Average Error: 0 → 0
Time: 4.8s
Precision: 64
\[2 \cdot \left(\left(1 \cdot \frac{1}{9} + \frac{1}{9} \cdot \frac{1}{9}\right) + \frac{1}{9} \cdot 1\right)\]
↓
\[\mathsf{fma}\left(2, 1, \frac{1}{9}\right) \cdot \left(\frac{1}{9} \cdot 2\right)\]
2 \cdot \left(\left(1 \cdot \frac{1}{9} + \frac{1}{9} \cdot \frac{1}{9}\right) + \frac{1}{9} \cdot 1\right)
↓
\mathsf{fma}\left(2, 1, \frac{1}{9}\right) \cdot \left(\frac{1}{9} \cdot 2\right)
double f() {
        double r4742882 = 2.0;
        double r4742883 = 1.0;
        double r4742884 = 9.0;
        double r4742885 = r4742883 / r4742884;
        double r4742886 = r4742883 * r4742885;
        double r4742887 = r4742885 * r4742885;
        double r4742888 = r4742886 + r4742887;
        double r4742889 = r4742885 * r4742883;
        double r4742890 = r4742888 + r4742889;
        double r4742891 = r4742882 * r4742890;
        return r4742891;
}
↓
double f() {
        double r4742892 = 2.0;
        double r4742893 = 1.0;
        double r4742894 = 9.0;
        double r4742895 = r4742893 / r4742894;
        double r4742896 = fma(r4742892, r4742893, r4742895);
        double r4742897 = 2.0;
        double r4742898 = r4742895 * r4742897;
        double r4742899 = r4742896 * r4742898;
        return r4742899;
}

Error

Target

Original0
Target0
Herbie0
\[\left(\left(\frac{1}{9} \cdot 1\right) \cdot 2 + 2 \cdot \left(\frac{1}{9} \cdot \frac{1}{9}\right)\right) + 2 \cdot \left(1 \cdot \frac{1}{9}\right)\]

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. Simplified0

    \[\leadsto \color{blue}{\left(\frac{1}{9} \cdot 2\right) \cdot \mathsf{fma}\left(2, 1, \frac{1}{9}\right)}\]

  3. Final simplification0

    \[\leadsto \mathsf{fma}\left(2, 1, \frac{1}{9}\right) \cdot \left(\frac{1}{9} \cdot 2\right)\]

Reproduce

herbie shell --seed 2019170 +o rules:numerics
(FPCore ()
  :name "Rectangular parallelepiped of dimension a×b×c"

  :herbie-target
  (+ (+ (* (* (/ 1.0 9.0) 1.0) 2.0) (* 2.0 (* (/ 1.0 9.0) (/ 1.0 9.0)))) (* 2.0 (* 1.0 (/ 1.0 9.0))))

  (* 2.0 (+ (+ (* 1.0 (/ 1.0 9.0)) (* (/ 1.0 9.0) (/ 1.0 9.0))) (* (/ 1.0 9.0) 1.0))))