Average Error: 0.1 → 0.4
Time: 5.8s
Precision: 64
\[x \cdot \cos y + z \cdot \sin y\]
↓
\[\left(x \cdot \mathsf{expm1}\left(\mathsf{log1p}\left(\sqrt[3]{\cos y} \cdot \sqrt[3]{\cos y}\right)\right)\right) \cdot \left(\sqrt[3]{\sqrt[3]{\cos y} \cdot \mathsf{log1p}\left(\mathsf{expm1}\left(\sqrt[3]{\cos y}\right)\right)} \cdot \sqrt[3]{\sqrt[3]{\cos y}}\right) + z \cdot \sin y\]
x \cdot \cos y + z \cdot \sin y
↓
\left(x \cdot \mathsf{expm1}\left(\mathsf{log1p}\left(\sqrt[3]{\cos y} \cdot \sqrt[3]{\cos y}\right)\right)\right) \cdot \left(\sqrt[3]{\sqrt[3]{\cos y} \cdot \mathsf{log1p}\left(\mathsf{expm1}\left(\sqrt[3]{\cos y}\right)\right)} \cdot \sqrt[3]{\sqrt[3]{\cos y}}\right) + z \cdot \sin y
double f(double x, double y, double z) {
        double r199244 = x;
        double r199245 = y;
        double r199246 = cos(r199245);
        double r199247 = r199244 * r199246;
        double r199248 = z;
        double r199249 = sin(r199245);
        double r199250 = r199248 * r199249;
        double r199251 = r199247 + r199250;
        return r199251;
}
↓
double f(double x, double y, double z) {
        double r199252 = x;
        double r199253 = y;
        double r199254 = cos(r199253);
        double r199255 = cbrt(r199254);
        double r199256 = r199255 * r199255;
        double r199257 = log1p(r199256);
        double r199258 = expm1(r199257);
        double r199259 = r199252 * r199258;
        double r199260 = expm1(r199255);
        double r199261 = log1p(r199260);
        double r199262 = r199255 * r199261;
        double r199263 = cbrt(r199262);
        double r199264 = cbrt(r199255);
        double r199265 = r199263 * r199264;
        double r199266 = r199259 * r199265;
        double r199267 = z;
        double r199268 = sin(r199253);
        double r199269 = r199267 * r199268;
        double r199270 = r199266 + r199269;
        return r199270;
}

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 expm1-log1p-u0.4

    \[\leadsto \left(x \cdot \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\sqrt[3]{\cos y} \cdot \sqrt[3]{\cos y}\right)\right)}\right) \cdot \sqrt[3]{\cos y} + z \cdot \sin y\]
  7. Using strategy rm

  8. Applied add-cube-cbrt0.4

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

  9. Applied cbrt-prod0.4

    \[\leadsto \left(x \cdot \mathsf{expm1}\left(\mathsf{log1p}\left(\sqrt[3]{\cos y} \cdot \sqrt[3]{\cos y}\right)\right)\right) \cdot \color{blue}{\left(\sqrt[3]{\sqrt[3]{\cos y} \cdot \sqrt[3]{\cos y}} \cdot \sqrt[3]{\sqrt[3]{\cos y}}\right)} + z \cdot \sin y\]
  10. Using strategy rm

  11. Applied log1p-expm1-u0.4

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

  12. Final simplification0.4

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

Reproduce

herbie shell --seed 2020021 +o rules:numerics
(FPCore (x y z)
  :name "Diagrams.ThreeD.Transform:aboutY from diagrams-lib-1.3.0.3"
  :precision binary64
  (+ (* x (cos y)) (* z (sin y))))