Average Error: 0.1 → 0.6
Time: 16.9s
Precision: 64
\[x \cdot \cos y + z \cdot \sin y\]
↓
\[x \cdot \cos y + \left(\sqrt[3]{z} \cdot \sqrt[3]{z}\right) \cdot \left(\sqrt[3]{z} \cdot \sin y\right)\]
x \cdot \cos y + z \cdot \sin y
↓
x \cdot \cos y + \left(\sqrt[3]{z} \cdot \sqrt[3]{z}\right) \cdot \left(\sqrt[3]{z} \cdot \sin y\right)
double f(double x, double y, double z) {
        double r146206 = x;
        double r146207 = y;
        double r146208 = cos(r146207);
        double r146209 = r146206 * r146208;
        double r146210 = z;
        double r146211 = sin(r146207);
        double r146212 = r146210 * r146211;
        double r146213 = r146209 + r146212;
        return r146213;
}
↓
double f(double x, double y, double z) {
        double r146214 = x;
        double r146215 = y;
        double r146216 = cos(r146215);
        double r146217 = r146214 * r146216;
        double r146218 = z;
        double r146219 = cbrt(r146218);
        double r146220 = r146219 * r146219;
        double r146221 = sin(r146215);
        double r146222 = r146219 * r146221;
        double r146223 = r146220 * r146222;
        double r146224 = r146217 + r146223;
        return r146224;
}

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

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

  3. Applied add-cube-cbrt0.6

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

  4. Applied associate-*l*0.6

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

  5. Final simplification0.6

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

Reproduce

herbie shell --seed 2019303 
(FPCore (x y z)
  :name "Diagrams.ThreeD.Transform:aboutY from diagrams-lib-1.3.0.3"
  :precision binary64
  (+ (* x (cos y)) (* z (sin y))))