Average Error: 44.8 → 0
Time: 4.7s
Precision: 64
\[(x \cdot y + z)_* - \left(1 + \left(x \cdot y + z\right)\right)\]
↓
\[-1\]
double f(double x, double y, double z) {
        double r3942227 = x;
        double r3942228 = y;
        double r3942229 = z;
        double r3942230 = fma(r3942227, r3942228, r3942229);
        double r3942231 = 1.0;
        double r3942232 = r3942227 * r3942228;
        double r3942233 = r3942232 + r3942229;
        double r3942234 = r3942231 + r3942233;
        double r3942235 = r3942230 - r3942234;
        return r3942235;
}
↓
double f(double __attribute__((unused)) x, double __attribute__((unused)) y, double __attribute__((unused)) z) {
        double r3942236 = -1.0;
        return r3942236;
}


(x \cdot y + z)_* - \left(1 + \left(x \cdot y + z\right)\right)
↓
-1

Error

Bits error versus x

Bits error versus y

Bits error versus z

Target

Original44.8
Target0
Herbie0
\[-1\]

Derivation

  1. Initial program 44.8

    \[(x \cdot y + z)_* - \left(1 + \left(x \cdot y + z\right)\right)\]

  2. Simplified0

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

  3. Final simplification0

    \[\leadsto -1\]

Reproduce

herbie shell --seed 2019102 +o rules:numerics
(FPCore (x y z)
  :name "simple fma test"

  :herbie-target
  -1

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