Average Error: 44.8 → 0
Time: 12.3s
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 r2786043 = x;
        double r2786044 = y;
        double r2786045 = z;
        double r2786046 = fma(r2786043, r2786044, r2786045);
        double r2786047 = 1.0;
        double r2786048 = r2786043 * r2786044;
        double r2786049 = r2786048 + r2786045;
        double r2786050 = r2786047 + r2786049;
        double r2786051 = r2786046 - r2786050;
        return r2786051;
}
↓
double f(double __attribute__((unused)) x, double __attribute__((unused)) y, double __attribute__((unused)) z) {
        double r2786052 = 1.0;
        double r2786053 = -r2786052;
        return r2786053;
}

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

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

  2. Simplified0

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

  3. Final simplification0

    \[\leadsto -1\]

Reproduce

herbie shell --seed 2019200 +o rules:numerics
(FPCore (x y z)
  :name "simple fma test"

  :herbie-target
  -1.0

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