Average Error: 0.5 → 0.4
Time: 14.7s
Precision: 64
\[\left(\frac{\left(\left(d1 \cdot d2\right) - \left(d1 \cdot d3\right)\right)}{\left(d4 \cdot d1\right)}\right) - \left(d1 \cdot d1\right)\]
↓
\[d1 \cdot d2 + d1 \cdot \left(d4 - \left(d3 + d1\right)\right)\]
\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)
↓
d1 \cdot d2 + d1 \cdot \left(d4 - \left(d3 + d1\right)\right)
double f(double d1, double d2, double d3, double d4) {
        double r3180865 = d1;
        double r3180866 = d2;
        double r3180867 = r3180865 * r3180866;
        double r3180868 = d3;
        double r3180869 = r3180865 * r3180868;
        double r3180870 = r3180867 - r3180869;
        double r3180871 = d4;
        double r3180872 = r3180871 * r3180865;
        double r3180873 = r3180870 + r3180872;
        double r3180874 = r3180865 * r3180865;
        double r3180875 = r3180873 - r3180874;
        return r3180875;
}
↓
double f(double d1, double d2, double d3, double d4) {
        double r3180876 = d1;
        double r3180877 = d2;
        double r3180878 = r3180876 * r3180877;
        double r3180879 = d4;
        double r3180880 = d3;
        double r3180881 = r3180880 + r3180876;
        double r3180882 = r3180879 - r3180881;
        double r3180883 = r3180876 * r3180882;
        double r3180884 = r3180878 + r3180883;
        return r3180884;
}

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--l+0.4

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

  6. Applied distribute-lft-in0.4

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

  7. Final simplification0.4

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

Reproduce

herbie shell --seed 2019128 
(FPCore (d1 d2 d3 d4)
  :name "FastMath dist4"
  (-.p16 (+.p16 (-.p16 (*.p16 d1 d2) (*.p16 d1 d3)) (*.p16 d4 d1)) (*.p16 d1 d1)))