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

↓

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

double f(double d1, double d2, double d3, double d4) {
        double r2027063 = d1;
        double r2027064 = d2;
        double r2027065 = r2027063 * r2027064;
        double r2027066 = d3;
        double r2027067 = r2027063 * r2027066;
        double r2027068 = r2027065 - r2027067;
        double r2027069 = d4;
        double r2027070 = r2027069 * r2027063;
        double r2027071 = r2027068 + r2027070;
        double r2027072 = r2027063 * r2027063;
        double r2027073 = r2027071 - r2027072;
        return r2027073;
}

↓

double f(double d1, double d2, double d3, double d4) {
        double r2027074 = d1;
        double r2027075 = d2;
        double r2027076 = d3;
        double r2027077 = r2027075 - r2027076;
        double r2027078 = d4;
        double r2027079 = r2027078 - r2027074;
        double r2027080 = r2027077 + r2027079;
        double r2027081 = r2027074 * r2027080;
        return r2027081;
}

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

↓

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

Error

The X axis uses an exponential scale — Bits error versus `d1`

Derivation

Initial program 0.5
\[\left(\frac{\left(\left(d1 \cdot d2\right) - \left(d1 \cdot d3\right)\right)}{\left(d4 \cdot d1\right)}\right) - \left(d1 \cdot d1\right)\]
Simplified0.4
\[\leadsto \color{blue}{d1 \cdot \left(\frac{\left(d2 - d3\right)}{\left(d4 - d1\right)}\right)}\]
Final simplification0.4
\[\leadsto d1 \cdot \left(\left(d2 - d3\right) + \left(d4 - d1\right)\right)\]

Reproduce

herbie shell --seed 2019101 +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)))