Average Error: 0.0 → 0.0
Time: 6.9s
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 r30821 = x;
        double r30822 = 1.0;
        double r30823 = r30821 + r30822;
        double r30824 = y;
        double r30825 = r30823 * r30824;
        double r30826 = r30825 - r30821;
        return r30826;
}
↓
double f(double x, double y) {
        double r30827 = x;
        double r30828 = 1.0;
        double r30829 = r30827 + r30828;
        double r30830 = y;
        double r30831 = -r30827;
        double r30832 = fma(r30829, r30830, r30831);
        return r30832;
}

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 add-cube-cbrt0.6

    \[\leadsto \left(x + 1\right) \cdot y - \color{blue}{\left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right) \cdot \sqrt[3]{x}}\]

  4. Applied prod-diff0.6

    \[\leadsto \color{blue}{\mathsf{fma}\left(x + 1, y, -\sqrt[3]{x} \cdot \left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right)\right) + \mathsf{fma}\left(-\sqrt[3]{x}, \sqrt[3]{x} \cdot \sqrt[3]{x}, \sqrt[3]{x} \cdot \left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right)\right)}\]

  5. Simplified0.0

    \[\leadsto \color{blue}{\mathsf{fma}\left(x + 1, y, -x\right)} + \mathsf{fma}\left(-\sqrt[3]{x}, \sqrt[3]{x} \cdot \sqrt[3]{x}, \sqrt[3]{x} \cdot \left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right)\right)\]

  6. Simplified0.0

    \[\leadsto \mathsf{fma}\left(x + 1, y, -x\right) + \color{blue}{0}\]

  7. Final simplification0.0

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

Reproduce

herbie shell --seed 2019315 +o rules:numerics
(FPCore (x y)
  :name "Data.Colour.SRGB:transferFunction from colour-2.3.3"
  :precision binary64
  (- (* (+ x 1) y) x))