Average Error: 45.2 → 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 r67819 = x;
        double r67820 = y;
        double r67821 = z;
        double r67822 = fma(r67819, r67820, r67821);
        double r67823 = 1.0;
        double r67824 = r67819 * r67820;
        double r67825 = r67824 + r67821;
        double r67826 = r67823 + r67825;
        double r67827 = r67822 - r67826;
        return r67827;
}
↓
double f(double __attribute__((unused)) x, double __attribute__((unused)) y, double __attribute__((unused)) z) {
        double r67828 = 1.0;
        double r67829 = -r67828;
        return r67829;
}

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 2020043 +o rules:numerics
(FPCore (x y z)
  :name "simple fma test"
  :precision binary64

  :herbie-target
  -1

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