Average Error: 45.3 → 0
Time: 1.1s
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 r82894 = x;
        double r82895 = y;
        double r82896 = z;
        double r82897 = fma(r82894, r82895, r82896);
        double r82898 = 1.0;
        double r82899 = r82894 * r82895;
        double r82900 = r82899 + r82896;
        double r82901 = r82898 + r82900;
        double r82902 = r82897 - r82901;
        return r82902;
}
↓
double f(double __attribute__((unused)) x, double __attribute__((unused)) y, double __attribute__((unused)) z) {
        double r82903 = 1.0;
        double r82904 = -r82903;
        return r82904;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Target

Original45.3
Target0
Herbie0
\[-1\]

Derivation

  1. Initial program 45.3

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

  2. Simplified0

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

  3. Final simplification0

    \[\leadsto -1\]

Reproduce

herbie shell --seed 2020024 +o rules:numerics
(FPCore (x y z)
  :name "simple fma test"
  :precision binary64

  :herbie-target
  -1

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