Average Error: 0.5 → 0.4
Time: 11.6s
Precision: 64
\[\left(\frac{\left(\left(d1 \cdot d2\right) - \left(d1 \cdot d3\right)\right)}{\left(d4 \cdot d1\right)}\right) - \left(d1 \cdot d1\right)\]
↓
\[d1 \cdot \left(\left(d2 - d3\right) + \left(d4 - d1\right)\right)\]
\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(\left(d2 - d3\right) + \left(d4 - d1\right)\right)
double f(double d1, double d2, double d3, double d4) {
        double r2677264 = d1;
        double r2677265 = d2;
        double r2677266 = r2677264 * r2677265;
        double r2677267 = d3;
        double r2677268 = r2677264 * r2677267;
        double r2677269 = r2677266 - r2677268;
        double r2677270 = d4;
        double r2677271 = r2677270 * r2677264;
        double r2677272 = r2677269 + r2677271;
        double r2677273 = r2677264 * r2677264;
        double r2677274 = r2677272 - r2677273;
        return r2677274;
}
↓
double f(double d1, double d2, double d3, double d4) {
        double r2677275 = d1;
        double r2677276 = d2;
        double r2677277 = d3;
        double r2677278 = r2677276 - r2677277;
        double r2677279 = d4;
        double r2677280 = r2677279 - r2677275;
        double r2677281 = r2677278 + r2677280;
        double r2677282 = r2677275 * r2677281;
        return r2677282;
}

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

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

  3. Final simplification0.4

    \[\leadsto d1 \cdot \left(\left(d2 - d3\right) + \left(d4 - d1\right)\right)\]

Reproduce

herbie shell --seed 2019125 
(FPCore (d1 d2 d3 d4)
  :name "FastMath dist4"
  (-.p16 (+.p16 (-.p16 (*.p16 d1 d2) (*.p16 d1 d3)) (*.p16 d4 d1)) (*.p16 d1 d1)))