Average Error: 44.8 → 0
Time: 12.3s
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 r2796868 = x;
        double r2796869 = y;
        double r2796870 = z;
        double r2796871 = fma(r2796868, r2796869, r2796870);
        double r2796872 = 1.0;
        double r2796873 = r2796868 * r2796869;
        double r2796874 = r2796873 + r2796870;
        double r2796875 = r2796872 + r2796874;
        double r2796876 = r2796871 - r2796875;
        return r2796876;
}
↓
double f(double __attribute__((unused)) x, double __attribute__((unused)) y, double __attribute__((unused)) z) {
        double r2796877 = 1.0;
        double r2796878 = -r2796877;
        return r2796878;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Target

Original44.8
Target0
Herbie0
\[-1\]

Derivation

  1. Initial program 44.8

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

  2. Simplified0

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

  3. Final simplification0

    \[\leadsto -1\]

Reproduce

herbie shell --seed 2019200 +o rules:numerics
(FPCore (x y z)
  :name "simple fma test"

  :herbie-target
  -1.0

  (- (fma x y z) (+ 1.0 (+ (* x y) z))))