Average Error: 0.3 → 0.3
Time: 11.2s
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 r2494132 = d1;
        double r2494133 = d2;
        double r2494134 = r2494132 * r2494133;
        double r2494135 = d3;
        double r2494136 = 5.0;
        double r2494137 = /* ERROR: no posit support in C */;
        double r2494138 = r2494135 + r2494137;
        double r2494139 = r2494138 * r2494132;
        double r2494140 = r2494134 + r2494139;
        double r2494141 = 32.0;
        double r2494142 = /* ERROR: no posit support in C */;
        double r2494143 = r2494132 * r2494142;
        double r2494144 = r2494140 + r2494143;
        return r2494144;
}
↓
double f(double d1, double d2, double d3) {
        double r2494145 = d1;
        double r2494146 = d2;
        double r2494147 = r2494145 * r2494146;
        double r2494148 = d3;
        double r2494149 = 5.0;
        double r2494150 = r2494148 + r2494149;
        double r2494151 = r2494150 * r2494145;
        double r2494152 = r2494147 + r2494151;
        double r2494153 = 32.0;
        double r2494154 = r2494145 * r2494153;
        double r2494155 = r2494152 + r2494154;
        return r2494155;
}

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 2019104 +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))))