Average Error: 45.1 → 0
Time: 10.3s
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 r58705 = x;
        double r58706 = y;
        double r58707 = z;
        double r58708 = fma(r58705, r58706, r58707);
        double r58709 = 1.0;
        double r58710 = r58705 * r58706;
        double r58711 = r58710 + r58707;
        double r58712 = r58709 + r58711;
        double r58713 = r58708 - r58712;
        return r58713;
}
↓
double f(double __attribute__((unused)) x, double __attribute__((unused)) y, double __attribute__((unused)) z) {
        double r58714 = 1.0;
        double r58715 = -r58714;
        return r58715;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Target

Original45.1
Target0
Herbie0
\[-1\]

Derivation

  1. Initial program 45.1

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

  2. Simplified0

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

  3. Final simplification0

    \[\leadsto -1\]

Reproduce

herbie shell --seed 2019303 +o rules:numerics
(FPCore (x y z)
  :name "simple fma test"
  :precision binary64

  :herbie-target
  -1

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