Average Error: 45.7 → 0
Time: 4.9s
Precision: 64
\[(x \cdot y + z)_* - \left(1 + \left(x \cdot y + z\right)\right)\]
↓
\[-1\]
(x \cdot y + z)_* - \left(1 + \left(x \cdot y + z\right)\right)
↓
-1
double f(double x, double y, double z) {
        double r4906761 = x;
        double r4906762 = y;
        double r4906763 = z;
        double r4906764 = fma(r4906761, r4906762, r4906763);
        double r4906765 = 1.0;
        double r4906766 = r4906761 * r4906762;
        double r4906767 = r4906766 + r4906763;
        double r4906768 = r4906765 + r4906767;
        double r4906769 = r4906764 - r4906768;
        return r4906769;
}
↓
double f(double __attribute__((unused)) x, double __attribute__((unused)) y, double __attribute__((unused)) z) {
        double r4906770 = -1.0;
        return r4906770;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Target

Original45.7
Target0
Herbie0
\[-1\]

Derivation

  1. Initial program 45.7

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

  2. Simplified0

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

  3. Final simplification0

    \[\leadsto -1\]

Reproduce

herbie shell --seed 2019119 +o rules:numerics
(FPCore (x y z)
  :name "simple fma test"

  :herbie-target
  -1

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