Average Error: 0.5 → 0.3
Time: 7.1s
Precision: 64
\[\frac{\left(\frac{\left(d1 \cdot \left(3\right)\right)}{\left(d1 \cdot d2\right)}\right)}{\left(d1 \cdot d3\right)}\]
↓
\[\left(\left(3 + d2\right) + d3\right) \cdot d1\]
\frac{\left(\frac{\left(d1 \cdot \left(3\right)\right)}{\left(d1 \cdot d2\right)}\right)}{\left(d1 \cdot d3\right)}
↓
\left(\left(3 + d2\right) + d3\right) \cdot d1
double f(double d1, double d2, double d3) {
        double r1554452 = d1;
        double r1554453 = 3.0;
        double r1554454 = /* ERROR: no posit support in C */;
        double r1554455 = r1554452 * r1554454;
        double r1554456 = d2;
        double r1554457 = r1554452 * r1554456;
        double r1554458 = r1554455 + r1554457;
        double r1554459 = d3;
        double r1554460 = r1554452 * r1554459;
        double r1554461 = r1554458 + r1554460;
        return r1554461;
}
↓
double f(double d1, double d2, double d3) {
        double r1554462 = 3.0;
        double r1554463 = d2;
        double r1554464 = r1554462 + r1554463;
        double r1554465 = d3;
        double r1554466 = r1554464 + r1554465;
        double r1554467 = d1;
        double r1554468 = r1554466 * r1554467;
        return r1554468;
}

Error

Bits error versus d1

Bits error versus d2

Bits error versus d3

Derivation

  1. Initial program 0.5

    \[\frac{\left(\frac{\left(d1 \cdot \left(3\right)\right)}{\left(d1 \cdot d2\right)}\right)}{\left(d1 \cdot d3\right)}\]

  2. Simplified0.3

    \[\leadsto \color{blue}{\left(\frac{\left(3\right)}{\left(\frac{d2}{d3}\right)}\right) \cdot d1}\]
  3. Using strategy rm

  4. Applied associate-+r+0.3

    \[\leadsto \color{blue}{\left(\frac{\left(\frac{\left(3\right)}{d2}\right)}{d3}\right)} \cdot d1\]

  5. Final simplification0.3

    \[\leadsto \left(\left(3 + d2\right) + d3\right) \cdot d1\]

Reproduce

herbie shell --seed 2019125 +o rules:numerics
(FPCore (d1 d2 d3)
  :name "FastMath test3"
  (+.p16 (+.p16 (*.p16 d1 (real->posit16 3)) (*.p16 d1 d2)) (*.p16 d1 d3)))