Rectangular parallelepiped of dimension a×b×c

Average Error: 0 → 0

Time: 3.9s

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 r10337 = 2.0;
        double r10338 = 1.0;
        double r10339 = 9.0;
        double r10340 = r10338 / r10339;
        double r10341 = r10338 * r10340;
        double r10342 = r10340 * r10340;
        double r10343 = r10341 + r10342;
        double r10344 = r10340 * r10338;
        double r10345 = r10343 + r10344;
        double r10346 = r10337 * r10345;
        return r10346;
}

↓

double f() {
        double r10347 = 2.0;
        double r10348 = 1.0;
        double r10349 = 9.0;
        double r10350 = r10348 / r10349;
        double r10351 = r10348 * r10350;
        double r10352 = r10350 * r10350;
        double r10353 = r10351 + r10352;
        double r10354 = r10350 * r10348;
        double r10355 = r10353 + r10354;
        double r10356 = r10347 * r10355;
        return r10356;
}

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 2019315 
(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))))