Average Error: 0.1 → 0.3
Time: 9.5s
Precision: 64
\[x \cdot \cos y + z \cdot \sin y\]
↓
\[\left(x \cdot \left(\sqrt{{\left({\left(\cos y\right)}^{2}\right)}^{\frac{1}{3}}} \cdot \sqrt{\sqrt[3]{{\left(\cos y\right)}^{2}}}\right)\right) \cdot \sqrt[3]{\cos y} + z \cdot \sin y\]
x \cdot \cos y + z \cdot \sin y
↓
\left(x \cdot \left(\sqrt{{\left({\left(\cos y\right)}^{2}\right)}^{\frac{1}{3}}} \cdot \sqrt{\sqrt[3]{{\left(\cos y\right)}^{2}}}\right)\right) \cdot \sqrt[3]{\cos y} + z \cdot \sin y
double f(double x, double y, double z) {
        double r138082 = x;
        double r138083 = y;
        double r138084 = cos(r138083);
        double r138085 = r138082 * r138084;
        double r138086 = z;
        double r138087 = sin(r138083);
        double r138088 = r138086 * r138087;
        double r138089 = r138085 + r138088;
        return r138089;
}
↓
double f(double x, double y, double z) {
        double r138090 = x;
        double r138091 = y;
        double r138092 = cos(r138091);
        double r138093 = 2.0;
        double r138094 = pow(r138092, r138093);
        double r138095 = 0.3333333333333333;
        double r138096 = pow(r138094, r138095);
        double r138097 = sqrt(r138096);
        double r138098 = cbrt(r138094);
        double r138099 = sqrt(r138098);
        double r138100 = r138097 * r138099;
        double r138101 = r138090 * r138100;
        double r138102 = cbrt(r138092);
        double r138103 = r138101 * r138102;
        double r138104 = z;
        double r138105 = sin(r138091);
        double r138106 = r138104 * r138105;
        double r138107 = r138103 + r138106;
        return r138107;
}

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. Using strategy rm

  6. Applied cbrt-unprod0.3

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

  7. Simplified0.3

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

  9. Applied add-sqr-sqrt0.3

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

  11. Applied pow1/30.3

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

  12. Final simplification0.3

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

Reproduce

herbie shell --seed 2019304 
(FPCore (x y z)
  :name "Diagrams.ThreeD.Transform:aboutY from diagrams-lib-1.3.0.3"
  :precision binary64
  (+ (* x (cos y)) (* z (sin y))))