Average Error: 0.1 → 0.2
Time: 5.1s
Precision: 64
\[x \cdot \sin y + z \cdot \cos y\]
↓
\[x \cdot \sin y + \left(z \cdot {\left({\left(\sqrt{{\left(\cos y\right)}^{2}}\right)}^{\frac{2}{3}} \cdot \left({\left(\sqrt{{\left(\cos y\right)}^{2}}\right)}^{\frac{2}{3}} \cdot {\left({\left(\cos y\right)}^{2}\right)}^{\frac{1}{3}}\right)\right)}^{\frac{1}{3}}\right) \cdot \sqrt[3]{\cos y}\]
x \cdot \sin y + z \cdot \cos y
↓
x \cdot \sin y + \left(z \cdot {\left({\left(\sqrt{{\left(\cos y\right)}^{2}}\right)}^{\frac{2}{3}} \cdot \left({\left(\sqrt{{\left(\cos y\right)}^{2}}\right)}^{\frac{2}{3}} \cdot {\left({\left(\cos y\right)}^{2}\right)}^{\frac{1}{3}}\right)\right)}^{\frac{1}{3}}\right) \cdot \sqrt[3]{\cos y}
double f(double x, double y, double z) {
        double r247098 = x;
        double r247099 = y;
        double r247100 = sin(r247099);
        double r247101 = r247098 * r247100;
        double r247102 = z;
        double r247103 = cos(r247099);
        double r247104 = r247102 * r247103;
        double r247105 = r247101 + r247104;
        return r247105;
}
↓
double f(double x, double y, double z) {
        double r247106 = x;
        double r247107 = y;
        double r247108 = sin(r247107);
        double r247109 = r247106 * r247108;
        double r247110 = z;
        double r247111 = cos(r247107);
        double r247112 = 2.0;
        double r247113 = pow(r247111, r247112);
        double r247114 = sqrt(r247113);
        double r247115 = 0.6666666666666666;
        double r247116 = pow(r247114, r247115);
        double r247117 = 0.3333333333333333;
        double r247118 = pow(r247113, r247117);
        double r247119 = r247116 * r247118;
        double r247120 = r247116 * r247119;
        double r247121 = pow(r247120, r247117);
        double r247122 = r247110 * r247121;
        double r247123 = cbrt(r247111);
        double r247124 = r247122 * r247123;
        double r247125 = r247109 + r247124;
        return r247125;
}

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-cbrt0.4

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

  4. Applied associate-*r*0.4

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

  6. Applied pow1/316.0

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

  7. Applied pow1/315.9

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

  8. Applied pow-prod-down0.2

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

  9. Simplified0.2

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

  11. Applied add-cube-cbrt0.3

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

  12. Simplified0.2

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

  13. Simplified0.2

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

  15. Applied add-sqr-sqrt0.2

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

  16. Applied unpow-prod-down0.2

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

  17. Applied associate-*l*0.2

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

  18. Final simplification0.2

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

Reproduce

herbie shell --seed 2020049 
(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))))