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 r65081 = 2.0;
        double r65082 = 1.0;
        double r65083 = 9.0;
        double r65084 = r65082 / r65083;
        double r65085 = r65082 * r65084;
        double r65086 = r65084 * r65084;
        double r65087 = r65085 + r65086;
        double r65088 = r65084 * r65082;
        double r65089 = r65087 + r65088;
        double r65090 = r65081 * r65089;
        return r65090;
}

↓

double f() {
        double r65091 = 2.0;
        double r65092 = 1.0;
        double r65093 = 9.0;
        double r65094 = r65092 / r65093;
        double r65095 = r65092 * r65094;
        double r65096 = r65094 * r65094;
        double r65097 = r65095 + r65096;
        double r65098 = r65094 * r65092;
        double r65099 = r65097 + r65098;
        double r65100 = r65091 * r65099;
        return r65100;
}

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 2020018 
(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))))