Rectangular parallelepiped of dimension a×b×c

Average Error: 0 → 0

Time: 392.0ms

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 r67001 = 2.0;
        double r67002 = 1.0;
        double r67003 = 9.0;
        double r67004 = r67002 / r67003;
        double r67005 = r67002 * r67004;
        double r67006 = r67004 * r67004;
        double r67007 = r67005 + r67006;
        double r67008 = r67004 * r67002;
        double r67009 = r67007 + r67008;
        double r67010 = r67001 * r67009;
        return r67010;
}

↓

double f() {
        double r67011 = 2.0;
        double r67012 = 1.0;
        double r67013 = 9.0;
        double r67014 = r67012 / r67013;
        double r67015 = r67012 * r67014;
        double r67016 = r67014 * r67014;
        double r67017 = r67015 + r67016;
        double r67018 = r67014 * r67012;
        double r67019 = r67017 + r67018;
        double r67020 = r67011 * r67019;
        return r67020;
}

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 2020021 
(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))))