Average Error: 0.2 → 0
Time: 4.1s
Precision: 64
\[\frac{\left(d \cdot \left(10\right)\right)}{\left(d \cdot \left(20\right)\right)}\]
↓
\[d \cdot \left(20 + 10\right)\]
\frac{\left(d \cdot \left(10\right)\right)}{\left(d \cdot \left(20\right)\right)}
↓
d \cdot \left(20 + 10\right)
double f(double d) {
        double r1096133 = d;
        double r1096134 = 10.0;
        double r1096135 = /* ERROR: no posit support in C */;
        double r1096136 = r1096133 * r1096135;
        double r1096137 = 20.0;
        double r1096138 = /* ERROR: no posit support in C */;
        double r1096139 = r1096133 * r1096138;
        double r1096140 = r1096136 + r1096139;
        return r1096140;
}
↓
double f(double d) {
        double r1096141 = d;
        double r1096142 = 20.0;
        double r1096143 = 10.0;
        double r1096144 = r1096142 + r1096143;
        double r1096145 = r1096141 * r1096144;
        return r1096145;
}

Error

Bits error versus d

Derivation

  1. Initial program 0.2

    \[\frac{\left(d \cdot \left(10\right)\right)}{\left(d \cdot \left(20\right)\right)}\]

  2. Simplified0

    \[\leadsto \color{blue}{d \cdot \left(\frac{\left(20\right)}{\left(10\right)}\right)}\]

  3. Final simplification0

    \[\leadsto d \cdot \left(20 + 10\right)\]

Reproduce

herbie shell --seed 2019153 
(FPCore (d)
  :name "FastMath test1"
  (+.p16 (*.p16 d (real->posit16 10)) (*.p16 d (real->posit16 20))))