Rectangular parallelepiped of dimension a×b×c

Average Error: 0 → 0

Time: 378.0ms

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 r90191 = 2.0;
        double r90192 = 1.0;
        double r90193 = 9.0;
        double r90194 = r90192 / r90193;
        double r90195 = r90192 * r90194;
        double r90196 = r90194 * r90194;
        double r90197 = r90195 + r90196;
        double r90198 = r90194 * r90192;
        double r90199 = r90197 + r90198;
        double r90200 = r90191 * r90199;
        return r90200;
}

↓

double f() {
        double r90201 = 2.0;
        double r90202 = 1.0;
        double r90203 = 9.0;
        double r90204 = r90202 / r90203;
        double r90205 = r90202 * r90204;
        double r90206 = r90204 * r90204;
        double r90207 = r90205 + r90206;
        double r90208 = r90204 * r90202;
        double r90209 = r90207 + r90208;
        double r90210 = r90201 * r90209;
        return r90210;
}

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 2020003 
(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))))