Average Error: 44.4 → 0
Time: 11.5s
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 r949098 = x;
        double r949099 = y;
        double r949100 = z;
        double r949101 = fma(r949098, r949099, r949100);
        double r949102 = 1.0;
        double r949103 = r949098 * r949099;
        double r949104 = r949103 + r949100;
        double r949105 = r949102 + r949104;
        double r949106 = r949101 - r949105;
        return r949106;
}
↓
double f(double __attribute__((unused)) x, double __attribute__((unused)) y, double __attribute__((unused)) z) {
        double r949107 = -1.0;
        return r949107;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Target

Original44.4
Target0
Herbie0
\[-1\]

Derivation

  1. Initial program 44.4

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

  2. Simplified0

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

  3. Final simplification0

    \[\leadsto -1\]

Reproduce

herbie shell --seed 2019146 +o rules:numerics
(FPCore (x y z)
  :name "simple fma test"

  :herbie-target
  -1

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