Average Error: 45.5 → 0
Time: 12.0s
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 r1121677 = x;
        double r1121678 = y;
        double r1121679 = z;
        double r1121680 = fma(r1121677, r1121678, r1121679);
        double r1121681 = 1.0;
        double r1121682 = r1121677 * r1121678;
        double r1121683 = r1121682 + r1121679;
        double r1121684 = r1121681 + r1121683;
        double r1121685 = r1121680 - r1121684;
        return r1121685;
}
↓
double f(double __attribute__((unused)) x, double __attribute__((unused)) y, double __attribute__((unused)) z) {
        double r1121686 = -1.0;
        return r1121686;
}

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 2019132 +o rules:numerics
(FPCore (x y z)
  :name "simple fma test"

  :herbie-target
  -1

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