Average Error: 44.3 → 0
Time: 3.9s
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 r60661 = x;
        double r60662 = y;
        double r60663 = z;
        double r60664 = fma(r60661, r60662, r60663);
        double r60665 = 1.0;
        double r60666 = r60661 * r60662;
        double r60667 = r60666 + r60663;
        double r60668 = r60665 + r60667;
        double r60669 = r60664 - r60668;
        return r60669;
}
↓
double f(double __attribute__((unused)) x, double __attribute__((unused)) y, double __attribute__((unused)) z) {
        double r60670 = 1.0;
        double r60671 = -r60670;
        return r60671;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Target

Original44.3
Target0
Herbie0
\[-1\]

Derivation

  1. Initial program 44.3

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

  2. Simplified0

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

  3. Final simplification0

    \[\leadsto -1\]

Reproduce

herbie shell --seed 2019208 +o rules:numerics
(FPCore (x y z)
  :name "simple fma test"
  :precision binary64

  :herbie-target
  -1

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