Average Error: 0.3 → 0.3
Time: 11.1s
Precision: 64
\[\frac{\left(\frac{\left(d1 \cdot d2\right)}{\left(\left(\frac{d3}{\left(5\right)}\right) \cdot d1\right)}\right)}{\left(d1 \cdot \left(32\right)\right)}\]
↓
\[\left(d1 \cdot d2 + \left(d3 + 5\right) \cdot d1\right) + d1 \cdot 32\]
\frac{\left(\frac{\left(d1 \cdot d2\right)}{\left(\left(\frac{d3}{\left(5\right)}\right) \cdot d1\right)}\right)}{\left(d1 \cdot \left(32\right)\right)}
↓
\left(d1 \cdot d2 + \left(d3 + 5\right) \cdot d1\right) + d1 \cdot 32
double f(double d1, double d2, double d3) {
        double r1060019 = d1;
        double r1060020 = d2;
        double r1060021 = r1060019 * r1060020;
        double r1060022 = d3;
        double r1060023 = 5.0;
        double r1060024 = /* ERROR: no posit support in C */;
        double r1060025 = r1060022 + r1060024;
        double r1060026 = r1060025 * r1060019;
        double r1060027 = r1060021 + r1060026;
        double r1060028 = 32.0;
        double r1060029 = /* ERROR: no posit support in C */;
        double r1060030 = r1060019 * r1060029;
        double r1060031 = r1060027 + r1060030;
        return r1060031;
}
↓
double f(double d1, double d2, double d3) {
        double r1060032 = d1;
        double r1060033 = d2;
        double r1060034 = r1060032 * r1060033;
        double r1060035 = d3;
        double r1060036 = 5.0;
        double r1060037 = r1060035 + r1060036;
        double r1060038 = r1060037 * r1060032;
        double r1060039 = r1060034 + r1060038;
        double r1060040 = 32.0;
        double r1060041 = r1060032 * r1060040;
        double r1060042 = r1060039 + r1060041;
        return r1060042;
}

Error

Bits error versus d1

Bits error versus d2

Bits error versus d3

Derivation

  1. Initial program 0.3

    \[\frac{\left(\frac{\left(d1 \cdot d2\right)}{\left(\left(\frac{d3}{\left(5\right)}\right) \cdot d1\right)}\right)}{\left(d1 \cdot \left(32\right)\right)}\]

  2. Final simplification0.3

    \[\leadsto \left(d1 \cdot d2 + \left(d3 + 5\right) \cdot d1\right) + d1 \cdot 32\]

Reproduce

herbie shell --seed 2019119 +o rules:numerics
(FPCore (d1 d2 d3)
  :name "FastMath dist3"
  (+.p16 (+.p16 (*.p16 d1 d2) (*.p16 (+.p16 d3 (real->posit16 5)) d1)) (*.p16 d1 (real->posit16 32))))