Average Error: 0.3 → 0.3
Time: 10.3s
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 r2481660 = d1;
        double r2481661 = d2;
        double r2481662 = r2481660 * r2481661;
        double r2481663 = d3;
        double r2481664 = 5.0;
        double r2481665 = /* ERROR: no posit support in C */;
        double r2481666 = r2481663 + r2481665;
        double r2481667 = r2481666 * r2481660;
        double r2481668 = r2481662 + r2481667;
        double r2481669 = 32.0;
        double r2481670 = /* ERROR: no posit support in C */;
        double r2481671 = r2481660 * r2481670;
        double r2481672 = r2481668 + r2481671;
        return r2481672;
}
↓
double f(double d1, double d2, double d3) {
        double r2481673 = d1;
        double r2481674 = d2;
        double r2481675 = r2481673 * r2481674;
        double r2481676 = d3;
        double r2481677 = 5.0;
        double r2481678 = r2481676 + r2481677;
        double r2481679 = r2481678 * r2481673;
        double r2481680 = r2481675 + r2481679;
        double r2481681 = 32.0;
        double r2481682 = r2481673 * r2481681;
        double r2481683 = r2481680 + r2481682;
        return r2481683;
}

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 2019119 
(FPCore (d1 d2 d3)
  :name "FastMath dist3"
  (+.p16 (+.p16 (*.p16 d1 d2) (*.p16 (+.p16 d3 (real->posit16 5)) d1)) (*.p16 d1 (real->posit16 32))))