Average Error: 0.5 → 0.3
Time: 57.4s
Precision: 64
\[\left(\frac{\left(\left(d1 \cdot d2\right) - \left(d1 \cdot d3\right)\right)}{\left(d4 \cdot d1\right)}\right) - \left(d1 \cdot d1\right)\]
↓
\[d1 \cdot \left(\mathsf{qma}\left(\left(\mathsf{qms}\left(\left(\left(d4 - d1\right)\right), d3, 1.0\right)\right), d2, 1.0\right)\right)\]
\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(\mathsf{qma}\left(\left(\mathsf{qms}\left(\left(\left(d4 - d1\right)\right), d3, 1.0\right)\right), d2, 1.0\right)\right)
double f(double d1, double d2, double d3, double d4) {
        double r3217569 = d1;
        double r3217570 = d2;
        double r3217571 = r3217569 * r3217570;
        double r3217572 = d3;
        double r3217573 = r3217569 * r3217572;
        double r3217574 = r3217571 - r3217573;
        double r3217575 = d4;
        double r3217576 = r3217575 * r3217569;
        double r3217577 = r3217574 + r3217576;
        double r3217578 = r3217569 * r3217569;
        double r3217579 = r3217577 - r3217578;
        return r3217579;
}
↓
double f(double d1, double d2, double d3, double d4) {
        double r3217580 = d1;
        double r3217581 = d4;
        double r3217582 = r3217581 - r3217580;
        double r3217583 = /*Error: no posit support in C */;
        double r3217584 = d3;
        double r3217585 = 1.0;
        double r3217586 = /*Error: no posit support in C */;
        double r3217587 = d2;
        double r3217588 = /*Error: no posit support in C */;
        double r3217589 = /*Error: no posit support in C */;
        double r3217590 = r3217580 * r3217589;
        return r3217590;
}

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 associate--r+0.4

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

  6. Applied introduce-quire0.4

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

  7. Applied insert-quire-sub0.4

    \[\leadsto d1 \cdot \left(\frac{\color{blue}{\left(\left(\mathsf{qms}\left(\left(\left(d4 - d1\right)\right), d3, \left(1.0\right)\right)\right)\right)}}{d2}\right)\]

  8. Applied insert-quire-add0.3

    \[\leadsto d1 \cdot \color{blue}{\left(\left(\mathsf{qma}\left(\left(\mathsf{qms}\left(\left(\left(d4 - d1\right)\right), d3, \left(1.0\right)\right)\right), d2, \left(1.0\right)\right)\right)\right)}\]

  9. Final simplification0.3

    \[\leadsto d1 \cdot \left(\mathsf{qma}\left(\left(\mathsf{qms}\left(\left(\left(d4 - d1\right)\right), d3, 1.0\right)\right), d2, 1.0\right)\right)\]

Reproduce

herbie shell --seed 2019165 
(FPCore (d1 d2 d3 d4)
  :name "FastMath dist4"
  (-.p16 (+.p16 (-.p16 (*.p16 d1 d2) (*.p16 d1 d3)) (*.p16 d4 d1)) (*.p16 d1 d1)))