Average Error: 0.5 → 0.4
Time: 36.7s
Precision: 64
\[\left(\frac{\left(\left(d1 \cdot d2\right) - \left(d1 \cdot d3\right)\right)}{\left(d4 \cdot d1\right)}\right) - \left(d1 \cdot d1\right)\]
↓
\[\left(\left(d1 \cdot \left(\left(d4 + d2\right) - \left(d3 + d1\right)\right)\right)\right)\]
\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)
↓
\left(\left(d1 \cdot \left(\left(d4 + d2\right) - \left(d3 + d1\right)\right)\right)\right)
double f(double d1, double d2, double d3, double d4) {
        double r6512478 = d1;
        double r6512479 = d2;
        double r6512480 = r6512478 * r6512479;
        double r6512481 = d3;
        double r6512482 = r6512478 * r6512481;
        double r6512483 = r6512480 - r6512482;
        double r6512484 = d4;
        double r6512485 = r6512484 * r6512478;
        double r6512486 = r6512483 + r6512485;
        double r6512487 = r6512478 * r6512478;
        double r6512488 = r6512486 - r6512487;
        return r6512488;
}
↓
double f(double d1, double d2, double d3, double d4) {
        double r6512489 = d1;
        double r6512490 = d4;
        double r6512491 = d2;
        double r6512492 = r6512490 + r6512491;
        double r6512493 = d3;
        double r6512494 = r6512493 + r6512489;
        double r6512495 = r6512492 - r6512494;
        double r6512496 = r6512489 * r6512495;
        double r6512497 = /*Error: no posit support in C */;
        double r6512498 = /*Error: no posit support in C */;
        return r6512498;
}

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 sub-neg0.4

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

  5. Applied associate-+l+0.4

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

  6. Simplified0.4

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

  8. Applied associate-+r-0.4

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

  10. Applied introduce-quire0.4

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

  11. Final simplification0.4

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

Reproduce

herbie shell --seed 2019162 
(FPCore (d1 d2 d3 d4)
  :name "FastMath dist4"
  (-.p16 (+.p16 (-.p16 (*.p16 d1 d2) (*.p16 d1 d3)) (*.p16 d4 d1)) (*.p16 d1 d1)))