Average Error: 45.0 → 0
Time: 17.2s
Precision: 64
\[\mathsf{fma}\left(x, y, z\right) - \left(1.0 + \left(x \cdot y + z\right)\right)\]
↓
\[-1.0\]
\mathsf{fma}\left(x, y, z\right) - \left(1.0 + \left(x \cdot y + z\right)\right)
↓
-1.0
double f(double x, double y, double z) {
        double r2420560 = x;
        double r2420561 = y;
        double r2420562 = z;
        double r2420563 = fma(r2420560, r2420561, r2420562);
        double r2420564 = 1.0;
        double r2420565 = r2420560 * r2420561;
        double r2420566 = r2420565 + r2420562;
        double r2420567 = r2420564 + r2420566;
        double r2420568 = r2420563 - r2420567;
        return r2420568;
}
↓
double f(double __attribute__((unused)) x, double __attribute__((unused)) y, double __attribute__((unused)) z) {
        double r2420569 = 1.0;
        double r2420570 = -r2420569;
        return r2420570;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Target

Original45.0
Target0
Herbie0
\[-1.0\]

Derivation

  1. Initial program 45.0

    \[\mathsf{fma}\left(x, y, z\right) - \left(1.0 + \left(x \cdot y + z\right)\right)\]

  2. Simplified0

    \[\leadsto \color{blue}{-1.0}\]

  3. Final simplification0

    \[\leadsto -1.0\]

Reproduce

herbie shell --seed 2019165 +o rules:numerics
(FPCore (x y z)
  :name "simple fma test"

  :herbie-target
  -1.0

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