Average Error: 44.6 → 0
Time: 4.7s
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 r21968 = x;
        double r21969 = y;
        double r21970 = z;
        double r21971 = fma(r21968, r21969, r21970);
        double r21972 = 1.0;
        double r21973 = r21968 * r21969;
        double r21974 = r21973 + r21970;
        double r21975 = r21972 + r21974;
        double r21976 = r21971 - r21975;
        return r21976;
}
↓
double f(double __attribute__((unused)) x, double __attribute__((unused)) y, double __attribute__((unused)) z) {
        double r21977 = 1.0;
        double r21978 = -r21977;
        return r21978;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Target

Original44.6
Target0
Herbie0
\[-1\]

Derivation

  1. Initial program 44.6

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

  2. Simplified0

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

  3. Final simplification0

    \[\leadsto -1\]

Reproduce

herbie shell --seed 2019195 +o rules:numerics
(FPCore (x y z)
  :name "simple fma test"

  :herbie-target
  -1.0

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