Average Error: 44.5 → 0
Time: 1.1s
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 r67832 = x;
        double r67833 = y;
        double r67834 = z;
        double r67835 = fma(r67832, r67833, r67834);
        double r67836 = 1.0;
        double r67837 = r67832 * r67833;
        double r67838 = r67837 + r67834;
        double r67839 = r67836 + r67838;
        double r67840 = r67835 - r67839;
        return r67840;
}
↓
double f(double __attribute__((unused)) x, double __attribute__((unused)) y, double __attribute__((unused)) z) {
        double r67841 = 1.0;
        double r67842 = -r67841;
        return r67842;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Target

Original44.5
Target0
Herbie0
\[-1\]

Derivation

  1. Initial program 44.5

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

  2. Simplified0

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

  3. Final simplification0

    \[\leadsto -1\]

Reproduce

herbie shell --seed 2019362 +o rules:numerics
(FPCore (x y z)
  :name "simple fma test"
  :precision binary64

  :herbie-target
  -1

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