Average Error: 0.3 → 0.3
Time: 8.1s
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 r2481164 = d1;
        double r2481165 = d2;
        double r2481166 = r2481164 * r2481165;
        double r2481167 = d3;
        double r2481168 = 5.0;
        double r2481169 = /* ERROR: no posit support in C */;
        double r2481170 = r2481167 + r2481169;
        double r2481171 = r2481170 * r2481164;
        double r2481172 = r2481166 + r2481171;
        double r2481173 = 32.0;
        double r2481174 = /* ERROR: no posit support in C */;
        double r2481175 = r2481164 * r2481174;
        double r2481176 = r2481172 + r2481175;
        return r2481176;
}
↓
double f(double d1, double d2, double d3) {
        double r2481177 = d1;
        double r2481178 = d2;
        double r2481179 = r2481177 * r2481178;
        double r2481180 = d3;
        double r2481181 = 5.0;
        double r2481182 = r2481180 + r2481181;
        double r2481183 = r2481182 * r2481177;
        double r2481184 = r2481179 + r2481183;
        double r2481185 = 32.0;
        double r2481186 = r2481177 * r2481185;
        double r2481187 = r2481184 + r2481186;
        return r2481187;
}

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 2019121 
(FPCore (d1 d2 d3)
  :name "FastMath dist3"
  (+.p16 (+.p16 (*.p16 d1 d2) (*.p16 (+.p16 d3 (real->posit16 5)) d1)) (*.p16 d1 (real->posit16 32))))