FastMath test2

Average Error: 0.3 → 0.3

Time: 9.1s

Precision: 64

Math

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

↓

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

C

double f(double d1, double d2) {
        double r906974 = d1;
        double r906975 = 10.0;
        double r906976 = /* ERROR: no posit support in C */;
        double r906977 = r906974 * r906976;
        double r906978 = d2;
        double r906979 = r906974 * r906978;
        double r906980 = r906977 + r906979;
        double r906981 = 20.0;
        double r906982 = /* ERROR: no posit support in C */;
        double r906983 = r906974 * r906982;
        double r906984 = r906980 + r906983;
        return r906984;
}

↓

double f(double d1, double d2) {
        double r906985 = d1;
        double r906986 = 10.0;
        double r906987 = d2;
        double r906988 = r906986 + r906987;
        double r906989 = r906985 * r906988;
        double r906990 = 20.0;
        double r906991 = r906985 * r906990;
        double r906992 = r906989 + r906991;
        return r906992;
}

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. Using strategy rm

3. Applied distribute-lft-out 0.3

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

4. Final simplification 0.3

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

Reproduce

herbie shell --seed 2019119 
(FPCore (d1 d2)
  :name "FastMath test2"
  (+.p16 (+.p16 (*.p16 d1 (real->posit16 10)) (*.p16 d1 d2)) (*.p16 d1 (real->posit16 20))))