Average Error: 45.4 → 0
Time: 3.8s
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 r80314 = x;
        double r80315 = y;
        double r80316 = z;
        double r80317 = fma(r80314, r80315, r80316);
        double r80318 = 1.0;
        double r80319 = r80314 * r80315;
        double r80320 = r80319 + r80316;
        double r80321 = r80318 + r80320;
        double r80322 = r80317 - r80321;
        return r80322;
}
↓
double f(double __attribute__((unused)) x, double __attribute__((unused)) y, double __attribute__((unused)) z) {
        double r80323 = 1.0;
        double r80324 = -r80323;
        return r80324;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Target

Original45.4
Target0
Herbie0
\[-1\]

Derivation

  1. Initial program 45.4

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

  2. Simplified0

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

  3. Final simplification0

    \[\leadsto -1\]

Reproduce

herbie shell --seed 2019174 +o rules:numerics
(FPCore (x y z)
  :name "simple fma test"

  :herbie-target
  -1.0

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