Average Error: 45.1 → 0
Time: 8.7s
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 r2836417 = x;
        double r2836418 = y;
        double r2836419 = z;
        double r2836420 = fma(r2836417, r2836418, r2836419);
        double r2836421 = 1.0;
        double r2836422 = r2836417 * r2836418;
        double r2836423 = r2836422 + r2836419;
        double r2836424 = r2836421 + r2836423;
        double r2836425 = r2836420 - r2836424;
        return r2836425;
}
↓
double f(double __attribute__((unused)) x, double __attribute__((unused)) y, double __attribute__((unused)) z) {
        double r2836426 = 1.0;
        double r2836427 = -r2836426;
        return r2836427;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Target

Original45.1
Target0
Herbie0
\[-1\]

Derivation

  1. Initial program 45.1

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

  2. Simplified0

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

  3. Final simplification0

    \[\leadsto -1\]

Reproduce

herbie shell --seed 2019169 +o rules:numerics
(FPCore (x y z)
  :name "simple fma test"

  :herbie-target
  -1.0

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