Average Error: 44.4 → 0
Time: 7.6s
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 r1444303 = x;
        double r1444304 = y;
        double r1444305 = z;
        double r1444306 = fma(r1444303, r1444304, r1444305);
        double r1444307 = 1.0;
        double r1444308 = r1444303 * r1444304;
        double r1444309 = r1444308 + r1444305;
        double r1444310 = r1444307 + r1444309;
        double r1444311 = r1444306 - r1444310;
        return r1444311;
}
↓
double f(double __attribute__((unused)) x, double __attribute__((unused)) y, double __attribute__((unused)) z) {
        double r1444312 = -1.0;
        return r1444312;
}

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 2019158 +o rules:numerics
(FPCore (x y z)
  :name "simple fma test"

  :herbie-target
  -1

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