Average Error: 45.6 → 0
Time: 1.2s
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 r45768 = x;
        double r45769 = y;
        double r45770 = z;
        double r45771 = fma(r45768, r45769, r45770);
        double r45772 = 1.0;
        double r45773 = r45768 * r45769;
        double r45774 = r45773 + r45770;
        double r45775 = r45772 + r45774;
        double r45776 = r45771 - r45775;
        return r45776;
}
↓
double f(double __attribute__((unused)) x, double __attribute__((unused)) y, double __attribute__((unused)) z) {
        double r45777 = 1.0;
        double r45778 = -r45777;
        return r45778;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Target

Original45.6
Target0
Herbie0
\[-1\]

Derivation

  1. Initial program 45.6

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

  2. Simplified0

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

  3. Final simplification0

    \[\leadsto -1\]

Reproduce

herbie shell --seed 2020025 +o rules:numerics
(FPCore (x y z)
  :name "simple fma test"
  :precision binary64

  :herbie-target
  -1

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