Rectangular parallelepiped of dimension a×b×c

Average Error: 0 → 0

Time: 1.5s

Precision: 64

• Falling back on racket egraph because egg-herbie package not installed

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 r69197 = 2.0;
        double r69198 = 1.0;
        double r69199 = 9.0;
        double r69200 = r69198 / r69199;
        double r69201 = r69198 * r69200;
        double r69202 = r69200 * r69200;
        double r69203 = r69201 + r69202;
        double r69204 = r69200 * r69198;
        double r69205 = r69203 + r69204;
        double r69206 = r69197 * r69205;
        return r69206;
}

↓

double f() {
        double r69207 = 2.0;
        double r69208 = 1.0;
        double r69209 = 9.0;
        double r69210 = r69208 / r69209;
        double r69211 = r69208 * r69210;
        double r69212 = r69210 * r69210;
        double r69213 = r69211 + r69212;
        double r69214 = r69210 * r69208;
        double r69215 = r69213 + r69214;
        double r69216 = r69207 * r69215;
        return r69216;
}

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 2020045 
(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))))