Average Error: 45.6 → 0
Time: 5.4s
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 r934340 = x;
        double r934341 = y;
        double r934342 = z;
        double r934343 = fma(r934340, r934341, r934342);
        double r934344 = 1.0;
        double r934345 = r934340 * r934341;
        double r934346 = r934345 + r934342;
        double r934347 = r934344 + r934346;
        double r934348 = r934343 - r934347;
        return r934348;
}
↓
double f(double __attribute__((unused)) x, double __attribute__((unused)) y, double __attribute__((unused)) z) {
        double r934349 = -1.0;
        return r934349;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Target

Original45.6
Target0
Herbie0
\[-1\]

Derivation

  1. Initial program 45.6

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

  2. Simplified0

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

  3. Final simplification0

    \[\leadsto -1\]

Reproduce

herbie shell --seed 2019152 +o rules:numerics
(FPCore (x y z)
  :name "simple fma test"

  :herbie-target
  -1

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