Average Error: 0.5 → 0.3
Time: 8.5s
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 r1490397 = d1;
        double r1490398 = 3.0;
        double r1490399 = /* ERROR: no posit support in C */;
        double r1490400 = r1490397 * r1490399;
        double r1490401 = d2;
        double r1490402 = r1490397 * r1490401;
        double r1490403 = r1490400 + r1490402;
        double r1490404 = d3;
        double r1490405 = r1490397 * r1490404;
        double r1490406 = r1490403 + r1490405;
        return r1490406;
}
↓
double f(double d1, double d2, double d3) {
        double r1490407 = 3.0;
        double r1490408 = d2;
        double r1490409 = r1490407 + r1490408;
        double r1490410 = d3;
        double r1490411 = r1490409 + r1490410;
        double r1490412 = d1;
        double r1490413 = r1490411 * r1490412;
        return r1490413;
}

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 2019124 
(FPCore (d1 d2 d3)
  :name "FastMath test3"
  (+.p16 (+.p16 (*.p16 d1 (real->posit16 3)) (*.p16 d1 d2)) (*.p16 d1 d3)))