Average Error: 0.3 → 0.3
Time: 12.0s
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 r4127774 = d1;
        double r4127775 = d2;
        double r4127776 = r4127774 * r4127775;
        double r4127777 = d3;
        double r4127778 = 5.0;
        double r4127779 = /* ERROR: no posit support in C */;
        double r4127780 = r4127777 + r4127779;
        double r4127781 = r4127780 * r4127774;
        double r4127782 = r4127776 + r4127781;
        double r4127783 = 32.0;
        double r4127784 = /* ERROR: no posit support in C */;
        double r4127785 = r4127774 * r4127784;
        double r4127786 = r4127782 + r4127785;
        return r4127786;
}
↓
double f(double d1, double d2, double d3) {
        double r4127787 = d1;
        double r4127788 = d2;
        double r4127789 = r4127787 * r4127788;
        double r4127790 = d3;
        double r4127791 = 5.0;
        double r4127792 = r4127790 + r4127791;
        double r4127793 = r4127792 * r4127787;
        double r4127794 = r4127789 + r4127793;
        double r4127795 = 32.0;
        double r4127796 = r4127787 * r4127795;
        double r4127797 = r4127794 + r4127796;
        return r4127797;
}

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 2019134 +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))))