Average Error: 0.3 → 0.3
Time: 10.2s
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 r3148013 = d1;
        double r3148014 = d2;
        double r3148015 = r3148013 * r3148014;
        double r3148016 = d3;
        double r3148017 = 5.0;
        double r3148018 = /* ERROR: no posit support in C */;
        double r3148019 = r3148016 + r3148018;
        double r3148020 = r3148019 * r3148013;
        double r3148021 = r3148015 + r3148020;
        double r3148022 = 32.0;
        double r3148023 = /* ERROR: no posit support in C */;
        double r3148024 = r3148013 * r3148023;
        double r3148025 = r3148021 + r3148024;
        return r3148025;
}
↓
double f(double d1, double d2, double d3) {
        double r3148026 = d1;
        double r3148027 = d2;
        double r3148028 = r3148026 * r3148027;
        double r3148029 = d3;
        double r3148030 = 5.0;
        double r3148031 = r3148029 + r3148030;
        double r3148032 = r3148031 * r3148026;
        double r3148033 = r3148028 + r3148032;
        double r3148034 = 32.0;
        double r3148035 = r3148026 * r3148034;
        double r3148036 = r3148033 + r3148035;
        return r3148036;
}

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 2019107 +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))))