Average Error: 0.3 → 0.1
Time: 23.3s
Precision: 64
\[\frac{\left(\frac{\left(d1 \cdot \left(10\right)\right)}{\left(d1 \cdot d2\right)}\right)}{\left(d1 \cdot \left(20\right)\right)}\]
↓
\[\left(\mathsf{qma}\left(\left(\mathsf{qma}\left(\left(\left(d1 \cdot \left(10\right)\right)\right), d1, d2\right)\right), d1, \left(20\right)\right)\right)\]
\frac{\left(\frac{\left(d1 \cdot \left(10\right)\right)}{\left(d1 \cdot d2\right)}\right)}{\left(d1 \cdot \left(20\right)\right)}
↓
\left(\mathsf{qma}\left(\left(\mathsf{qma}\left(\left(\left(d1 \cdot \left(10\right)\right)\right), d1, d2\right)\right), d1, \left(20\right)\right)\right)
double f(double d1, double d2) {
        double r3403123 = d1;
        double r3403124 = 10.0;
        double r3403125 = /* ERROR: no posit support in C */;
        double r3403126 = r3403123 * r3403125;
        double r3403127 = d2;
        double r3403128 = r3403123 * r3403127;
        double r3403129 = r3403126 + r3403128;
        double r3403130 = 20.0;
        double r3403131 = /* ERROR: no posit support in C */;
        double r3403132 = r3403123 * r3403131;
        double r3403133 = r3403129 + r3403132;
        return r3403133;
}
↓
double f(double d1, double d2) {
        double r3403134 = d1;
        double r3403135 = 10.0;
        double r3403136 = /* ERROR: no posit support in C */;
        double r3403137 = r3403134 * r3403136;
        double r3403138 = /*Error: no posit support in C */;
        double r3403139 = d2;
        double r3403140 = /*Error: no posit support in C */;
        double r3403141 = 20.0;
        double r3403142 = /* ERROR: no posit support in C */;
        double r3403143 = /*Error: no posit support in C */;
        double r3403144 = /*Error: no posit support in C */;
        return r3403144;
}

Error

Bits error versus d1

Bits error versus d2

Derivation

  1. Initial program 0.3

    \[\frac{\left(\frac{\left(d1 \cdot \left(10\right)\right)}{\left(d1 \cdot d2\right)}\right)}{\left(d1 \cdot \left(20\right)\right)}\]
  2. Using strategy rm

  3. Applied introduce-quire0.3

    \[\leadsto \frac{\left(\frac{\color{blue}{\left(\left(\left(d1 \cdot \left(10\right)\right)\right)\right)}}{\left(d1 \cdot d2\right)}\right)}{\left(d1 \cdot \left(20\right)\right)}\]

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

    \[\leadsto \frac{\color{blue}{\left(\left(\mathsf{qma}\left(\left(\left(d1 \cdot \left(10\right)\right)\right), d1, d2\right)\right)\right)}}{\left(d1 \cdot \left(20\right)\right)}\]

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

    \[\leadsto \color{blue}{\left(\mathsf{qma}\left(\left(\mathsf{qma}\left(\left(\left(d1 \cdot \left(10\right)\right)\right), d1, d2\right)\right), d1, \left(20\right)\right)\right)}\]

  6. Final simplification0.1

    \[\leadsto \left(\mathsf{qma}\left(\left(\mathsf{qma}\left(\left(\left(d1 \cdot \left(10\right)\right)\right), d1, d2\right)\right), d1, \left(20\right)\right)\right)\]

Reproduce

herbie shell --seed 2019168 
(FPCore (d1 d2)
  :name "FastMath test2"
  (+.p16 (+.p16 (*.p16 d1 (real->posit16 10)) (*.p16 d1 d2)) (*.p16 d1 (real->posit16 20))))