Average Error: 0.1 → 0.2
Time: 20.1s
Precision: 64
\[x \cdot \cos y + z \cdot \sin y\]
↓
\[z \cdot \sin y + \sqrt[3]{\cos y} \cdot \left({\left(e^{\log \left(\cos y \cdot \cos y\right)}\right)}^{\frac{1}{3}} \cdot x\right)\]
x \cdot \cos y + z \cdot \sin y
↓
z \cdot \sin y + \sqrt[3]{\cos y} \cdot \left({\left(e^{\log \left(\cos y \cdot \cos y\right)}\right)}^{\frac{1}{3}} \cdot x\right)
double f(double x, double y, double z) {
        double r8549123 = x;
        double r8549124 = y;
        double r8549125 = cos(r8549124);
        double r8549126 = r8549123 * r8549125;
        double r8549127 = z;
        double r8549128 = sin(r8549124);
        double r8549129 = r8549127 * r8549128;
        double r8549130 = r8549126 + r8549129;
        return r8549130;
}
↓
double f(double x, double y, double z) {
        double r8549131 = z;
        double r8549132 = y;
        double r8549133 = sin(r8549132);
        double r8549134 = r8549131 * r8549133;
        double r8549135 = cos(r8549132);
        double r8549136 = cbrt(r8549135);
        double r8549137 = r8549135 * r8549135;
        double r8549138 = log(r8549137);
        double r8549139 = exp(r8549138);
        double r8549140 = 0.3333333333333333;
        double r8549141 = pow(r8549139, r8549140);
        double r8549142 = x;
        double r8549143 = r8549141 * r8549142;
        double r8549144 = r8549136 * r8549143;
        double r8549145 = r8549134 + r8549144;
        return r8549145;
}

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 pow1/316.3

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

  7. Applied pow1/316.3

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

  8. Applied pow-prod-down0.2

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

  10. Applied add-exp-log0.2

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

  11. Final simplification0.2

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

Reproduce

herbie shell --seed 2019165 
(FPCore (x y z)
  :name "Diagrams.ThreeD.Transform:aboutY from diagrams-lib-1.3.0.3"
  (+ (* x (cos y)) (* z (sin y))))