Average Error: 0.0 → 0.0
Time: 13.0s
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 r149013 = x;
        double r149014 = 1.0;
        double r149015 = r149013 + r149014;
        double r149016 = y;
        double r149017 = r149015 * r149016;
        double r149018 = r149017 - r149013;
        return r149018;
}
↓
double f(double x, double y) {
        double r149019 = x;
        double r149020 = 1.0;
        double r149021 = r149019 + r149020;
        double r149022 = y;
        double r149023 = -r149019;
        double r149024 = fma(r149021, r149022, r149023);
        return r149024;
}

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 2019323 +o rules:numerics
(FPCore (x y)
  :name "Data.Colour.SRGB:transferFunction from colour-2.3.3"
  :precision binary64
  (- (* (+ x 1) y) x))