Average Error: 0.1 → 0.4
Time: 6.0s
Precision: 64
\[x \cdot \sin y + z \cdot \cos y\]
↓
\[x \cdot \sin y + \left(z \cdot \left(\sqrt[3]{\cos y} \cdot \sqrt[3]{\cos y}\right)\right) \cdot \sqrt[3]{\cos y}\]
x \cdot \sin y + z \cdot \cos y
↓
x \cdot \sin y + \left(z \cdot \left(\sqrt[3]{\cos y} \cdot \sqrt[3]{\cos y}\right)\right) \cdot \sqrt[3]{\cos y}
double f(double x, double y, double z) {
        double r292542 = x;
        double r292543 = y;
        double r292544 = sin(r292543);
        double r292545 = r292542 * r292544;
        double r292546 = z;
        double r292547 = cos(r292543);
        double r292548 = r292546 * r292547;
        double r292549 = r292545 + r292548;
        return r292549;
}
↓
double f(double x, double y, double z) {
        double r292550 = x;
        double r292551 = y;
        double r292552 = sin(r292551);
        double r292553 = r292550 * r292552;
        double r292554 = z;
        double r292555 = cos(r292551);
        double r292556 = cbrt(r292555);
        double r292557 = r292556 * r292556;
        double r292558 = r292554 * r292557;
        double r292559 = r292558 * r292556;
        double r292560 = r292553 + r292559;
        return r292560;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.1

    \[x \cdot \sin y + z \cdot \cos y\]
  2. Using strategy rm

  3. Applied add-cube-cbrt0.4

    \[\leadsto x \cdot \sin y + z \cdot \color{blue}{\left(\left(\sqrt[3]{\cos y} \cdot \sqrt[3]{\cos y}\right) \cdot \sqrt[3]{\cos y}\right)}\]

  4. Applied associate-*r*0.4

    \[\leadsto x \cdot \sin y + \color{blue}{\left(z \cdot \left(\sqrt[3]{\cos y} \cdot \sqrt[3]{\cos y}\right)\right) \cdot \sqrt[3]{\cos y}}\]

  5. Final simplification0.4

    \[\leadsto x \cdot \sin y + \left(z \cdot \left(\sqrt[3]{\cos y} \cdot \sqrt[3]{\cos y}\right)\right) \cdot \sqrt[3]{\cos y}\]

Reproduce

herbie shell --seed 2020065 
(FPCore (x y z)
  :name "Diagrams.ThreeD.Transform:aboutX from diagrams-lib-1.3.0.3, B"
  :precision binary64
  (+ (* x (sin y)) (* z (cos y))))