Rectangular parallelepiped of dimension a×b×c

Average Error: 0 → 0

Time: 374.0ms

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 r67042 = 2.0;
        double r67043 = 1.0;
        double r67044 = 9.0;
        double r67045 = r67043 / r67044;
        double r67046 = r67043 * r67045;
        double r67047 = r67045 * r67045;
        double r67048 = r67046 + r67047;
        double r67049 = r67045 * r67043;
        double r67050 = r67048 + r67049;
        double r67051 = r67042 * r67050;
        return r67051;
}

↓

double f() {
        double r67052 = 2.0;
        double r67053 = 1.0;
        double r67054 = 9.0;
        double r67055 = r67053 / r67054;
        double r67056 = r67053 * r67055;
        double r67057 = r67055 * r67055;
        double r67058 = r67056 + r67057;
        double r67059 = r67055 * r67053;
        double r67060 = r67058 + r67059;
        double r67061 = r67052 * r67060;
        return r67061;
}

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 2020024 
(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))))