Average Error: 0.3 → 0.2
Time: 5.6s
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 r4142133 = d1;
        double r4142134 = d2;
        double r4142135 = r4142133 * r4142134;
        double r4142136 = d3;
        double r4142137 = r4142133 * r4142136;
        double r4142138 = r4142135 + r4142137;
        return r4142138;
}
↓
double f(double d1, double d2, double d3) {
        double r4142139 = d3;
        double r4142140 = d2;
        double r4142141 = r4142139 + r4142140;
        double r4142142 = d1;
        double r4142143 = r4142141 * r4142142;
        return r4142143;
}

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 +o rules:numerics
(FPCore (d1 d2 d3)
  :name "FastMath dist"
  (+.p16 (*.p16 d1 d2) (*.p16 d1 d3)))