Average Error: 0.3 → 0.2
Time: 5.7s
Precision: 64
\[\frac{\left(d1 \cdot d2\right)}{\left(d1 \cdot d3\right)}\]
↓
\[\left(\frac{d3}{d2}\right) \cdot d1\]
\frac{\left(d1 \cdot d2\right)}{\left(d1 \cdot d3\right)}
↓
\left(\frac{d3}{d2}\right) \cdot d1
double f(double d1, double d2, double d3) {
        double r4720188 = d1;
        double r4720189 = d2;
        double r4720190 = r4720188 * r4720189;
        double r4720191 = d3;
        double r4720192 = r4720188 * r4720191;
        double r4720193 = r4720190 + r4720192;
        return r4720193;
}
↓
double f(double d1, double d2, double d3) {
        double r4720194 = d3;
        double r4720195 = d2;
        double r4720196 = r4720194 + r4720195;
        double r4720197 = d1;
        double r4720198 = r4720196 * r4720197;
        return r4720198;
}

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

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

Reproduce

herbie shell --seed 2019164 
(FPCore (d1 d2 d3)
  :name "FastMath dist"
  (+.p16 (*.p16 d1 d2) (*.p16 d1 d3)))