Average Error: 0.3 → 0.3
Time: 1.9m
Precision: 64
\[\frac{\left(\frac{\left(d1 \cdot \left(10\right)\right)}{\left(d1 \cdot d2\right)}\right)}{\left(d1 \cdot \left(20\right)\right)}\]
↓
\[d1 \cdot \left(\left(20 + 10\right) + d2\right)\]
\frac{\left(\frac{\left(d1 \cdot \left(10\right)\right)}{\left(d1 \cdot d2\right)}\right)}{\left(d1 \cdot \left(20\right)\right)}
↓
d1 \cdot \left(\left(20 + 10\right) + d2\right)
double f(double d1, double d2) {
        double r3394229 = d1;
        double r3394230 = 10.0;
        double r3394231 = /* ERROR: no posit support in C */;
        double r3394232 = r3394229 * r3394231;
        double r3394233 = d2;
        double r3394234 = r3394229 * r3394233;
        double r3394235 = r3394232 + r3394234;
        double r3394236 = 20.0;
        double r3394237 = /* ERROR: no posit support in C */;
        double r3394238 = r3394229 * r3394237;
        double r3394239 = r3394235 + r3394238;
        return r3394239;
}
↓
double f(double d1, double d2) {
        double r3394240 = d1;
        double r3394241 = 20.0;
        double r3394242 = 10.0;
        double r3394243 = r3394241 + r3394242;
        double r3394244 = d2;
        double r3394245 = r3394243 + r3394244;
        double r3394246 = r3394240 * r3394245;
        return r3394246;
}

Error

Bits error versus d1

Bits error versus d2

Derivation

  1. Initial program 0.3

    \[\frac{\left(\frac{\left(d1 \cdot \left(10\right)\right)}{\left(d1 \cdot d2\right)}\right)}{\left(d1 \cdot \left(20\right)\right)}\]

  2. Simplified0.3

    \[\leadsto \color{blue}{d1 \cdot \left(\frac{\left(\frac{\left(20\right)}{\left(10\right)}\right)}{d2}\right)}\]

  3. Final simplification0.3

    \[\leadsto d1 \cdot \left(\left(20 + 10\right) + d2\right)\]

Reproduce

herbie shell --seed 2019158 
(FPCore (d1 d2)
  :name "FastMath test2"
  (+.p16 (+.p16 (*.p16 d1 (real->posit16 10)) (*.p16 d1 d2)) (*.p16 d1 (real->posit16 20))))