Rectangular parallelepiped of dimension a×b×c

Average Error: 0 → 0

Time: 360.0ms

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 r69000 = 2.0;
        double r69001 = 1.0;
        double r69002 = 9.0;
        double r69003 = r69001 / r69002;
        double r69004 = r69001 * r69003;
        double r69005 = r69003 * r69003;
        double r69006 = r69004 + r69005;
        double r69007 = r69003 * r69001;
        double r69008 = r69006 + r69007;
        double r69009 = r69000 * r69008;
        return r69009;
}

↓

double f() {
        double r69010 = 2.0;
        double r69011 = 1.0;
        double r69012 = 9.0;
        double r69013 = r69011 / r69012;
        double r69014 = r69011 * r69013;
        double r69015 = r69013 * r69013;
        double r69016 = r69014 + r69015;
        double r69017 = r69013 * r69011;
        double r69018 = r69016 + r69017;
        double r69019 = r69010 * r69018;
        return r69019;
}

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 2020056 
(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))))