Average Error: 0.5 → 0.4
Time: 27.2s
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 r7954728 = d1;
        double r7954729 = d2;
        double r7954730 = r7954728 * r7954729;
        double r7954731 = d3;
        double r7954732 = r7954728 * r7954731;
        double r7954733 = r7954730 - r7954732;
        double r7954734 = d4;
        double r7954735 = r7954734 * r7954728;
        double r7954736 = r7954733 + r7954735;
        double r7954737 = r7954728 * r7954728;
        double r7954738 = r7954736 - r7954737;
        return r7954738;
}
↓
double f(double d1, double d2, double d3, double d4) {
        double r7954739 = d1;
        double r7954740 = d2;
        double r7954741 = d4;
        double r7954742 = r7954740 + r7954741;
        double r7954743 = d3;
        double r7954744 = r7954742 - r7954743;
        double r7954745 = r7954744 - r7954739;
        double r7954746 = r7954739 * r7954745;
        return r7954746;
}

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 2019133 
(FPCore (d1 d2 d3 d4)
  :name "FastMath dist4"
  (-.p16 (+.p16 (-.p16 (*.p16 d1 d2) (*.p16 d1 d3)) (*.p16 d4 d1)) (*.p16 d1 d1)))