Average Error: 0.3 → 0.2
Time: 3.9s
Precision: 64
\[\frac{\left(d1 \cdot d2\right)}{\left(d1 \cdot d3\right)}\]
↓
\[\left(d3 + d2\right) \cdot d1\]
\frac{\left(d1 \cdot d2\right)}{\left(d1 \cdot d3\right)}
↓
\left(d3 + d2\right) \cdot d1
double f(double d1, double d2, double d3) {
        double r2242105 = d1;
        double r2242106 = d2;
        double r2242107 = r2242105 * r2242106;
        double r2242108 = d3;
        double r2242109 = r2242105 * r2242108;
        double r2242110 = r2242107 + r2242109;
        return r2242110;
}
↓
double f(double d1, double d2, double d3) {
        double r2242111 = d3;
        double r2242112 = d2;
        double r2242113 = r2242111 + r2242112;
        double r2242114 = d1;
        double r2242115 = r2242113 * r2242114;
        return r2242115;
}

Error

Bits error versus d1

Bits error versus d2

Bits error versus d3

Derivation

  1. Initial program 0.3

    \[\frac{\left(d1 \cdot d2\right)}{\left(d1 \cdot d3\right)}\]

  2. Simplified0.2

    \[\leadsto \color{blue}{\left(\frac{d3}{d2}\right) \cdot d1}\]

  3. Final simplification0.2

    \[\leadsto \left(d3 + d2\right) \cdot d1\]

Reproduce

herbie shell --seed 2019112 +o rules:numerics
(FPCore (d1 d2 d3)
  :name "FastMath dist"
  (+.p16 (*.p16 d1 d2) (*.p16 d1 d3)))