Average Error: 45.6 → 0
Time: 4.6s
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 r40557 = x;
        double r40558 = y;
        double r40559 = z;
        double r40560 = fma(r40557, r40558, r40559);
        double r40561 = 1.0;
        double r40562 = r40557 * r40558;
        double r40563 = r40562 + r40559;
        double r40564 = r40561 + r40563;
        double r40565 = r40560 - r40564;
        return r40565;
}
↓
double f(double __attribute__((unused)) x, double __attribute__((unused)) y, double __attribute__((unused)) z) {
        double r40566 = 1.0;
        double r40567 = -r40566;
        return r40567;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Target

Original45.6
Target0
Herbie0
\[-1\]

Derivation

  1. Initial program 45.6

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

  2. Simplified0

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

  3. Final simplification0

    \[\leadsto -1\]

Reproduce

herbie shell --seed 2019194 +o rules:numerics
(FPCore (x y z)
  :name "simple fma test"

  :herbie-target
  -1.0

  (- (fma x y z) (+ 1.0 (+ (* x y) z))))