Average Error: 45.0 → 0
Time: 4.2s
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 r2396702 = x;
        double r2396703 = y;
        double r2396704 = z;
        double r2396705 = fma(r2396702, r2396703, r2396704);
        double r2396706 = 1.0;
        double r2396707 = r2396702 * r2396703;
        double r2396708 = r2396707 + r2396704;
        double r2396709 = r2396706 + r2396708;
        double r2396710 = r2396705 - r2396709;
        return r2396710;
}
↓
double f(double __attribute__((unused)) x, double __attribute__((unused)) y, double __attribute__((unused)) z) {
        double r2396711 = 1.0;
        double r2396712 = -r2396711;
        return r2396712;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Target

Original45.0
Target0
Herbie0
\[-1\]

Derivation

  1. Initial program 45.0

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

  2. Simplified0

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

  3. Final simplification0

    \[\leadsto -1\]

Reproduce

herbie shell --seed 2019172 +o rules:numerics
(FPCore (x y z)
  :name "simple fma test"

  :herbie-target
  -1.0

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