Average Error: 0.5 → 0.3
Time: 1.8m
Precision: 64
\[\left(\frac{\left(\left(d1 \cdot d2\right) - \left(d1 \cdot d3\right)\right)}{\left(d4 \cdot d1\right)}\right) - \left(d1 \cdot d1\right)\]
↓
\[d1 \cdot \left(\mathsf{qma}\left(\left(\mathsf{qms}\left(\left(\left(d4 - d1\right)\right), d3, 1.0\right)\right), d2, 1.0\right)\right)\]
\left(\frac{\left(\left(d1 \cdot d2\right) - \left(d1 \cdot d3\right)\right)}{\left(d4 \cdot d1\right)}\right) - \left(d1 \cdot d1\right)
↓
d1 \cdot \left(\mathsf{qma}\left(\left(\mathsf{qms}\left(\left(\left(d4 - d1\right)\right), d3, 1.0\right)\right), d2, 1.0\right)\right)
double f(double d1, double d2, double d3, double d4) {
        double r1541138 = d1;
        double r1541139 = d2;
        double r1541140 = r1541138 * r1541139;
        double r1541141 = d3;
        double r1541142 = r1541138 * r1541141;
        double r1541143 = r1541140 - r1541142;
        double r1541144 = d4;
        double r1541145 = r1541144 * r1541138;
        double r1541146 = r1541143 + r1541145;
        double r1541147 = r1541138 * r1541138;
        double r1541148 = r1541146 - r1541147;
        return r1541148;
}
↓
double f(double d1, double d2, double d3, double d4) {
        double r1541149 = d1;
        double r1541150 = d4;
        double r1541151 = r1541150 - r1541149;
        double r1541152 = /*Error: no posit support in C */;
        double r1541153 = d3;
        double r1541154 = 1.0;
        double r1541155 = /*Error: no posit support in C */;
        double r1541156 = d2;
        double r1541157 = /*Error: no posit support in C */;
        double r1541158 = /*Error: no posit support in C */;
        double r1541159 = r1541149 * r1541158;
        return r1541159;
}

Error

Bits error versus d1

Bits error versus d2

Bits error versus d3

Bits error versus d4

Derivation

  1. Initial program 0.5

    \[\left(\frac{\left(\left(d1 \cdot d2\right) - \left(d1 \cdot d3\right)\right)}{\left(d4 \cdot d1\right)}\right) - \left(d1 \cdot d1\right)\]

  2. Simplified0.4

    \[\leadsto \color{blue}{d1 \cdot \left(\frac{\left(d4 - \left(\frac{d1}{d3}\right)\right)}{d2}\right)}\]
  3. Using strategy rm

  4. Applied associate--r+0.4

    \[\leadsto d1 \cdot \left(\frac{\color{blue}{\left(\left(d4 - d1\right) - d3\right)}}{d2}\right)\]
  5. Using strategy rm

  6. Applied introduce-quire0.4

    \[\leadsto d1 \cdot \left(\frac{\left(\color{blue}{\left(\left(\left(d4 - d1\right)\right)\right)} - d3\right)}{d2}\right)\]

  7. Applied insert-quire-sub0.4

    \[\leadsto d1 \cdot \left(\frac{\color{blue}{\left(\left(\mathsf{qms}\left(\left(\left(d4 - d1\right)\right), d3, \left(1.0\right)\right)\right)\right)}}{d2}\right)\]

  8. Applied insert-quire-add0.3

    \[\leadsto d1 \cdot \color{blue}{\left(\left(\mathsf{qma}\left(\left(\mathsf{qms}\left(\left(\left(d4 - d1\right)\right), d3, \left(1.0\right)\right)\right), d2, \left(1.0\right)\right)\right)\right)}\]

  9. Final simplification0.3

    \[\leadsto d1 \cdot \left(\mathsf{qma}\left(\left(\mathsf{qms}\left(\left(\left(d4 - d1\right)\right), d3, 1.0\right)\right), d2, 1.0\right)\right)\]

Reproduce

herbie shell --seed 2019155 
(FPCore (d1 d2 d3 d4)
  :name "FastMath dist4"
  (-.p16 (+.p16 (-.p16 (*.p16 d1 d2) (*.p16 d1 d3)) (*.p16 d4 d1)) (*.p16 d1 d1)))