Average Error: 44.8 → 0
Time: 1.1s
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 r77018 = x;
        double r77019 = y;
        double r77020 = z;
        double r77021 = fma(r77018, r77019, r77020);
        double r77022 = 1.0;
        double r77023 = r77018 * r77019;
        double r77024 = r77023 + r77020;
        double r77025 = r77022 + r77024;
        double r77026 = r77021 - r77025;
        return r77026;
}
↓
double f(double __attribute__((unused)) x, double __attribute__((unused)) y, double __attribute__((unused)) z) {
        double r77027 = 1.0;
        double r77028 = -r77027;
        return r77028;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Target

Original44.8
Target0
Herbie0
\[-1\]

Derivation

  1. Initial program 44.8

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

  2. Simplified0

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

  3. Final simplification0

    \[\leadsto -1\]

Reproduce

herbie shell --seed 2020039 +o rules:numerics
(FPCore (x y z)
  :name "simple fma test"
  :precision binary64

  :herbie-target
  -1

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