Average Error: 0.5 → 0.4
Time: 22.6s
Precision: 64
\[\left(\frac{\left(\left(d1 \cdot d2\right) - \left(d1 \cdot d3\right)\right)}{\left(d4 \cdot d1\right)}\right) - \left(d1 \cdot d1\right)\]
↓
\[\left(\left(\left(\left(d2 + d4\right) - \left(d3 + d1\right)\right) \cdot d1\right)\right)\]
\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)
↓
\left(\left(\left(\left(d2 + d4\right) - \left(d3 + d1\right)\right) \cdot d1\right)\right)
double f(double d1, double d2, double d3, double d4) {
        double r1406417 = d1;
        double r1406418 = d2;
        double r1406419 = r1406417 * r1406418;
        double r1406420 = d3;
        double r1406421 = r1406417 * r1406420;
        double r1406422 = r1406419 - r1406421;
        double r1406423 = d4;
        double r1406424 = r1406423 * r1406417;
        double r1406425 = r1406422 + r1406424;
        double r1406426 = r1406417 * r1406417;
        double r1406427 = r1406425 - r1406426;
        return r1406427;
}
↓
double f(double d1, double d2, double d3, double d4) {
        double r1406428 = d2;
        double r1406429 = d4;
        double r1406430 = r1406428 + r1406429;
        double r1406431 = d3;
        double r1406432 = d1;
        double r1406433 = r1406431 + r1406432;
        double r1406434 = r1406430 - r1406433;
        double r1406435 = r1406434 * r1406432;
        double r1406436 = /*Error: no posit support in C */;
        double r1406437 = /*Error: no posit support in C */;
        return r1406437;
}

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

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

  7. Simplified0.4

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

  8. Final simplification0.4

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

Reproduce

herbie shell --seed 2019152 
(FPCore (d1 d2 d3 d4)
  :name "FastMath dist4"
  (-.p16 (+.p16 (-.p16 (*.p16 d1 d2) (*.p16 d1 d3)) (*.p16 d4 d1)) (*.p16 d1 d1)))