Average Error: 0.3 → 0.3
Time: 12.0s
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 r2639232 = d1;
        double r2639233 = d2;
        double r2639234 = r2639232 * r2639233;
        double r2639235 = d3;
        double r2639236 = 5.0;
        double r2639237 = /* ERROR: no posit support in C */;
        double r2639238 = r2639235 + r2639237;
        double r2639239 = r2639238 * r2639232;
        double r2639240 = r2639234 + r2639239;
        double r2639241 = 32.0;
        double r2639242 = /* ERROR: no posit support in C */;
        double r2639243 = r2639232 * r2639242;
        double r2639244 = r2639240 + r2639243;
        return r2639244;
}
↓
double f(double d1, double d2, double d3) {
        double r2639245 = d1;
        double r2639246 = d2;
        double r2639247 = r2639245 * r2639246;
        double r2639248 = d3;
        double r2639249 = 5.0;
        double r2639250 = r2639248 + r2639249;
        double r2639251 = r2639250 * r2639245;
        double r2639252 = r2639247 + r2639251;
        double r2639253 = 32.0;
        double r2639254 = r2639245 * r2639253;
        double r2639255 = r2639252 + r2639254;
        return r2639255;
}

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 2019128 
(FPCore (d1 d2 d3)
  :name "FastMath dist3"
  (+.p16 (+.p16 (*.p16 d1 d2) (*.p16 (+.p16 d3 (real->posit16 5)) d1)) (*.p16 d1 (real->posit16 32))))