Average Error: 0.3 → 0.3
Time: 12.8s
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 r3968462 = d1;
        double r3968463 = d2;
        double r3968464 = r3968462 * r3968463;
        double r3968465 = d3;
        double r3968466 = 5.0;
        double r3968467 = /* ERROR: no posit support in C */;
        double r3968468 = r3968465 + r3968467;
        double r3968469 = r3968468 * r3968462;
        double r3968470 = r3968464 + r3968469;
        double r3968471 = 32.0;
        double r3968472 = /* ERROR: no posit support in C */;
        double r3968473 = r3968462 * r3968472;
        double r3968474 = r3968470 + r3968473;
        return r3968474;
}
↓
double f(double d1, double d2, double d3) {
        double r3968475 = d1;
        double r3968476 = d2;
        double r3968477 = r3968475 * r3968476;
        double r3968478 = d3;
        double r3968479 = 5.0;
        double r3968480 = r3968478 + r3968479;
        double r3968481 = r3968480 * r3968475;
        double r3968482 = r3968477 + r3968481;
        double r3968483 = 32.0;
        double r3968484 = r3968475 * r3968483;
        double r3968485 = r3968482 + r3968484;
        return r3968485;
}

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 +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))))