Average Error: 0.5 → 0.3
Time: 9.5s
Precision: 64
\[\frac{\left(\frac{\left(d1 \cdot \left(3\right)\right)}{\left(d1 \cdot d2\right)}\right)}{\left(d1 \cdot d3\right)}\]
↓
\[\left(\left(3 + d2\right) + d3\right) \cdot d1\]
\frac{\left(\frac{\left(d1 \cdot \left(3\right)\right)}{\left(d1 \cdot d2\right)}\right)}{\left(d1 \cdot d3\right)}
↓
\left(\left(3 + d2\right) + d3\right) \cdot d1
double f(double d1, double d2, double d3) {
        double r2626127 = d1;
        double r2626128 = 3.0;
        double r2626129 = /* ERROR: no posit support in C */;
        double r2626130 = r2626127 * r2626129;
        double r2626131 = d2;
        double r2626132 = r2626127 * r2626131;
        double r2626133 = r2626130 + r2626132;
        double r2626134 = d3;
        double r2626135 = r2626127 * r2626134;
        double r2626136 = r2626133 + r2626135;
        return r2626136;
}
↓
double f(double d1, double d2, double d3) {
        double r2626137 = 3.0;
        double r2626138 = d2;
        double r2626139 = r2626137 + r2626138;
        double r2626140 = d3;
        double r2626141 = r2626139 + r2626140;
        double r2626142 = d1;
        double r2626143 = r2626141 * r2626142;
        return r2626143;
}

Error

Bits error versus d1

Bits error versus d2

Bits error versus d3

Derivation

  1. Initial program 0.5

    \[\frac{\left(\frac{\left(d1 \cdot \left(3\right)\right)}{\left(d1 \cdot d2\right)}\right)}{\left(d1 \cdot d3\right)}\]

  2. Simplified0.3

    \[\leadsto \color{blue}{\left(\frac{\left(3\right)}{\left(\frac{d2}{d3}\right)}\right) \cdot d1}\]
  3. Using strategy rm

  4. Applied associate-+r+0.3

    \[\leadsto \color{blue}{\left(\frac{\left(\frac{\left(3\right)}{d2}\right)}{d3}\right)} \cdot d1\]

  5. Final simplification0.3

    \[\leadsto \left(\left(3 + d2\right) + d3\right) \cdot d1\]

Reproduce

herbie shell --seed 2019128 
(FPCore (d1 d2 d3)
  :name "FastMath test3"
  (+.p16 (+.p16 (*.p16 d1 (real->posit16 3)) (*.p16 d1 d2)) (*.p16 d1 d3)))