Average Error: 0.0 → 0.0
Time: 9.1s
Precision: 64
\[200 \cdot \left(x - y\right)\]
↓
\[\mathsf{fma}\left(x, {\left(\sqrt[3]{200}\right)}^{3}, {\left(\sqrt[3]{200}\right)}^{3} \cdot \left(-y\right)\right)\]
200 \cdot \left(x - y\right)
↓
\mathsf{fma}\left(x, {\left(\sqrt[3]{200}\right)}^{3}, {\left(\sqrt[3]{200}\right)}^{3} \cdot \left(-y\right)\right)
double f(double x, double y) {
        double r247479 = 200.0;
        double r247480 = x;
        double r247481 = y;
        double r247482 = r247480 - r247481;
        double r247483 = r247479 * r247482;
        return r247483;
}
↓
double f(double x, double y) {
        double r247484 = x;
        double r247485 = 200.0;
        double r247486 = cbrt(r247485);
        double r247487 = 3.0;
        double r247488 = pow(r247486, r247487);
        double r247489 = y;
        double r247490 = -r247489;
        double r247491 = r247488 * r247490;
        double r247492 = fma(r247484, r247488, r247491);
        return r247492;
}

Error

Bits error versus x

Bits error versus y

Derivation

  1. Initial program 0.0

    \[200 \cdot \left(x - y\right)\]
  2. Using strategy rm

  3. Applied add-cube-cbrt0.9

    \[\leadsto \color{blue}{\left(\left(\sqrt[3]{200} \cdot \sqrt[3]{200}\right) \cdot \sqrt[3]{200}\right)} \cdot \left(x - y\right)\]

  4. Applied associate-*l*0.5

    \[\leadsto \color{blue}{\left(\sqrt[3]{200} \cdot \sqrt[3]{200}\right) \cdot \left(\sqrt[3]{200} \cdot \left(x - y\right)\right)}\]
  5. Using strategy rm

  6. Applied sub-neg0.5

    \[\leadsto \left(\sqrt[3]{200} \cdot \sqrt[3]{200}\right) \cdot \left(\sqrt[3]{200} \cdot \color{blue}{\left(x + \left(-y\right)\right)}\right)\]

  7. Applied distribute-rgt-in0.5

    \[\leadsto \left(\sqrt[3]{200} \cdot \sqrt[3]{200}\right) \cdot \color{blue}{\left(x \cdot \sqrt[3]{200} + \left(-y\right) \cdot \sqrt[3]{200}\right)}\]

  8. Applied distribute-lft-in0.5

    \[\leadsto \color{blue}{\left(\sqrt[3]{200} \cdot \sqrt[3]{200}\right) \cdot \left(x \cdot \sqrt[3]{200}\right) + \left(\sqrt[3]{200} \cdot \sqrt[3]{200}\right) \cdot \left(\left(-y\right) \cdot \sqrt[3]{200}\right)}\]

  9. Simplified0.3

    \[\leadsto \color{blue}{x \cdot {\left(\sqrt[3]{200}\right)}^{3}} + \left(\sqrt[3]{200} \cdot \sqrt[3]{200}\right) \cdot \left(\left(-y\right) \cdot \sqrt[3]{200}\right)\]

  10. Simplified0.0

    \[\leadsto x \cdot {\left(\sqrt[3]{200}\right)}^{3} + \color{blue}{{\left(\sqrt[3]{200}\right)}^{3} \cdot \left(-y\right)}\]
  11. Using strategy rm

  12. Applied fma-def0.0

    \[\leadsto \color{blue}{\mathsf{fma}\left(x, {\left(\sqrt[3]{200}\right)}^{3}, {\left(\sqrt[3]{200}\right)}^{3} \cdot \left(-y\right)\right)}\]

  13. Final simplification0.0

    \[\leadsto \mathsf{fma}\left(x, {\left(\sqrt[3]{200}\right)}^{3}, {\left(\sqrt[3]{200}\right)}^{3} \cdot \left(-y\right)\right)\]

Reproduce

herbie shell --seed 2019212 +o rules:numerics
(FPCore (x y)
  :name "Data.Colour.CIE:cieLABView from colour-2.3.3, C"
  :precision binary64
  (* 200 (- x y)))