Rectangular parallelepiped of dimension a×b×c

Average Error: 0 → 0

Time: 3.2m

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 r83198 = 2.0;
        double r83199 = 1.0;
        double r83200 = 9.0;
        double r83201 = r83199 / r83200;
        double r83202 = r83199 * r83201;
        double r83203 = r83201 * r83201;
        double r83204 = r83202 + r83203;
        double r83205 = r83201 * r83199;
        double r83206 = r83204 + r83205;
        double r83207 = r83198 * r83206;
        return r83207;
}

↓

double f() {
        double r83208 = 2.0;
        double r83209 = 1.0;
        double r83210 = 9.0;
        double r83211 = r83209 / r83210;
        double r83212 = r83209 * r83211;
        double r83213 = r83211 * r83211;
        double r83214 = r83212 + r83213;
        double r83215 = r83211 * r83209;
        double r83216 = r83214 + r83215;
        double r83217 = r83208 * r83216;
        return r83217;
}

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 
(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))))