Average Error: 0.5 → 0.4
Time: 33.8s
Precision: 64
\[\left(\frac{\left(\left(d1 \cdot d2\right) - \left(d1 \cdot d3\right)\right)}{\left(d4 \cdot d1\right)}\right) - \left(d1 \cdot d1\right)\]
↓
\[d1 \cdot \left(\left(\left(d2 + d4\right) - d3\right) - d1\right)\]
\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(\left(d2 + d4\right) - d3\right) - d1\right)
double f(double d1, double d2, double d3, double d4) {
        double r4563690 = d1;
        double r4563691 = d2;
        double r4563692 = r4563690 * r4563691;
        double r4563693 = d3;
        double r4563694 = r4563690 * r4563693;
        double r4563695 = r4563692 - r4563694;
        double r4563696 = d4;
        double r4563697 = r4563696 * r4563690;
        double r4563698 = r4563695 + r4563697;
        double r4563699 = r4563690 * r4563690;
        double r4563700 = r4563698 - r4563699;
        return r4563700;
}
↓
double f(double d1, double d2, double d3, double d4) {
        double r4563701 = d1;
        double r4563702 = d2;
        double r4563703 = d4;
        double r4563704 = r4563702 + r4563703;
        double r4563705 = d3;
        double r4563706 = r4563704 - r4563705;
        double r4563707 = r4563706 - r4563701;
        double r4563708 = r4563701 * r4563707;
        return r4563708;
}

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

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

  4. Applied associate--r+0.4

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

  5. Final simplification0.4

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

Reproduce

herbie shell --seed 2019132 +o rules:numerics
(FPCore (d1 d2 d3 d4)
  :name "FastMath dist4"
  (-.p16 (+.p16 (-.p16 (*.p16 d1 d2) (*.p16 d1 d3)) (*.p16 d4 d1)) (*.p16 d1 d1)))