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

↓

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

double f(double d1, double d2, double d3, double d4) {
        double r2497199 = d1;
        double r2497200 = d2;
        double r2497201 = r2497199 * r2497200;
        double r2497202 = d3;
        double r2497203 = r2497199 * r2497202;
        double r2497204 = r2497201 - r2497203;
        double r2497205 = d4;
        double r2497206 = r2497205 * r2497199;
        double r2497207 = r2497204 + r2497206;
        double r2497208 = r2497199 * r2497199;
        double r2497209 = r2497207 - r2497208;
        return r2497209;
}

↓

double f(double d1, double d2, double d3, double d4) {
        double r2497210 = d1;
        double r2497211 = d2;
        double r2497212 = d3;
        double r2497213 = d4;
        double r2497214 = r2497213 - r2497210;
        double r2497215 = r2497212 - r2497214;
        double r2497216 = r2497211 - r2497215;
        double r2497217 = r2497210 * r2497216;
        return r2497217;
}

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

↓

d1 \cdot \left(d2 - \left(d3 - \left(d4 - d1\right)\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
\[\leadsto \color{blue}{d1 \cdot \left(\frac{\left(d2 - d3\right)}{\left(d4 - d1\right)}\right)}\]
Using strategy rm
Applied associate-+l-0.4
\[\leadsto d1 \cdot \color{blue}{\left(d2 - \left(d3 - \left(d4 - d1\right)\right)\right)}\]
Final simplification0.4
\[\leadsto d1 \cdot \left(d2 - \left(d3 - \left(d4 - d1\right)\right)\right)\]

Reproduce

herbie shell --seed 2019102 +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)))