Average Error: 0.3 → 0.3
Time: 8.0s
Precision: 64
\[\frac{\left(\frac{\left(d1 \cdot d2\right)}{\left(\left(\frac{d3}{\left(5\right)}\right) \cdot d1\right)}\right)}{\left(d1 \cdot \left(32\right)\right)}\]
↓
\[\left(d1 \cdot d2 + \left(d3 + 5\right) \cdot d1\right) + d1 \cdot 32\]
\frac{\left(\frac{\left(d1 \cdot d2\right)}{\left(\left(\frac{d3}{\left(5\right)}\right) \cdot d1\right)}\right)}{\left(d1 \cdot \left(32\right)\right)}
↓
\left(d1 \cdot d2 + \left(d3 + 5\right) \cdot d1\right) + d1 \cdot 32
double f(double d1, double d2, double d3) {
        double r2700480 = d1;
        double r2700481 = d2;
        double r2700482 = r2700480 * r2700481;
        double r2700483 = d3;
        double r2700484 = 5.0;
        double r2700485 = /* ERROR: no posit support in C */;
        double r2700486 = r2700483 + r2700485;
        double r2700487 = r2700486 * r2700480;
        double r2700488 = r2700482 + r2700487;
        double r2700489 = 32.0;
        double r2700490 = /* ERROR: no posit support in C */;
        double r2700491 = r2700480 * r2700490;
        double r2700492 = r2700488 + r2700491;
        return r2700492;
}
↓
double f(double d1, double d2, double d3) {
        double r2700493 = d1;
        double r2700494 = d2;
        double r2700495 = r2700493 * r2700494;
        double r2700496 = d3;
        double r2700497 = 5.0;
        double r2700498 = r2700496 + r2700497;
        double r2700499 = r2700498 * r2700493;
        double r2700500 = r2700495 + r2700499;
        double r2700501 = 32.0;
        double r2700502 = r2700493 * r2700501;
        double r2700503 = r2700500 + r2700502;
        return r2700503;
}

Error

Bits error versus d1

Bits error versus d2

Bits error versus d3

Derivation

  1. Initial program 0.3

    \[\frac{\left(\frac{\left(d1 \cdot d2\right)}{\left(\left(\frac{d3}{\left(5\right)}\right) \cdot d1\right)}\right)}{\left(d1 \cdot \left(32\right)\right)}\]

  2. Final simplification0.3

    \[\leadsto \left(d1 \cdot d2 + \left(d3 + 5\right) \cdot d1\right) + d1 \cdot 32\]

Reproduce

herbie shell --seed 2019121 +o rules:numerics
(FPCore (d1 d2 d3)
  :name "FastMath dist3"
  (+.p16 (+.p16 (*.p16 d1 d2) (*.p16 (+.p16 d3 (real->posit16 5)) d1)) (*.p16 d1 (real->posit16 32))))