Average Error: 45.1 → 0
Time: 15.2s
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 r3136503 = x;
        double r3136504 = y;
        double r3136505 = z;
        double r3136506 = fma(r3136503, r3136504, r3136505);
        double r3136507 = 1.0;
        double r3136508 = r3136503 * r3136504;
        double r3136509 = r3136508 + r3136505;
        double r3136510 = r3136507 + r3136509;
        double r3136511 = r3136506 - r3136510;
        return r3136511;
}
↓
double f(double __attribute__((unused)) x, double __attribute__((unused)) y, double __attribute__((unused)) z) {
        double r3136512 = 1.0;
        double r3136513 = -r3136512;
        return r3136513;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Target

Original45.1
Target0
Herbie0
\[-1\]

Derivation

  1. Initial program 45.1

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

  2. Simplified0

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

  3. Final simplification0

    \[\leadsto -1\]

Reproduce

herbie shell --seed 2019168 +o rules:numerics
(FPCore (x y z)
  :name "simple fma test"

  :herbie-target
  -1.0

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