Average Error: 0.5 → 0.4
Time: 33.1s
Precision: 64
\[\left(\frac{\left(\left(d1 \cdot d2\right) - \left(d1 \cdot d3\right)\right)}{\left(d4 \cdot d1\right)}\right) - \left(d1 \cdot d1\right)\]
↓
\[d1 \cdot \left(\left(d4 - d3\right) - \left(d1 - d2\right)\right)\]
\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 \left(\left(d4 - d3\right) - \left(d1 - d2\right)\right)
double f(double d1, double d2, double d3, double d4) {
        double r3024795 = d1;
        double r3024796 = d2;
        double r3024797 = r3024795 * r3024796;
        double r3024798 = d3;
        double r3024799 = r3024795 * r3024798;
        double r3024800 = r3024797 - r3024799;
        double r3024801 = d4;
        double r3024802 = r3024801 * r3024795;
        double r3024803 = r3024800 + r3024802;
        double r3024804 = r3024795 * r3024795;
        double r3024805 = r3024803 - r3024804;
        return r3024805;
}
↓
double f(double d1, double d2, double d3, double d4) {
        double r3024806 = d1;
        double r3024807 = d4;
        double r3024808 = d3;
        double r3024809 = r3024807 - r3024808;
        double r3024810 = d2;
        double r3024811 = r3024806 - r3024810;
        double r3024812 = r3024809 - r3024811;
        double r3024813 = r3024806 * r3024812;
        return r3024813;
}

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

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

  4. Applied +-commutative0.4

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

  5. Applied associate--r+0.4

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

  6. Applied associate-+l-0.4

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

  7. Final simplification0.4

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

Reproduce

herbie shell --seed 2019158 
(FPCore (d1 d2 d3 d4)
  :name "FastMath dist4"
  (-.p16 (+.p16 (-.p16 (*.p16 d1 d2) (*.p16 d1 d3)) (*.p16 d4 d1)) (*.p16 d1 d1)))