Average Error: 44.6 → 0
Time: 4.1s
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 r31852 = x;
        double r31853 = y;
        double r31854 = z;
        double r31855 = fma(r31852, r31853, r31854);
        double r31856 = 1.0;
        double r31857 = r31852 * r31853;
        double r31858 = r31857 + r31854;
        double r31859 = r31856 + r31858;
        double r31860 = r31855 - r31859;
        return r31860;
}
↓
double f(double __attribute__((unused)) x, double __attribute__((unused)) y, double __attribute__((unused)) z) {
        double r31861 = 1.0;
        double r31862 = -r31861;
        return r31862;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Target

Original44.6
Target0
Herbie0
\[-1\]

Derivation

  1. Initial program 44.6

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

  2. Simplified0

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

  3. Final simplification0

    \[\leadsto -1\]

Reproduce

herbie shell --seed 2019195 +o rules:numerics
(FPCore (x y z)
  :name "simple fma test"

  :herbie-target
  -1.0

  (- (fma x y z) (+ 1.0 (+ (* x y) z))))