Average Error: 44.3 → 0
Time: 6.3s
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 r1802029 = x;
        double r1802030 = y;
        double r1802031 = z;
        double r1802032 = fma(r1802029, r1802030, r1802031);
        double r1802033 = 1.0;
        double r1802034 = r1802029 * r1802030;
        double r1802035 = r1802034 + r1802031;
        double r1802036 = r1802033 + r1802035;
        double r1802037 = r1802032 - r1802036;
        return r1802037;
}
↓
double f(double __attribute__((unused)) x, double __attribute__((unused)) y, double __attribute__((unused)) z) {
        double r1802038 = -1.0;
        return r1802038;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Target

Original44.3
Target0
Herbie0
\[-1\]

Derivation

  1. Initial program 44.3

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

  2. Simplified0

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

  3. Final simplification0

    \[\leadsto -1\]

Reproduce

herbie shell --seed 2019164 +o rules:numerics
(FPCore (x y z)
  :name "simple fma test"

  :herbie-target
  -1

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