Average Error: 0.5 → 0.4
Time: 9.8s
Precision: 64
\[\left(\frac{\left(\left(d1 \cdot d2\right) - \left(d1 \cdot d3\right)\right)}{\left(d4 \cdot d1\right)}\right) - \left(d1 \cdot d1\right)\]
↓
\[d1 \cdot \left(d2 + \left(\left(-d3\right) + \left(d4 - d1\right)\right)\right)\]
\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\right) + \left(d4 - d1\right)\right)\right)
double f(double d1, double d2, double d3, double d4) {
        double r2543320 = d1;
        double r2543321 = d2;
        double r2543322 = r2543320 * r2543321;
        double r2543323 = d3;
        double r2543324 = r2543320 * r2543323;
        double r2543325 = r2543322 - r2543324;
        double r2543326 = d4;
        double r2543327 = r2543326 * r2543320;
        double r2543328 = r2543325 + r2543327;
        double r2543329 = r2543320 * r2543320;
        double r2543330 = r2543328 - r2543329;
        return r2543330;
}
↓
double f(double d1, double d2, double d3, double d4) {
        double r2543331 = d1;
        double r2543332 = d2;
        double r2543333 = d3;
        double r2543334 = -r2543333;
        double r2543335 = d4;
        double r2543336 = r2543335 - r2543331;
        double r2543337 = r2543334 + r2543336;
        double r2543338 = r2543332 + r2543337;
        double r2543339 = r2543331 * r2543338;
        return r2543339;
}

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 sub-neg0.4

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

  5. Applied associate-+l+0.4

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

  6. Final simplification0.4

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

Reproduce

herbie shell --seed 2019119 
(FPCore (d1 d2 d3 d4)
  :name "FastMath dist4"
  (-.p16 (+.p16 (-.p16 (*.p16 d1 d2) (*.p16 d1 d3)) (*.p16 d4 d1)) (*.p16 d1 d1)))