Average Error: 45.3 → 0
Time: 10.1s
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 r9075 = x;
        double r9076 = y;
        double r9077 = z;
        double r9078 = fma(r9075, r9076, r9077);
        double r9079 = 1.0;
        double r9080 = r9075 * r9076;
        double r9081 = r9080 + r9077;
        double r9082 = r9079 + r9081;
        double r9083 = r9078 - r9082;
        return r9083;
}
↓
double f(double __attribute__((unused)) x, double __attribute__((unused)) y, double __attribute__((unused)) z) {
        double r9084 = 1.0;
        double r9085 = -r9084;
        return r9085;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Target

Original45.3
Target0
Herbie0
\[-1\]

Derivation

  1. Initial program 45.3

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

  2. Simplified0

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

  3. Final simplification0

    \[\leadsto -1\]

Reproduce

herbie shell --seed 2019315 +o rules:numerics
(FPCore (x y z)
  :name "simple fma test"
  :precision binary64

  :herbie-target
  -1

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