Average Error: 45.5 → 0
Time: 6.8s
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 r1698084 = x;
        double r1698085 = y;
        double r1698086 = z;
        double r1698087 = fma(r1698084, r1698085, r1698086);
        double r1698088 = 1.0;
        double r1698089 = r1698084 * r1698085;
        double r1698090 = r1698089 + r1698086;
        double r1698091 = r1698088 + r1698090;
        double r1698092 = r1698087 - r1698091;
        return r1698092;
}
↓
double f(double __attribute__((unused)) x, double __attribute__((unused)) y, double __attribute__((unused)) z) {
        double r1698093 = -1.0;
        return r1698093;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Target

Original45.5
Target0
Herbie0
\[-1\]

Derivation

  1. Initial program 45.5

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

  2. Simplified0

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

  3. Final simplification0

    \[\leadsto -1\]

Reproduce

herbie shell --seed 2019163 +o rules:numerics
(FPCore (x y z)
  :name "simple fma test"

  :herbie-target
  -1

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