Average Error: 44.4 → 0
Time: 2.2s
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 r34555 = x;
        double r34556 = y;
        double r34557 = z;
        double r34558 = fma(r34555, r34556, r34557);
        double r34559 = 1.0;
        double r34560 = r34555 * r34556;
        double r34561 = r34560 + r34557;
        double r34562 = r34559 + r34561;
        double r34563 = r34558 - r34562;
        return r34563;
}
↓
double f(double __attribute__((unused)) x, double __attribute__((unused)) y, double __attribute__((unused)) z) {
        double r34564 = 1.0;
        double r34565 = -r34564;
        return r34565;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Target

Original44.4
Target0
Herbie0
\[-1\]

Derivation

  1. Initial program 44.4

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

  2. Simplified0

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

  3. Final simplification0

    \[\leadsto -1\]

Reproduce

herbie shell --seed 2020035 +o rules:numerics
(FPCore (x y z)
  :name "simple fma test"
  :precision binary64

  :herbie-target
  -1

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