Average Error: 0.3 → 0.3
Time: 8.5s
Precision: 64
\[\frac{\left(\frac{\left(d1 \cdot \left(10\right)\right)}{\left(d1 \cdot d2\right)}\right)}{\left(d1 \cdot \left(20\right)\right)}\]
↓
\[d1 \cdot \left(10 + d2\right) + d1 \cdot 20\]
\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
double f(double d1, double d2) {
        double r1853179 = d1;
        double r1853180 = 10.0;
        double r1853181 = /* ERROR: no posit support in C */;
        double r1853182 = r1853179 * r1853181;
        double r1853183 = d2;
        double r1853184 = r1853179 * r1853183;
        double r1853185 = r1853182 + r1853184;
        double r1853186 = 20.0;
        double r1853187 = /* ERROR: no posit support in C */;
        double r1853188 = r1853179 * r1853187;
        double r1853189 = r1853185 + r1853188;
        return r1853189;
}
↓
double f(double d1, double d2) {
        double r1853190 = d1;
        double r1853191 = 10.0;
        double r1853192 = d2;
        double r1853193 = r1853191 + r1853192;
        double r1853194 = r1853190 * r1853193;
        double r1853195 = 20.0;
        double r1853196 = r1853190 * r1853195;
        double r1853197 = r1853194 + r1853196;
        return r1853197;
}

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-out0.3

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

  4. Final simplification0.3

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

Reproduce

herbie shell --seed 2019128 +o rules:numerics
(FPCore (d1 d2)
  :name "FastMath test2"
  (+.p16 (+.p16 (*.p16 d1 (real->posit16 10)) (*.p16 d1 d2)) (*.p16 d1 (real->posit16 20))))