Average Error: 0.3 → 0.3
Time: 11.2s
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 r4186637 = d1;
        double r4186638 = d2;
        double r4186639 = r4186637 * r4186638;
        double r4186640 = d3;
        double r4186641 = 5.0;
        double r4186642 = /* ERROR: no posit support in C */;
        double r4186643 = r4186640 + r4186642;
        double r4186644 = r4186643 * r4186637;
        double r4186645 = r4186639 + r4186644;
        double r4186646 = 32.0;
        double r4186647 = /* ERROR: no posit support in C */;
        double r4186648 = r4186637 * r4186647;
        double r4186649 = r4186645 + r4186648;
        return r4186649;
}
↓
double f(double d1, double d2, double d3) {
        double r4186650 = d1;
        double r4186651 = d2;
        double r4186652 = r4186650 * r4186651;
        double r4186653 = d3;
        double r4186654 = 5.0;
        double r4186655 = r4186653 + r4186654;
        double r4186656 = r4186655 * r4186650;
        double r4186657 = r4186652 + r4186656;
        double r4186658 = 32.0;
        double r4186659 = r4186650 * r4186658;
        double r4186660 = r4186657 + r4186659;
        return r4186660;
}

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 2019133 
(FPCore (d1 d2 d3)
  :name "FastMath dist3"
  (+.p16 (+.p16 (*.p16 d1 d2) (*.p16 (+.p16 d3 (real->posit16 5)) d1)) (*.p16 d1 (real->posit16 32))))