Average Error: 0.3 → 0.3
Time: 10.6s
Precision: 64
\[\frac{\left(\frac{\left(d1 \cdot d2\right)}{\left(\left(\frac{d3}{\left(5\right)}\right) \cdot d1\right)}\right)}{\left(d1 \cdot \left(32\right)\right)}\]
↓
\[\left(d1 \cdot d2 + \left(d3 + 5\right) \cdot d1\right) + d1 \cdot 32\]
\frac{\left(\frac{\left(d1 \cdot d2\right)}{\left(\left(\frac{d3}{\left(5\right)}\right) \cdot d1\right)}\right)}{\left(d1 \cdot \left(32\right)\right)}
↓
\left(d1 \cdot d2 + \left(d3 + 5\right) \cdot d1\right) + d1 \cdot 32
double f(double d1, double d2, double d3) {
        double r3553378 = d1;
        double r3553379 = d2;
        double r3553380 = r3553378 * r3553379;
        double r3553381 = d3;
        double r3553382 = 5.0;
        double r3553383 = /* ERROR: no posit support in C */;
        double r3553384 = r3553381 + r3553383;
        double r3553385 = r3553384 * r3553378;
        double r3553386 = r3553380 + r3553385;
        double r3553387 = 32.0;
        double r3553388 = /* ERROR: no posit support in C */;
        double r3553389 = r3553378 * r3553388;
        double r3553390 = r3553386 + r3553389;
        return r3553390;
}
↓
double f(double d1, double d2, double d3) {
        double r3553391 = d1;
        double r3553392 = d2;
        double r3553393 = r3553391 * r3553392;
        double r3553394 = d3;
        double r3553395 = 5.0;
        double r3553396 = r3553394 + r3553395;
        double r3553397 = r3553396 * r3553391;
        double r3553398 = r3553393 + r3553397;
        double r3553399 = 32.0;
        double r3553400 = r3553391 * r3553399;
        double r3553401 = r3553398 + r3553400;
        return r3553401;
}

Error

Bits error versus d1

Bits error versus d2

Bits error versus d3

Derivation

  1. Initial program 0.3

    \[\frac{\left(\frac{\left(d1 \cdot d2\right)}{\left(\left(\frac{d3}{\left(5\right)}\right) \cdot d1\right)}\right)}{\left(d1 \cdot \left(32\right)\right)}\]

  2. Final simplification0.3

    \[\leadsto \left(d1 \cdot d2 + \left(d3 + 5\right) \cdot d1\right) + d1 \cdot 32\]

Reproduce

herbie shell --seed 2019125 
(FPCore (d1 d2 d3)
  :name "FastMath dist3"
  (+.p16 (+.p16 (*.p16 d1 d2) (*.p16 (+.p16 d3 (real->posit16 5)) d1)) (*.p16 d1 (real->posit16 32))))