Rectangular parallelepiped of dimension a×b×c

Average Error: 0 → 0

Time: 5.5s

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 r50064 = 2.0;
        double r50065 = 1.0;
        double r50066 = 9.0;
        double r50067 = r50065 / r50066;
        double r50068 = r50065 * r50067;
        double r50069 = r50067 * r50067;
        double r50070 = r50068 + r50069;
        double r50071 = r50067 * r50065;
        double r50072 = r50070 + r50071;
        double r50073 = r50064 * r50072;
        return r50073;
}

↓

double f() {
        double r50074 = 2.0;
        double r50075 = 1.0;
        double r50076 = 9.0;
        double r50077 = r50075 / r50076;
        double r50078 = r50075 * r50077;
        double r50079 = r50077 * r50077;
        double r50080 = r50078 + r50079;
        double r50081 = r50077 * r50075;
        double r50082 = r50080 + r50081;
        double r50083 = r50074 * r50082;
        return r50083;
}

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 2019323 +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))))