Average Error: 45.2 → 0
Time: 4.4s
Precision: 64
\[(x \cdot y + z)_* - \left(1 + \left(x \cdot y + z\right)\right)\]
↓
\[-1\]
(x \cdot y + z)_* - \left(1 + \left(x \cdot y + z\right)\right)
↓
-1
double f(double x, double y, double z) {
        double r1902188 = x;
        double r1902189 = y;
        double r1902190 = z;
        double r1902191 = fma(r1902188, r1902189, r1902190);
        double r1902192 = 1.0;
        double r1902193 = r1902188 * r1902189;
        double r1902194 = r1902193 + r1902190;
        double r1902195 = r1902192 + r1902194;
        double r1902196 = r1902191 - r1902195;
        return r1902196;
}
↓
double f(double __attribute__((unused)) x, double __attribute__((unused)) y, double __attribute__((unused)) z) {
        double r1902197 = -1.0;
        return r1902197;
}

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

    \[(x \cdot y + z)_* - \left(1 + \left(x \cdot y + z\right)\right)\]

  2. Simplified0

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

  3. Final simplification0

    \[\leadsto -1\]

Reproduce

herbie shell --seed 2019104 +o rules:numerics
(FPCore (x y z)
  :name "simple fma test"

  :herbie-target
  -1

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