Average Error: 0.3 → 0.3
Time: 9.5s
Precision: 64
\[\left(d1 \cdot d2 + \left(d3 + 5\right) \cdot d1\right) + d1 \cdot 32\]
↓
\[\left(d1 \cdot d2 + \left(d3 + 5\right) \cdot d1\right) + d1 \cdot 32\]
double f(double d1, double d2, double d3) {
        double r1243428 = d1;
        double r1243429 = d2;
        double r1243430 = r1243428 * r1243429;
        double r1243431 = d3;
        double r1243432 = 5.0;
        double r1243433 = r1243431 + r1243432;
        double r1243434 = r1243433 * r1243428;
        double r1243435 = r1243430 + r1243434;
        double r1243436 = 32.0;
        double r1243437 = r1243428 * r1243436;
        double r1243438 = r1243435 + r1243437;
        return r1243438;
}
↓
double f(double d1, double d2, double d3) {
        double r1243439 = d1;
        double r1243440 = d2;
        double r1243441 = r1243439 * r1243440;
        double r1243442 = d3;
        double r1243443 = 5.0;
        double r1243444 = r1243442 + r1243443;
        double r1243445 = r1243444 * r1243439;
        double r1243446 = r1243441 + r1243445;
        double r1243447 = 32.0;
        double r1243448 = r1243439 * r1243447;
        double r1243449 = r1243446 + r1243448;
        return r1243449;
}


\left(d1 \cdot d2 + \left(d3 + 5\right) \cdot d1\right) + d1 \cdot 32
↓
\left(d1 \cdot d2 + \left(d3 + 5\right) \cdot d1\right) + d1 \cdot 32

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 2019101 
(FPCore (d1 d2 d3)
  :name "FastMath dist3"
  (+.p16 (+.p16 (*.p16 d1 d2) (*.p16 (+.p16 d3 (real->posit16 5)) d1)) (*.p16 d1 (real->posit16 32))))