Average Error: 0.3 → 0.3
Time: 11.4s
Precision: 64
\[\left(d1 \cdot d2 + \left(d3 + 5\right) \cdot d1\right) + d1 \cdot 32\]
↓
\[\left(d1 \cdot d2 + \left(d3 + 5\right) \cdot d1\right) + d1 \cdot 32\]
double f(double d1, double d2, double d3) {
        double r1654903 = d1;
        double r1654904 = d2;
        double r1654905 = r1654903 * r1654904;
        double r1654906 = d3;
        double r1654907 = 5.0;
        double r1654908 = r1654906 + r1654907;
        double r1654909 = r1654908 * r1654903;
        double r1654910 = r1654905 + r1654909;
        double r1654911 = 32.0;
        double r1654912 = r1654903 * r1654911;
        double r1654913 = r1654910 + r1654912;
        return r1654913;
}
↓
double f(double d1, double d2, double d3) {
        double r1654914 = d1;
        double r1654915 = d2;
        double r1654916 = r1654914 * r1654915;
        double r1654917 = d3;
        double r1654918 = 5.0;
        double r1654919 = r1654917 + r1654918;
        double r1654920 = r1654919 * r1654914;
        double r1654921 = r1654916 + r1654920;
        double r1654922 = 32.0;
        double r1654923 = r1654914 * r1654922;
        double r1654924 = r1654921 + r1654923;
        return r1654924;
}


\left(d1 \cdot d2 + \left(d3 + 5\right) \cdot d1\right) + d1 \cdot 32
↓
\left(d1 \cdot d2 + \left(d3 + 5\right) \cdot d1\right) + d1 \cdot 32

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 2019101 +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))))