FastMath test2

Average Error: 0.3 → 0.3

Time: 7.3s

Precision: 64

Math

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

↓

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

C

double f(double d1, double d2) {
        double r1044091 = d1;
        double r1044092 = 10.0;
        double r1044093 = /* ERROR: no posit support in C */;
        double r1044094 = r1044091 * r1044093;
        double r1044095 = d2;
        double r1044096 = r1044091 * r1044095;
        double r1044097 = r1044094 + r1044096;
        double r1044098 = 20.0;
        double r1044099 = /* ERROR: no posit support in C */;
        double r1044100 = r1044091 * r1044099;
        double r1044101 = r1044097 + r1044100;
        return r1044101;
}

↓

double f(double d1, double d2) {
        double r1044102 = 20.0;
        double r1044103 = 10.0;
        double r1044104 = r1044102 + r1044103;
        double r1044105 = d2;
        double r1044106 = r1044104 + r1044105;
        double r1044107 = d1;
        double r1044108 = r1044106 * r1044107;
        return r1044108;
}

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. Simplified 0.3

   \[\leadsto \color{blue}{\left(\frac{\left(20\right)}{\left(\frac{\left(10\right)}{d2}\right)}\right) \cdot d1}\]
3. Using strategy rm

4. Applied associate-+r+ 0.3

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

5. Final simplification 0.3

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

Reproduce

herbie shell --seed 2019124 +o rules:numerics
(FPCore (d1 d2)
  :name "FastMath test2"
  (+.p16 (+.p16 (*.p16 d1 (real->posit16 10)) (*.p16 d1 d2)) (*.p16 d1 (real->posit16 20))))