Average Error: 45.1 → 0
Time: 4.4s
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 r1775908 = x;
        double r1775909 = y;
        double r1775910 = z;
        double r1775911 = fma(r1775908, r1775909, r1775910);
        double r1775912 = 1.0;
        double r1775913 = r1775908 * r1775909;
        double r1775914 = r1775913 + r1775910;
        double r1775915 = r1775912 + r1775914;
        double r1775916 = r1775911 - r1775915;
        return r1775916;
}
↓
double f(double __attribute__((unused)) x, double __attribute__((unused)) y, double __attribute__((unused)) z) {
        double r1775917 = 1.0;
        double r1775918 = -r1775917;
        return r1775918;
}

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 2019171 +o rules:numerics
(FPCore (x y z)
  :name "simple fma test"

  :herbie-target
  -1.0

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