Average Error: 0.3 → 0.1
Time: 17.8s
Precision: 64
\[\frac{\left(\frac{\left(d1 \cdot \left(10\right)\right)}{\left(d1 \cdot d2\right)}\right)}{\left(d1 \cdot \left(20\right)\right)}\]
↓
\[\left(\mathsf{qma}\left(\left(\mathsf{qma}\left(\left(\left(d1 \cdot 10\right)\right), d1, d2\right)\right), d1, 20\right)\right)\]
\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 10\right)\right), d1, d2\right)\right), d1, 20\right)\right)
double f(double d1, double d2) {
        double r1351101 = d1;
        double r1351102 = 10.0;
        double r1351103 = /* ERROR: no posit support in C */;
        double r1351104 = r1351101 * r1351103;
        double r1351105 = d2;
        double r1351106 = r1351101 * r1351105;
        double r1351107 = r1351104 + r1351106;
        double r1351108 = 20.0;
        double r1351109 = /* ERROR: no posit support in C */;
        double r1351110 = r1351101 * r1351109;
        double r1351111 = r1351107 + r1351110;
        return r1351111;
}
↓
double f(double d1, double d2) {
        double r1351112 = d1;
        double r1351113 = 10.0;
        double r1351114 = r1351112 * r1351113;
        double r1351115 = /*Error: no posit support in C */;
        double r1351116 = d2;
        double r1351117 = /*Error: no posit support in C */;
        double r1351118 = 20.0;
        double r1351119 = /*Error: no posit support in C */;
        double r1351120 = /*Error: no posit support in C */;
        return r1351120;
}

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

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

Reproduce

herbie shell --seed 2019152 +o rules:numerics
(FPCore (d1 d2)
  :name "FastMath test2"
  (+.p16 (+.p16 (*.p16 d1 (real->posit16 10)) (*.p16 d1 d2)) (*.p16 d1 (real->posit16 20))))