Average Error: 0.1 → 0.2
Time: 44.3s
Precision: 64
\[x \cdot \cos y - z \cdot \sin y\]
↓
\[\sqrt[3]{\cos y} \cdot \left({\left(e^{\log \left(\cos y \cdot \cos y\right)}\right)}^{\frac{1}{3}} \cdot x\right) - z \cdot \sin y\]
x \cdot \cos 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) - z \cdot \sin y
double f(double x, double y, double z) {
        double r8426634 = x;
        double r8426635 = y;
        double r8426636 = cos(r8426635);
        double r8426637 = r8426634 * r8426636;
        double r8426638 = z;
        double r8426639 = sin(r8426635);
        double r8426640 = r8426638 * r8426639;
        double r8426641 = r8426637 - r8426640;
        return r8426641;
}
↓
double f(double x, double y, double z) {
        double r8426642 = y;
        double r8426643 = cos(r8426642);
        double r8426644 = cbrt(r8426643);
        double r8426645 = r8426643 * r8426643;
        double r8426646 = log(r8426645);
        double r8426647 = exp(r8426646);
        double r8426648 = 0.3333333333333333;
        double r8426649 = pow(r8426647, r8426648);
        double r8426650 = x;
        double r8426651 = r8426649 * r8426650;
        double r8426652 = r8426644 * r8426651;
        double r8426653 = z;
        double r8426654 = sin(r8426642);
        double r8426655 = r8426653 * r8426654;
        double r8426656 = r8426652 - r8426655;
        return r8426656;
}

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 pow1/316.8

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

  7. Applied pow1/316.8

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

  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

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

Reproduce

herbie shell --seed 2019165 +o rules:numerics
(FPCore (x y z)
  :name "Diagrams.ThreeD.Transform:aboutX from diagrams-lib-1.3.0.3, A"
  (- (* x (cos y)) (* z (sin y))))