Average Error: 0.1 → 0.2
Time: 19.1s
Precision: 64
\[x \cdot \sin y + z \cdot \cos y\]
↓
\[\sqrt[3]{\cos y} \cdot \left({\left(\sqrt[3]{\left(\cos y \cdot \left(\cos y \cdot \cos y\right)\right) \cdot \left(\cos y \cdot \left(\cos y \cdot \cos y\right)\right)}\right)}^{\frac{1}{3}} \cdot z\right) + x \cdot \sin y\]
x \cdot \sin y + z \cdot \cos y
↓
\sqrt[3]{\cos y} \cdot \left({\left(\sqrt[3]{\left(\cos y \cdot \left(\cos y \cdot \cos y\right)\right) \cdot \left(\cos y \cdot \left(\cos y \cdot \cos y\right)\right)}\right)}^{\frac{1}{3}} \cdot z\right) + x \cdot \sin y
double f(double x, double y, double z) {
        double r12112381 = x;
        double r12112382 = y;
        double r12112383 = sin(r12112382);
        double r12112384 = r12112381 * r12112383;
        double r12112385 = z;
        double r12112386 = cos(r12112382);
        double r12112387 = r12112385 * r12112386;
        double r12112388 = r12112384 + r12112387;
        return r12112388;
}
↓
double f(double x, double y, double z) {
        double r12112389 = y;
        double r12112390 = cos(r12112389);
        double r12112391 = cbrt(r12112390);
        double r12112392 = r12112390 * r12112390;
        double r12112393 = r12112390 * r12112392;
        double r12112394 = r12112393 * r12112393;
        double r12112395 = cbrt(r12112394);
        double r12112396 = 0.3333333333333333;
        double r12112397 = pow(r12112395, r12112396);
        double r12112398 = z;
        double r12112399 = r12112397 * r12112398;
        double r12112400 = r12112391 * r12112399;
        double r12112401 = x;
        double r12112402 = sin(r12112389);
        double r12112403 = r12112401 * r12112402;
        double r12112404 = r12112400 + r12112403;
        return r12112404;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

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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 pow1/316.4

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

  7. Applied pow1/316.4

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

  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. Using strategy rm

  10. Applied add-cbrt-cube0.2

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

  11. Applied add-cbrt-cube0.3

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

  12. Applied cbrt-unprod0.2

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

  13. Final simplification0.2

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

Reproduce

herbie shell --seed 2019179 
(FPCore (x y z)
  :name "Diagrams.ThreeD.Transform:aboutX from diagrams-lib-1.3.0.3, B"
  (+ (* x (sin y)) (* z (cos y))))