Average Error: 0.1 → 0.6
Time: 5.5s
Precision: 64
\[x \cdot \sin y + z \cdot \cos y\]
↓
\[\left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right) \cdot \left(\sqrt[3]{x} \cdot \sin y\right) + z \cdot \cos y\]
x \cdot \sin y + z \cdot \cos y
↓
\left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right) \cdot \left(\sqrt[3]{x} \cdot \sin y\right) + z \cdot \cos y
double f(double x, double y, double z) {
        double r266097 = x;
        double r266098 = y;
        double r266099 = sin(r266098);
        double r266100 = r266097 * r266099;
        double r266101 = z;
        double r266102 = cos(r266098);
        double r266103 = r266101 * r266102;
        double r266104 = r266100 + r266103;
        return r266104;
}
↓
double f(double x, double y, double z) {
        double r266105 = x;
        double r266106 = cbrt(r266105);
        double r266107 = r266106 * r266106;
        double r266108 = y;
        double r266109 = sin(r266108);
        double r266110 = r266106 * r266109;
        double r266111 = r266107 * r266110;
        double r266112 = z;
        double r266113 = cos(r266108);
        double r266114 = r266112 * r266113;
        double r266115 = r266111 + r266114;
        return r266115;
}

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-cbrt0.6

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

  4. Applied associate-*l*0.6

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

  5. Final simplification0.6

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

Reproduce

herbie shell --seed 2019353 
(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))))