Average Error: 44.7 → 0
Time: 5.2s
Precision: 64
\[\mathsf{fma}\left(x, y, z\right) - \left(1 + \left(x \cdot y + z\right)\right)\]
↓
\[-1\]
\mathsf{fma}\left(x, y, z\right) - \left(1 + \left(x \cdot y + z\right)\right)
↓
-1
double f(double x, double y, double z) {
        double r742513 = x;
        double r742514 = y;
        double r742515 = z;
        double r742516 = fma(r742513, r742514, r742515);
        double r742517 = 1.0;
        double r742518 = r742513 * r742514;
        double r742519 = r742518 + r742515;
        double r742520 = r742517 + r742519;
        double r742521 = r742516 - r742520;
        return r742521;
}
↓
double f(double __attribute__((unused)) x, double __attribute__((unused)) y, double __attribute__((unused)) z) {
        double r742522 = -1.0;
        return r742522;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Target

Original44.7
Target0
Herbie0
\[-1\]

Derivation

  1. Initial program 44.7

    \[\mathsf{fma}\left(x, y, z\right) - \left(1 + \left(x \cdot y + z\right)\right)\]

  2. Simplified0

    \[\leadsto \color{blue}{-1}\]

  3. Final simplification0

    \[\leadsto -1\]

Reproduce

herbie shell --seed 2019154 +o rules:numerics
(FPCore (x y z)
  :name "simple fma test"

  :herbie-target
  -1

  (- (fma x y z) (+ 1 (+ (* x y) z))))