Average Error: 0.3 → 0.1
Time: 28.1s
Precision: 64
\[\frac{\left(\frac{\left(d1 \cdot d2\right)}{\left(\left(\frac{d3}{\left(5\right)}\right) \cdot d1\right)}\right)}{\left(d1 \cdot \left(32\right)\right)}\]
↓
\[\left(\mathsf{qma}\left(\left(\mathsf{qma}\left(\left(\left(d1 \cdot d2\right)\right), \left(\frac{d3}{\left(5\right)}\right), d1\right)\right), d1, \left(32\right)\right)\right)\]
\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(\mathsf{qma}\left(\left(\mathsf{qma}\left(\left(\left(d1 \cdot d2\right)\right), \left(\frac{d3}{\left(5\right)}\right), d1\right)\right), d1, \left(32\right)\right)\right)
double f(double d1, double d2, double d3) {
        double r3657789 = d1;
        double r3657790 = d2;
        double r3657791 = r3657789 * r3657790;
        double r3657792 = d3;
        double r3657793 = 5.0;
        double r3657794 = /* ERROR: no posit support in C */;
        double r3657795 = r3657792 + r3657794;
        double r3657796 = r3657795 * r3657789;
        double r3657797 = r3657791 + r3657796;
        double r3657798 = 32.0;
        double r3657799 = /* ERROR: no posit support in C */;
        double r3657800 = r3657789 * r3657799;
        double r3657801 = r3657797 + r3657800;
        return r3657801;
}
↓
double f(double d1, double d2, double d3) {
        double r3657802 = d1;
        double r3657803 = d2;
        double r3657804 = r3657802 * r3657803;
        double r3657805 = /*Error: no posit support in C */;
        double r3657806 = d3;
        double r3657807 = 5.0;
        double r3657808 = /* ERROR: no posit support in C */;
        double r3657809 = r3657806 + r3657808;
        double r3657810 = /*Error: no posit support in C */;
        double r3657811 = 32.0;
        double r3657812 = /* ERROR: no posit support in C */;
        double r3657813 = /*Error: no posit support in C */;
        double r3657814 = /*Error: no posit support in C */;
        return r3657814;
}

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. Using strategy rm

  3. Applied introduce-quire0.3

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

  4. Applied insert-quire-fdp-add0.3

    \[\leadsto \frac{\color{blue}{\left(\left(\mathsf{qma}\left(\left(\left(d1 \cdot d2\right)\right), \left(\frac{d3}{\left(5\right)}\right), d1\right)\right)\right)}}{\left(d1 \cdot \left(32\right)\right)}\]

  5. Applied insert-quire-fdp-add0.1

    \[\leadsto \color{blue}{\left(\mathsf{qma}\left(\left(\mathsf{qma}\left(\left(\left(d1 \cdot d2\right)\right), \left(\frac{d3}{\left(5\right)}\right), d1\right)\right), d1, \left(32\right)\right)\right)}\]

  6. Final simplification0.1

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

Reproduce

herbie shell --seed 2019163 +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))))