Average Error: 0.0 → 0.0
Time: 7.5s
Precision: 64
\[\left(x + 1\right) \cdot y - x\]
↓
\[\mathsf{fma}\left(y, x + 1, -x\right) + \left(x - x\right)\]
\left(x + 1\right) \cdot y - x
↓
\mathsf{fma}\left(y, x + 1, -x\right) + \left(x - x\right)
double f(double x, double y) {
        double r225944 = x;
        double r225945 = 1.0;
        double r225946 = r225944 + r225945;
        double r225947 = y;
        double r225948 = r225946 * r225947;
        double r225949 = r225948 - r225944;
        return r225949;
}
↓
double f(double x, double y) {
        double r225950 = y;
        double r225951 = x;
        double r225952 = 1.0;
        double r225953 = r225951 + r225952;
        double r225954 = -r225951;
        double r225955 = fma(r225950, r225953, r225954);
        double r225956 = r225951 - r225951;
        double r225957 = r225955 + r225956;
        return r225957;
}

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

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

  6. Simplified0.0

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

  7. Final simplification0.0

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

Reproduce

herbie shell --seed 2020043 +o rules:numerics
(FPCore (x y)
  :name "Data.Colour.SRGB:transferFunction from colour-2.3.3"
  :precision binary64
  (- (* (+ x 1) y) x))