Average Error: 0.3 → 0.2
Time: 6.3s
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 r1526731 = d1;
        double r1526732 = d2;
        double r1526733 = r1526731 * r1526732;
        double r1526734 = d3;
        double r1526735 = r1526731 * r1526734;
        double r1526736 = r1526733 + r1526735;
        return r1526736;
}
↓
double f(double d1, double d2, double d3) {
        double r1526737 = d3;
        double r1526738 = d2;
        double r1526739 = r1526737 + r1526738;
        double r1526740 = d1;
        double r1526741 = r1526739 * r1526740;
        return r1526741;
}

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 2019152 
(FPCore (d1 d2 d3)
  :name "FastMath dist"
  (+.p16 (*.p16 d1 d2) (*.p16 d1 d3)))