Average Error: 0.3 → 0.3
Time: 12.1s
Precision: 64
\[\frac{\left(\frac{\left(d1 \cdot d2\right)}{\left(\left(\frac{d3}{\left(5\right)}\right) \cdot d1\right)}\right)}{\left(d1 \cdot \left(32\right)\right)}\]
↓
\[\left(d1 \cdot d2 + \left(d3 + 5\right) \cdot d1\right) + d1 \cdot 32\]
\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 r5476011 = d1;
        double r5476012 = d2;
        double r5476013 = r5476011 * r5476012;
        double r5476014 = d3;
        double r5476015 = 5.0;
        double r5476016 = /* ERROR: no posit support in C */;
        double r5476017 = r5476014 + r5476016;
        double r5476018 = r5476017 * r5476011;
        double r5476019 = r5476013 + r5476018;
        double r5476020 = 32.0;
        double r5476021 = /* ERROR: no posit support in C */;
        double r5476022 = r5476011 * r5476021;
        double r5476023 = r5476019 + r5476022;
        return r5476023;
}
↓
double f(double d1, double d2, double d3) {
        double r5476024 = d1;
        double r5476025 = d2;
        double r5476026 = r5476024 * r5476025;
        double r5476027 = d3;
        double r5476028 = 5.0;
        double r5476029 = r5476027 + r5476028;
        double r5476030 = r5476029 * r5476024;
        double r5476031 = r5476026 + r5476030;
        double r5476032 = 32.0;
        double r5476033 = r5476024 * r5476032;
        double r5476034 = r5476031 + r5476033;
        return r5476034;
}

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 2019132 +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))))