Average Error: 45.6 → 0
Time: 11.1s
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 r1400537 = x;
        double r1400538 = y;
        double r1400539 = z;
        double r1400540 = fma(r1400537, r1400538, r1400539);
        double r1400541 = 1.0;
        double r1400542 = r1400537 * r1400538;
        double r1400543 = r1400542 + r1400539;
        double r1400544 = r1400541 + r1400543;
        double r1400545 = r1400540 - r1400544;
        return r1400545;
}
↓
double f(double __attribute__((unused)) x, double __attribute__((unused)) y, double __attribute__((unused)) z) {
        double r1400546 = -1.0;
        return r1400546;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Target

Original45.6
Target0
Herbie0
\[-1\]

Derivation

  1. Initial program 45.6

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

  2. Simplified0

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

  3. Final simplification0

    \[\leadsto -1\]

Reproduce

herbie shell --seed 2019152 +o rules:numerics
(FPCore (x y z)
  :name "simple fma test"

  :herbie-target
  -1

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