Average Error: 0.5 → 0.4
Time: 11.5s
Precision: 64
\[\left(\frac{\left(\left(d1 \cdot d2\right) - \left(d1 \cdot d3\right)\right)}{\left(d4 \cdot d1\right)}\right) - \left(d1 \cdot d1\right)\]
↓
\[d1 \cdot \left(d2 - \left(\left(d3 - d4\right) + d1\right)\right)\]
\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(d2 - \left(\left(d3 - d4\right) + d1\right)\right)
double f(double d1, double d2, double d3, double d4) {
        double r2282199 = d1;
        double r2282200 = d2;
        double r2282201 = r2282199 * r2282200;
        double r2282202 = d3;
        double r2282203 = r2282199 * r2282202;
        double r2282204 = r2282201 - r2282203;
        double r2282205 = d4;
        double r2282206 = r2282205 * r2282199;
        double r2282207 = r2282204 + r2282206;
        double r2282208 = r2282199 * r2282199;
        double r2282209 = r2282207 - r2282208;
        return r2282209;
}
↓
double f(double d1, double d2, double d3, double d4) {
        double r2282210 = d1;
        double r2282211 = d2;
        double r2282212 = d3;
        double r2282213 = d4;
        double r2282214 = r2282212 - r2282213;
        double r2282215 = r2282214 + r2282210;
        double r2282216 = r2282211 - r2282215;
        double r2282217 = r2282210 * r2282216;
        return r2282217;
}

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. Using strategy rm

  4. Applied associate-+l-0.4

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

  6. Applied associate--r-0.4

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

  7. Final simplification0.4

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

Reproduce

herbie shell --seed 2019121 
(FPCore (d1 d2 d3 d4)
  :name "FastMath dist4"
  (-.p16 (+.p16 (-.p16 (*.p16 d1 d2) (*.p16 d1 d3)) (*.p16 d4 d1)) (*.p16 d1 d1)))