Average Error: 45.2 → 0
Time: 4.2s
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 r3906599 = x;
        double r3906600 = y;
        double r3906601 = z;
        double r3906602 = fma(r3906599, r3906600, r3906601);
        double r3906603 = 1.0;
        double r3906604 = r3906599 * r3906600;
        double r3906605 = r3906604 + r3906601;
        double r3906606 = r3906603 + r3906605;
        double r3906607 = r3906602 - r3906606;
        return r3906607;
}
↓
double f(double __attribute__((unused)) x, double __attribute__((unused)) y, double __attribute__((unused)) z) {
        double r3906608 = -1.0;
        return r3906608;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Target

Original45.2
Target0
Herbie0
\[-1\]

Derivation

  1. Initial program 45.2

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

  2. Simplified0

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

  3. Final simplification0

    \[\leadsto -1\]

Reproduce

herbie shell --seed 2019120 +o rules:numerics
(FPCore (x y z)
  :name "simple fma test"

  :herbie-target
  -1

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