Average Error: 45.0 → 0
Time: 6.3s
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 r1278110 = x;
        double r1278111 = y;
        double r1278112 = z;
        double r1278113 = fma(r1278110, r1278111, r1278112);
        double r1278114 = 1.0;
        double r1278115 = r1278110 * r1278111;
        double r1278116 = r1278115 + r1278112;
        double r1278117 = r1278114 + r1278116;
        double r1278118 = r1278113 - r1278117;
        return r1278118;
}
↓
double f(double __attribute__((unused)) x, double __attribute__((unused)) y, double __attribute__((unused)) z) {
        double r1278119 = 1.0;
        double r1278120 = -r1278119;
        return r1278120;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Target

Original45.0
Target0
Herbie0
\[-1\]

Derivation

  1. Initial program 45.0

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

  2. Simplified0

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

  3. Final simplification0

    \[\leadsto -1\]

Reproduce

herbie shell --seed 2019134 +o rules:numerics
(FPCore (x y z)
  :name "simple fma test"

  :herbie-target
  -1

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