Average Error: 0.3 → 0.2
Time: 27.7s
Precision: 64
\[\frac{\left(\frac{\left(d1 \cdot d2\right)}{\left(\left(\frac{d3}{\left(5\right)}\right) \cdot d1\right)}\right)}{\left(d1 \cdot \left(32\right)\right)}\]
↓
\[\left(\mathsf{qma}\left(\left(\mathsf{qma}\left(\left(\left(d1 \cdot d2\right)\right), \left(\left(d3 + 5\right) \cdot d1\right), 1.0\right)\right), d1, 32\right)\right)\]
\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(\left(d3 + 5\right) \cdot d1\right), 1.0\right)\right), d1, 32\right)\right)
double f(double d1, double d2, double d3) {
        double r7684067 = d1;
        double r7684068 = d2;
        double r7684069 = r7684067 * r7684068;
        double r7684070 = d3;
        double r7684071 = 5.0;
        double r7684072 = /* ERROR: no posit support in C */;
        double r7684073 = r7684070 + r7684072;
        double r7684074 = r7684073 * r7684067;
        double r7684075 = r7684069 + r7684074;
        double r7684076 = 32.0;
        double r7684077 = /* ERROR: no posit support in C */;
        double r7684078 = r7684067 * r7684077;
        double r7684079 = r7684075 + r7684078;
        return r7684079;
}
↓
double f(double d1, double d2, double d3) {
        double r7684080 = d1;
        double r7684081 = d2;
        double r7684082 = r7684080 * r7684081;
        double r7684083 = /*Error: no posit support in C */;
        double r7684084 = d3;
        double r7684085 = 5.0;
        double r7684086 = r7684084 + r7684085;
        double r7684087 = r7684086 * r7684080;
        double r7684088 = 1.0;
        double r7684089 = /*Error: no posit support in C */;
        double r7684090 = 32.0;
        double r7684091 = /*Error: no posit support in C */;
        double r7684092 = /*Error: no posit support in C */;
        return r7684092;
}

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-add0.3

    \[\leadsto \frac{\color{blue}{\left(\left(\mathsf{qma}\left(\left(\left(d1 \cdot d2\right)\right), \left(\left(\frac{d3}{\left(5\right)}\right) \cdot d1\right), \left(1.0\right)\right)\right)\right)}}{\left(d1 \cdot \left(32\right)\right)}\]

  5. Applied insert-quire-fdp-add0.2

    \[\leadsto \color{blue}{\left(\mathsf{qma}\left(\left(\mathsf{qma}\left(\left(\left(d1 \cdot d2\right)\right), \left(\left(\frac{d3}{\left(5\right)}\right) \cdot d1\right), \left(1.0\right)\right)\right), d1, \left(32\right)\right)\right)}\]

  6. Final simplification0.2

    \[\leadsto \left(\mathsf{qma}\left(\left(\mathsf{qma}\left(\left(\left(d1 \cdot d2\right)\right), \left(\left(d3 + 5\right) \cdot d1\right), 1.0\right)\right), d1, 32\right)\right)\]

Reproduce

herbie shell --seed 2019162 +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))))