Average Error: 45.1 → 0
Time: 4.1s
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 r2056078 = x;
        double r2056079 = y;
        double r2056080 = z;
        double r2056081 = fma(r2056078, r2056079, r2056080);
        double r2056082 = 1.0;
        double r2056083 = r2056078 * r2056079;
        double r2056084 = r2056083 + r2056080;
        double r2056085 = r2056082 + r2056084;
        double r2056086 = r2056081 - r2056085;
        return r2056086;
}
↓
double f(double __attribute__((unused)) x, double __attribute__((unused)) y, double __attribute__((unused)) z) {
        double r2056087 = 1.0;
        double r2056088 = -r2056087;
        return r2056088;
}

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 2019192 +o rules:numerics
(FPCore (x y z)
  :name "simple fma test"

  :herbie-target
  -1.0

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