Average Error: 0.1 → 0.2
Time: 20.3s
Precision: 64
\[x \cdot \cos y + z \cdot \sin y\]
↓
\[\sqrt[3]{\cos y} \cdot \left({\left(\cos y \cdot \cos y\right)}^{\frac{1}{3}} \cdot x\right) + z \cdot \sin y\]
x \cdot \cos y + z \cdot \sin y
↓
\sqrt[3]{\cos y} \cdot \left({\left(\cos y \cdot \cos y\right)}^{\frac{1}{3}} \cdot x\right) + z \cdot \sin y
double f(double x, double y, double z) {
        double r9816594 = x;
        double r9816595 = y;
        double r9816596 = cos(r9816595);
        double r9816597 = r9816594 * r9816596;
        double r9816598 = z;
        double r9816599 = sin(r9816595);
        double r9816600 = r9816598 * r9816599;
        double r9816601 = r9816597 + r9816600;
        return r9816601;
}
↓
double f(double x, double y, double z) {
        double r9816602 = y;
        double r9816603 = cos(r9816602);
        double r9816604 = cbrt(r9816603);
        double r9816605 = r9816603 * r9816603;
        double r9816606 = 0.3333333333333333;
        double r9816607 = pow(r9816605, r9816606);
        double r9816608 = x;
        double r9816609 = r9816607 * r9816608;
        double r9816610 = r9816604 * r9816609;
        double r9816611 = z;
        double r9816612 = sin(r9816602);
        double r9816613 = r9816611 * r9816612;
        double r9816614 = r9816610 + r9816613;
        return r9816614;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

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Your Program's Arguments

Results

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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 pow1/315.2

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

  7. Applied pow1/315.2

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

  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. Final simplification0.2

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

Reproduce

herbie shell --seed 2019164 
(FPCore (x y z)
  :name "Diagrams.ThreeD.Transform:aboutY from diagrams-lib-1.3.0.3"
  (+ (* x (cos y)) (* z (sin y))))