Average Error: 0.1 → 0.3
Time: 5.1s
Precision: 64
\[x \cdot \cos y - z \cdot \sin y\]
↓
\[\left(x \cdot \mathsf{expm1}\left(\mathsf{log1p}\left(\sqrt[3]{{\left(\cos y\right)}^{2}}\right)\right)\right) \cdot \sqrt[3]{\cos y} - z \cdot \sin y\]
x \cdot \cos y - z \cdot \sin y
↓
\left(x \cdot \mathsf{expm1}\left(\mathsf{log1p}\left(\sqrt[3]{{\left(\cos y\right)}^{2}}\right)\right)\right) \cdot \sqrt[3]{\cos y} - z \cdot \sin y
double f(double x, double y, double z) {
        double r235175 = x;
        double r235176 = y;
        double r235177 = cos(r235176);
        double r235178 = r235175 * r235177;
        double r235179 = z;
        double r235180 = sin(r235176);
        double r235181 = r235179 * r235180;
        double r235182 = r235178 - r235181;
        return r235182;
}
↓
double f(double x, double y, double z) {
        double r235183 = x;
        double r235184 = y;
        double r235185 = cos(r235184);
        double r235186 = 2.0;
        double r235187 = pow(r235185, r235186);
        double r235188 = cbrt(r235187);
        double r235189 = log1p(r235188);
        double r235190 = expm1(r235189);
        double r235191 = r235183 * r235190;
        double r235192 = cbrt(r235185);
        double r235193 = r235191 * r235192;
        double r235194 = z;
        double r235195 = sin(r235184);
        double r235196 = r235194 * r235195;
        double r235197 = r235193 - r235196;
        return r235197;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

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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 cbrt-unprod0.3

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

  7. Simplified0.3

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

  9. Applied expm1-log1p-u0.3

    \[\leadsto \left(x \cdot \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\sqrt[3]{{\left(\cos y\right)}^{2}}\right)\right)}\right) \cdot \sqrt[3]{\cos y} - z \cdot \sin y\]

  10. Final simplification0.3

    \[\leadsto \left(x \cdot \mathsf{expm1}\left(\mathsf{log1p}\left(\sqrt[3]{{\left(\cos y\right)}^{2}}\right)\right)\right) \cdot \sqrt[3]{\cos y} - z \cdot \sin y\]

Reproduce

herbie shell --seed 2020002 +o rules:numerics
(FPCore (x y z)
  :name "Diagrams.ThreeD.Transform:aboutX from diagrams-lib-1.3.0.3, A"
  :precision binary64
  (- (* x (cos y)) (* z (sin y))))