Average Error: 44.7 → 0
Time: 14.4s
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 r978115 = x;
        double r978116 = y;
        double r978117 = z;
        double r978118 = fma(r978115, r978116, r978117);
        double r978119 = 1.0;
        double r978120 = r978115 * r978116;
        double r978121 = r978120 + r978117;
        double r978122 = r978119 + r978121;
        double r978123 = r978118 - r978122;
        return r978123;
}
↓
double f(double __attribute__((unused)) x, double __attribute__((unused)) y, double __attribute__((unused)) z) {
        double r978124 = -1.0;
        return r978124;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Target

Original44.7
Target0
Herbie0
\[-1\]

Derivation

  1. Initial program 44.7

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

  2. Simplified0

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

  3. Final simplification0

    \[\leadsto -1\]

Reproduce

herbie shell --seed 2019138 +o rules:numerics
(FPCore (x y z)
  :name "simple fma test"

  :herbie-target
  -1

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