Average Error: 0.5 → 0.4
Time: 16.1s
Precision: 64
\[\left(\frac{\left(\left(d1 \cdot d2\right) - \left(d1 \cdot d3\right)\right)}{\left(d4 \cdot d1\right)}\right) - \left(d1 \cdot d1\right)\]
↓
\[\left(\mathsf{qma}\left(\left(\left(d1 \cdot \left(d4 - \left(d1 + d3\right)\right)\right)\right), d1, d2\right)\right)\]
\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)
↓
\left(\mathsf{qma}\left(\left(\left(d1 \cdot \left(d4 - \left(d1 + d3\right)\right)\right)\right), d1, d2\right)\right)
double f(double d1, double d2, double d3, double d4) {
        double r1306482 = d1;
        double r1306483 = d2;
        double r1306484 = r1306482 * r1306483;
        double r1306485 = d3;
        double r1306486 = r1306482 * r1306485;
        double r1306487 = r1306484 - r1306486;
        double r1306488 = d4;
        double r1306489 = r1306488 * r1306482;
        double r1306490 = r1306487 + r1306489;
        double r1306491 = r1306482 * r1306482;
        double r1306492 = r1306490 - r1306491;
        return r1306492;
}
↓
double f(double d1, double d2, double d3, double d4) {
        double r1306493 = d1;
        double r1306494 = d4;
        double r1306495 = d3;
        double r1306496 = r1306493 + r1306495;
        double r1306497 = r1306494 - r1306496;
        double r1306498 = r1306493 * r1306497;
        double r1306499 = /*Error: no posit support in C */;
        double r1306500 = d2;
        double r1306501 = /*Error: no posit support in C */;
        double r1306502 = /*Error: no posit support in C */;
        return r1306502;
}

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 distribute-lft-in0.4

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

  6. Applied introduce-quire0.4

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

  7. Applied insert-quire-fdp-add0.4

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

  8. Final simplification0.4

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

Reproduce

herbie shell --seed 2019156 
(FPCore (d1 d2 d3 d4)
  :name "FastMath dist4"
  (-.p16 (+.p16 (-.p16 (*.p16 d1 d2) (*.p16 d1 d3)) (*.p16 d4 d1)) (*.p16 d1 d1)))