Average Error: 0.5 → 0.4
Time: 31.9s
Precision: 64
\[\left(\frac{\left(\left(d1 \cdot d2\right) - \left(d1 \cdot d3\right)\right)}{\left(d4 \cdot d1\right)}\right) - \left(d1 \cdot d1\right)\]
↓
\[d1 \cdot \left(\frac{\left(d4 - \left(\frac{d1}{d3}\right)\right)}{d2}\right)\]
\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(\frac{\left(d4 - \left(\frac{d1}{d3}\right)\right)}{d2}\right)
double f(double d1, double d2, double d3, double d4) {
        double r4186651 = d1;
        double r4186652 = d2;
        double r4186653 = r4186651 * r4186652;
        double r4186654 = d3;
        double r4186655 = r4186651 * r4186654;
        double r4186656 = r4186653 - r4186655;
        double r4186657 = d4;
        double r4186658 = r4186657 * r4186651;
        double r4186659 = r4186656 + r4186658;
        double r4186660 = r4186651 * r4186651;
        double r4186661 = r4186659 - r4186660;
        return r4186661;
}
↓
double f(double d1, double d2, double d3, double d4) {
        double r4186662 = d1;
        double r4186663 = d4;
        double r4186664 = d3;
        double r4186665 = r4186662 + r4186664;
        double r4186666 = r4186663 - r4186665;
        double r4186667 = d2;
        double r4186668 = r4186666 + r4186667;
        double r4186669 = r4186662 * r4186668;
        return r4186669;
}

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. Final simplification0.4

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

Reproduce

herbie shell --seed 2019168 
(FPCore (d1 d2 d3 d4)
  :name "FastMath dist4"
  (-.p16 (+.p16 (-.p16 (*.p16 d1 d2) (*.p16 d1 d3)) (*.p16 d4 d1)) (*.p16 d1 d1)))