Average Error: 0.2 → 0.0
Time: 18.9s
Precision: 64
\[\left(d1 \cdot 10 + d1 \cdot d2\right) + d1 \cdot 20\]
↓
\[\left(d2 + 30\right) \cdot d1\]
double f(double d1, double d2) {
        double r68124178 = d1;
        double r68124179 = 10.0;
        double r68124180 = r68124178 * r68124179;
        double r68124181 = d2;
        double r68124182 = r68124178 * r68124181;
        double r68124183 = r68124180 + r68124182;
        double r68124184 = 20.0;
        double r68124185 = r68124178 * r68124184;
        double r68124186 = r68124183 + r68124185;
        return r68124186;
}
↓
double f(double d1, double d2) {
        double r68124187 = d2;
        double r68124188 = 30.0;
        double r68124189 = r68124187 + r68124188;
        double r68124190 = d1;
        double r68124191 = r68124189 * r68124190;
        return r68124191;
}


\left(d1 \cdot 10 + d1 \cdot d2\right) + d1 \cdot 20
↓
\left(d2 + 30\right) \cdot d1

Error

Bits error versus d1

Bits error versus d2

Target

Original0.2
Target0.0
Herbie0.0
\[d1 \cdot \left(30 + d2\right)\]

Derivation

  1. Initial program 0.2

    \[\left(d1 \cdot 10 + d1 \cdot d2\right) + d1 \cdot 20\]

  2. Simplified0.0

    \[\leadsto \color{blue}{\left(30 + d2\right) \cdot d1}\]

  3. Final simplification0.0

    \[\leadsto \left(d2 + 30\right) \cdot d1\]

Reproduce

herbie shell --seed 2019102 +o rules:numerics
(FPCore (d1 d2)
  :name "FastMath test2"

  :herbie-target
  (* d1 (+ 30 d2))

  (+ (+ (* d1 10) (* d1 d2)) (* d1 20)))