Average Error: 45.7 → 0
Time: 1.4s
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 r82110 = x;
        double r82111 = y;
        double r82112 = z;
        double r82113 = fma(r82110, r82111, r82112);
        double r82114 = 1.0;
        double r82115 = r82110 * r82111;
        double r82116 = r82115 + r82112;
        double r82117 = r82114 + r82116;
        double r82118 = r82113 - r82117;
        return r82118;
}
↓
double f(double __attribute__((unused)) x, double __attribute__((unused)) y, double __attribute__((unused)) z) {
        double r82119 = 1.0;
        double r82120 = -r82119;
        return r82120;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Target

Original45.7
Target0
Herbie0
\[-1\]

Derivation

  1. Initial program 45.7

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

  2. Simplified0

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

  3. Final simplification0

    \[\leadsto -1\]

Reproduce

herbie shell --seed 2020033 +o rules:numerics
(FPCore (x y z)
  :name "simple fma test"
  :precision binary64

  :herbie-target
  -1

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