Average Error: 0.0 → 0.0
Time: 8.5s
Precision: 64
\[\left(x + 1\right) \cdot y - x\]
↓
\[\mathsf{fma}\left(1 + x, y, -x\right)\]
\left(x + 1\right) \cdot y - x
↓
\mathsf{fma}\left(1 + x, y, -x\right)
double f(double x, double y) {
        double r7533158 = x;
        double r7533159 = 1.0;
        double r7533160 = r7533158 + r7533159;
        double r7533161 = y;
        double r7533162 = r7533160 * r7533161;
        double r7533163 = r7533162 - r7533158;
        return r7533163;
}
↓
double f(double x, double y) {
        double r7533164 = 1.0;
        double r7533165 = x;
        double r7533166 = r7533164 + r7533165;
        double r7533167 = y;
        double r7533168 = -r7533165;
        double r7533169 = fma(r7533166, r7533167, r7533168);
        return r7533169;
}

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

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

Reproduce

herbie shell --seed 2019171 +o rules:numerics
(FPCore (x y)
  :name "Data.Colour.SRGB:transferFunction from colour-2.3.3"
  (- (* (+ x 1.0) y) x))