Average Error: 45.0 → 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 r3210806 = x;
        double r3210807 = y;
        double r3210808 = z;
        double r3210809 = fma(r3210806, r3210807, r3210808);
        double r3210810 = 1.0;
        double r3210811 = r3210806 * r3210807;
        double r3210812 = r3210811 + r3210808;
        double r3210813 = r3210810 + r3210812;
        double r3210814 = r3210809 - r3210813;
        return r3210814;
}
↓
double f(double __attribute__((unused)) x, double __attribute__((unused)) y, double __attribute__((unused)) z) {
        double r3210815 = 1.0;
        double r3210816 = -r3210815;
        return r3210816;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Target

Original45.0
Target0
Herbie0
\[-1\]

Derivation

  1. Initial program 45.0

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

  2. Simplified0

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

  3. Final simplification0

    \[\leadsto -1\]

Reproduce

herbie shell --seed 2019179 +o rules:numerics
(FPCore (x y z)
  :name "simple fma test"

  :herbie-target
  -1.0

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