Average Error: 0.3 → 0.3
Time: 10.7s
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 r1429576 = d1;
        double r1429577 = d2;
        double r1429578 = r1429576 * r1429577;
        double r1429579 = d3;
        double r1429580 = 5.0;
        double r1429581 = /* ERROR: no posit support in C */;
        double r1429582 = r1429579 + r1429581;
        double r1429583 = r1429582 * r1429576;
        double r1429584 = r1429578 + r1429583;
        double r1429585 = 32.0;
        double r1429586 = /* ERROR: no posit support in C */;
        double r1429587 = r1429576 * r1429586;
        double r1429588 = r1429584 + r1429587;
        return r1429588;
}
↓
double f(double d1, double d2, double d3) {
        double r1429589 = d1;
        double r1429590 = d2;
        double r1429591 = r1429589 * r1429590;
        double r1429592 = d3;
        double r1429593 = 5.0;
        double r1429594 = r1429592 + r1429593;
        double r1429595 = r1429594 * r1429589;
        double r1429596 = r1429591 + r1429595;
        double r1429597 = 32.0;
        double r1429598 = r1429589 * r1429597;
        double r1429599 = r1429596 + r1429598;
        return r1429599;
}

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 2019112 +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))))