Rectangular parallelepiped of dimension a×b×c

Average Error: 0 → 0

Time: 565.0ms

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 r86392 = 2.0;
        double r86393 = 1.0;
        double r86394 = 9.0;
        double r86395 = r86393 / r86394;
        double r86396 = r86393 * r86395;
        double r86397 = r86395 * r86395;
        double r86398 = r86396 + r86397;
        double r86399 = r86395 * r86393;
        double r86400 = r86398 + r86399;
        double r86401 = r86392 * r86400;
        return r86401;
}

↓

double f() {
        double r86402 = 2.0;
        double r86403 = 1.0;
        double r86404 = 9.0;
        double r86405 = r86403 / r86404;
        double r86406 = r86403 * r86405;
        double r86407 = r86405 * r86405;
        double r86408 = r86406 + r86407;
        double r86409 = r86405 * r86403;
        double r86410 = r86408 + r86409;
        double r86411 = r86402 * r86410;
        return r86411;
}

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 2019318 
(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))))