Average Error: 45.1 → 0
Time: 6.5s
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 r1847469 = x;
        double r1847470 = y;
        double r1847471 = z;
        double r1847472 = fma(r1847469, r1847470, r1847471);
        double r1847473 = 1.0;
        double r1847474 = r1847469 * r1847470;
        double r1847475 = r1847474 + r1847471;
        double r1847476 = r1847473 + r1847475;
        double r1847477 = r1847472 - r1847476;
        return r1847477;
}
↓
double f(double __attribute__((unused)) x, double __attribute__((unused)) y, double __attribute__((unused)) z) {
        double r1847478 = -1.0;
        return r1847478;
}

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 2019162 +o rules:numerics
(FPCore (x y z)
  :name "simple fma test"

  :herbie-target
  -1

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