Rectangular parallelepiped of dimension a×b×c

Average Error: 0 → 0

Time: 370.0ms

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 r67127 = 2.0;
        double r67128 = 1.0;
        double r67129 = 9.0;
        double r67130 = r67128 / r67129;
        double r67131 = r67128 * r67130;
        double r67132 = r67130 * r67130;
        double r67133 = r67131 + r67132;
        double r67134 = r67130 * r67128;
        double r67135 = r67133 + r67134;
        double r67136 = r67127 * r67135;
        return r67136;
}

↓

double f() {
        double r67137 = 2.0;
        double r67138 = 1.0;
        double r67139 = 9.0;
        double r67140 = r67138 / r67139;
        double r67141 = r67138 * r67140;
        double r67142 = r67140 * r67140;
        double r67143 = r67141 + r67142;
        double r67144 = r67140 * r67138;
        double r67145 = r67143 + r67144;
        double r67146 = r67137 * r67145;
        return r67146;
}

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 2020014 
(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))))