * r94465;
        return r94466;
}

↓

double f() {
        double r94467 = 2.0;
        double r94468 = 1.0;
        double r94469 = 9.0;
        double r94470 = r94468 / r94469;
        double r94471 = r94468 * r94470;
        double r94472 = r94470 * r94470;
        double r94473 = r94471 + r94472;
        double r94474 = r94470 * r94468;
        double r94475 = r94473 + r94474;
        double r94476 = r94467 * r94475;
        return r94476;
}

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 2020001 +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))))