Average Error: 0.1 → 0.3
Time: 18.2s
Precision: 64
\[x \cdot \sin y + z \cdot \cos y\]
↓
\[z \cdot \left({\left(\left(\sqrt[3]{{\left(\cos y\right)}^{2}} \cdot \sqrt[3]{{\left(\cos y\right)}^{2}}\right) \cdot \sqrt[3]{{\left(\cos y\right)}^{2}}\right)}^{\frac{1}{3}} \cdot \sqrt[3]{\cos y}\right) + x \cdot \sin y\]
x \cdot \sin y + z \cdot \cos y
↓
z \cdot \left({\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}} \cdot \sqrt[3]{\cos y}\right) + x \cdot \sin y
double f(double x, double y, double z) {
        double r120601 = x;
        double r120602 = y;
        double r120603 = sin(r120602);
        double r120604 = r120601 * r120603;
        double r120605 = z;
        double r120606 = cos(r120602);
        double r120607 = r120605 * r120606;
        double r120608 = r120604 + r120607;
        return r120608;
}
↓
double f(double x, double y, double z) {
        double r120609 = z;
        double r120610 = y;
        double r120611 = cos(r120610);
        double r120612 = 2.0;
        double r120613 = pow(r120611, r120612);
        double r120614 = cbrt(r120613);
        double r120615 = r120614 * r120614;
        double r120616 = r120615 * r120614;
        double r120617 = 0.3333333333333333;
        double r120618 = pow(r120616, r120617);
        double r120619 = cbrt(r120611);
        double r120620 = r120618 * r120619;
        double r120621 = r120609 * r120620;
        double r120622 = x;
        double r120623 = sin(r120610);
        double r120624 = r120622 * r120623;
        double r120625 = r120621 + r120624;
        return r120625;
}

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. Taylor expanded around inf 0.2

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

  7. Applied add-cube-cbrt0.3

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

  9. Applied add-log-exp0.3

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

  10. Final simplification0.3

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

Reproduce

herbie shell --seed 2019291 
(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))))