Rectangular parallelepiped of dimension a×b×c

Average Error: 0 → 0

Time: 537.0ms

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 r65144 = 2.0;
        double r65145 = 1.0;
        double r65146 = 9.0;
        double r65147 = r65145 / r65146;
        double r65148 = r65145 * r65147;
        double r65149 = r65147 * r65147;
        double r65150 = r65148 + r65149;
        double r65151 = r65147 * r65145;
        double r65152 = r65150 + r65151;
        double r65153 = r65144 * r65152;
        return r65153;
}

↓

double f() {
        double r65154 = 2.0;
        double r65155 = 1.0;
        double r65156 = 9.0;
        double r65157 = r65155 / r65156;
        double r65158 = r65155 * r65157;
        double r65159 = r65157 * r65157;
        double r65160 = r65158 + r65159;
        double r65161 = r65157 * r65155;
        double r65162 = r65160 + r65161;
        double r65163 = r65154 * r65162;
        return r65163;
}

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 2020020 
(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))))