Rectangular parallelepiped of dimension a×b×c

Average Error: 0 → 0

Time: 3.3s

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 r64131 = 2.0;
        double r64132 = 1.0;
        double r64133 = 9.0;
        double r64134 = r64132 / r64133;
        double r64135 = r64132 * r64134;
        double r64136 = r64134 * r64134;
        double r64137 = r64135 + r64136;
        double r64138 = r64134 * r64132;
        double r64139 = r64137 + r64138;
        double r64140 = r64131 * r64139;
        return r64140;
}

↓

double f() {
        double r64141 = 2.0;
        double r64142 = 1.0;
        double r64143 = 9.0;
        double r64144 = r64142 / r64143;
        double r64145 = r64142 * r64144;
        double r64146 = r64144 * r64144;
        double r64147 = r64145 + r64146;
        double r64148 = r64144 * r64142;
        double r64149 = r64147 + r64148;
        double r64150 = r64141 * r64149;
        return r64150;
}

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 
(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))))