Average Error: 0.3 → 0.3
Time: 11.5s
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 r2294544 = d1;
        double r2294545 = d2;
        double r2294546 = r2294544 * r2294545;
        double r2294547 = d3;
        double r2294548 = 5.0;
        double r2294549 = /* ERROR: no posit support in C */;
        double r2294550 = r2294547 + r2294549;
        double r2294551 = r2294550 * r2294544;
        double r2294552 = r2294546 + r2294551;
        double r2294553 = 32.0;
        double r2294554 = /* ERROR: no posit support in C */;
        double r2294555 = r2294544 * r2294554;
        double r2294556 = r2294552 + r2294555;
        return r2294556;
}
↓
double f(double d1, double d2, double d3) {
        double r2294557 = d1;
        double r2294558 = d2;
        double r2294559 = r2294557 * r2294558;
        double r2294560 = d3;
        double r2294561 = 5.0;
        double r2294562 = r2294560 + r2294561;
        double r2294563 = r2294562 * r2294557;
        double r2294564 = r2294559 + r2294563;
        double r2294565 = 32.0;
        double r2294566 = r2294557 * r2294565;
        double r2294567 = r2294564 + r2294566;
        return r2294567;
}

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 2019128 
(FPCore (d1 d2 d3)
  :name "FastMath dist3"
  (+.p16 (+.p16 (*.p16 d1 d2) (*.p16 (+.p16 d3 (real->posit16 5)) d1)) (*.p16 d1 (real->posit16 32))))