Average Error: 0.0 → 0.0
Time: 1.8s
Precision: 64
\[\left(x + 1\right) \cdot y - x\]
↓
\[\mathsf{fma}\left(x + 1, y, -x\right)\]
\left(x + 1\right) \cdot y - x
↓
\mathsf{fma}\left(x + 1, y, -x\right)
double f(double x, double y) {
        double r1092 = x;
        double r1093 = 1.0;
        double r1094 = r1092 + r1093;
        double r1095 = y;
        double r1096 = r1094 * r1095;
        double r1097 = r1096 - r1092;
        return r1097;
}
↓
double f(double x, double y) {
        double r1098 = x;
        double r1099 = 1.0;
        double r1100 = r1098 + r1099;
        double r1101 = y;
        double r1102 = -r1098;
        double r1103 = fma(r1100, r1101, r1102);
        return r1103;
}

Error

Bits error versus x

Bits error versus y

Derivation

  1. Initial program 0.0

    \[\left(x + 1\right) \cdot y - x\]
  2. Using strategy rm

  3. Applied fma-neg0.0

    \[\leadsto \color{blue}{\mathsf{fma}\left(x + 1, y, -x\right)}\]

  4. Final simplification0.0

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

Reproduce

herbie shell --seed 2020025 +o rules:numerics
(FPCore (x y)
  :name "Data.Colour.SRGB:transferFunction from colour-2.3.3"
  :precision binary64
  (- (* (+ x 1) y) x))