Average Error: 44.9 → 0
Time: 11.8s
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 r1314296 = x;
        double r1314297 = y;
        double r1314298 = z;
        double r1314299 = fma(r1314296, r1314297, r1314298);
        double r1314300 = 1.0;
        double r1314301 = r1314296 * r1314297;
        double r1314302 = r1314301 + r1314298;
        double r1314303 = r1314300 + r1314302;
        double r1314304 = r1314299 - r1314303;
        return r1314304;
}
↓
double f(double __attribute__((unused)) x, double __attribute__((unused)) y, double __attribute__((unused)) z) {
        double r1314305 = -1.0;
        return r1314305;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Target

Original44.9
Target0
Herbie0
\[-1\]

Derivation

  1. Initial program 44.9

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

  2. Simplified0

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

  3. Final simplification0

    \[\leadsto -1\]

Reproduce

herbie shell --seed 2019130 +o rules:numerics
(FPCore (x y z)
  :name "simple fma test"

  :herbie-target
  -1

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