Average Error: 45.4 → 0
Time: 5.8s
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 r39019 = x;
        double r39020 = y;
        double r39021 = z;
        double r39022 = fma(r39019, r39020, r39021);
        double r39023 = 1.0;
        double r39024 = r39019 * r39020;
        double r39025 = r39024 + r39021;
        double r39026 = r39023 + r39025;
        double r39027 = r39022 - r39026;
        return r39027;
}
↓
double f(double __attribute__((unused)) x, double __attribute__((unused)) y, double __attribute__((unused)) z) {
        double r39028 = 1.0;
        double r39029 = -r39028;
        return r39029;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Target

Original45.4
Target0
Herbie0
\[-1\]

Derivation

  1. Initial program 45.4

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

  2. Simplified0

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

  3. Final simplification0

    \[\leadsto -1\]

Reproduce

herbie shell --seed 2019199 +o rules:numerics
(FPCore (x y z)
  :name "simple fma test"

  :herbie-target
  -1.0

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