Average Error: 0.3 → 0.3
Time: 10.8s
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 r1594769 = d1;
        double r1594770 = d2;
        double r1594771 = r1594769 * r1594770;
        double r1594772 = d3;
        double r1594773 = 5.0;
        double r1594774 = /* ERROR: no posit support in C */;
        double r1594775 = r1594772 + r1594774;
        double r1594776 = r1594775 * r1594769;
        double r1594777 = r1594771 + r1594776;
        double r1594778 = 32.0;
        double r1594779 = /* ERROR: no posit support in C */;
        double r1594780 = r1594769 * r1594779;
        double r1594781 = r1594777 + r1594780;
        return r1594781;
}
↓
double f(double d1, double d2, double d3) {
        double r1594782 = d1;
        double r1594783 = d2;
        double r1594784 = r1594782 * r1594783;
        double r1594785 = d3;
        double r1594786 = 5.0;
        double r1594787 = r1594785 + r1594786;
        double r1594788 = r1594787 * r1594782;
        double r1594789 = r1594784 + r1594788;
        double r1594790 = 32.0;
        double r1594791 = r1594782 * r1594790;
        double r1594792 = r1594789 + r1594791;
        return r1594792;
}

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 +o rules:numerics
(FPCore (d1 d2 d3)
  :name "FastMath dist3"
  (+.p16 (+.p16 (*.p16 d1 d2) (*.p16 (+.p16 d3 (real->posit16 5)) d1)) (*.p16 d1 (real->posit16 32))))