Average Error: 0.3 → 0.3
Time: 13.1s
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 r6496145 = d1;
        double r6496146 = d2;
        double r6496147 = r6496145 * r6496146;
        double r6496148 = d3;
        double r6496149 = 5.0;
        double r6496150 = /* ERROR: no posit support in C */;
        double r6496151 = r6496148 + r6496150;
        double r6496152 = r6496151 * r6496145;
        double r6496153 = r6496147 + r6496152;
        double r6496154 = 32.0;
        double r6496155 = /* ERROR: no posit support in C */;
        double r6496156 = r6496145 * r6496155;
        double r6496157 = r6496153 + r6496156;
        return r6496157;
}
↓
double f(double d1, double d2, double d3) {
        double r6496158 = d1;
        double r6496159 = d2;
        double r6496160 = r6496158 * r6496159;
        double r6496161 = d3;
        double r6496162 = 5.0;
        double r6496163 = r6496161 + r6496162;
        double r6496164 = r6496163 * r6496158;
        double r6496165 = r6496160 + r6496164;
        double r6496166 = 32.0;
        double r6496167 = r6496158 * r6496166;
        double r6496168 = r6496165 + r6496167;
        return r6496168;
}

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 2019135 +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))))