Average Error: 45.4 → 0
Time: 8.5s
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 r2548662 = x;
        double r2548663 = y;
        double r2548664 = z;
        double r2548665 = fma(r2548662, r2548663, r2548664);
        double r2548666 = 1.0;
        double r2548667 = r2548662 * r2548663;
        double r2548668 = r2548667 + r2548664;
        double r2548669 = r2548666 + r2548668;
        double r2548670 = r2548665 - r2548669;
        return r2548670;
}
↓
double f(double __attribute__((unused)) x, double __attribute__((unused)) y, double __attribute__((unused)) z) {
        double r2548671 = 1.0;
        double r2548672 = -r2548671;
        return r2548672;
}

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 2019170 +o rules:numerics
(FPCore (x y z)
  :name "simple fma test"

  :herbie-target
  -1.0

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