FastMath test2

Average Error: 0.3 → 0.3

Time: 8.7s

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 r1023472 = d1;
        double r1023473 = 10.0;
        double r1023474 = /* ERROR: no posit support in C */;
        double r1023475 = r1023472 * r1023474;
        double r1023476 = d2;
        double r1023477 = r1023472 * r1023476;
        double r1023478 = r1023475 + r1023477;
        double r1023479 = 20.0;
        double r1023480 = /* ERROR: no posit support in C */;
        double r1023481 = r1023472 * r1023480;
        double r1023482 = r1023478 + r1023481;
        return r1023482;
}

↓

double f(double d1, double d2) {
        double r1023483 = 20.0;
        double r1023484 = 10.0;
        double r1023485 = r1023483 + r1023484;
        double r1023486 = d2;
        double r1023487 = r1023485 + r1023486;
        double r1023488 = d1;
        double r1023489 = r1023487 * r1023488;
        return r1023489;
}

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 2019107 +o rules:numerics
(FPCore (d1 d2)
  :name "FastMath test2"
  (+.p16 (+.p16 (*.p16 d1 (real->posit16 10)) (*.p16 d1 d2)) (*.p16 d1 (real->posit16 20))))