Rectangular parallelepiped of dimension a×b×c

Average Error: 0 → 0

Time: 728.0ms

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 r59721 = 2.0;
        double r59722 = 1.0;
        double r59723 = 9.0;
        double r59724 = r59722 / r59723;
        double r59725 = r59722 * r59724;
        double r59726 = r59724 * r59724;
        double r59727 = r59725 + r59726;
        double r59728 = r59724 * r59722;
        double r59729 = r59727 + r59728;
        double r59730 = r59721 * r59729;
        return r59730;
}

↓

double f() {
        double r59731 = 2.0;
        double r59732 = 1.0;
        double r59733 = 9.0;
        double r59734 = r59732 / r59733;
        double r59735 = r59732 * r59734;
        double r59736 = r59734 * r59734;
        double r59737 = r59735 + r59736;
        double r59738 = r59734 * r59732;
        double r59739 = r59737 + r59738;
        double r59740 = r59731 * r59739;
        return r59740;
}

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 2020036 
(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))))