Average Error: 0.1 → 0.2
Time: 17.7s
Precision: 64
\[x \cdot \cos y + z \cdot \sin y\]
↓
\[z \cdot \sin y + \left(x \cdot {\left({\left(\cos y\right)}^{2}\right)}^{\frac{1}{3}}\right) \cdot \sqrt[3]{\cos y}\]
x \cdot \cos y + z \cdot \sin y
↓
z \cdot \sin y + \left(x \cdot {\left({\left(\cos y\right)}^{2}\right)}^{\frac{1}{3}}\right) \cdot \sqrt[3]{\cos y}
double f(double x, double y, double z) {
        double r181097 = x;
        double r181098 = y;
        double r181099 = cos(r181098);
        double r181100 = r181097 * r181099;
        double r181101 = z;
        double r181102 = sin(r181098);
        double r181103 = r181101 * r181102;
        double r181104 = r181100 + r181103;
        return r181104;
}
↓
double f(double x, double y, double z) {
        double r181105 = z;
        double r181106 = y;
        double r181107 = sin(r181106);
        double r181108 = r181105 * r181107;
        double r181109 = x;
        double r181110 = cos(r181106);
        double r181111 = 2.0;
        double r181112 = pow(r181110, r181111);
        double r181113 = 0.3333333333333333;
        double r181114 = pow(r181112, r181113);
        double r181115 = r181109 * r181114;
        double r181116 = cbrt(r181110);
        double r181117 = r181115 * r181116;
        double r181118 = r181108 + r181117;
        return r181118;
}

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-cbrt0.4

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

  4. Applied associate-*r*0.4

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

  5. Simplified0.4

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

  6. Taylor expanded around inf 0.2

    \[\leadsto \color{blue}{\left(x \cdot {\left({\left(\cos y\right)}^{2}\right)}^{\frac{1}{3}}\right)} \cdot \sqrt[3]{\cos y} + z \cdot \sin y\]

  7. Simplified0.3

    \[\leadsto \color{blue}{\left(x \cdot \sqrt[3]{{\left(\cos y\right)}^{2}}\right)} \cdot \sqrt[3]{\cos y} + z \cdot \sin y\]
  8. Using strategy rm

  9. Applied pow1/30.2

    \[\leadsto \left(x \cdot \color{blue}{{\left({\left(\cos y\right)}^{2}\right)}^{\frac{1}{3}}}\right) \cdot \sqrt[3]{\cos y} + z \cdot \sin y\]

  10. Final simplification0.2

    \[\leadsto z \cdot \sin y + \left(x \cdot {\left({\left(\cos y\right)}^{2}\right)}^{\frac{1}{3}}\right) \cdot \sqrt[3]{\cos y}\]

Reproduce

herbie shell --seed 2019195 
(FPCore (x y z)
  :name "Diagrams.ThreeD.Transform:aboutY from diagrams-lib-1.3.0.3"
  (+ (* x (cos y)) (* z (sin y))))