Average Error: 0.1 → 0.3
Time: 20.3s
Precision: 64
\[x \cdot \cos y - z \cdot \sin y\]
↓
\[\left(\sqrt[3]{\cos y \cdot \cos y} \cdot x\right) \cdot \sqrt[3]{\cos y} - \sin y \cdot z\]
x \cdot \cos y - z \cdot \sin y
↓
\left(\sqrt[3]{\cos y \cdot \cos y} \cdot x\right) \cdot \sqrt[3]{\cos y} - \sin y \cdot z
double f(double x, double y, double z) {
        double r7806203 = x;
        double r7806204 = y;
        double r7806205 = cos(r7806204);
        double r7806206 = r7806203 * r7806205;
        double r7806207 = z;
        double r7806208 = sin(r7806204);
        double r7806209 = r7806207 * r7806208;
        double r7806210 = r7806206 - r7806209;
        return r7806210;
}
↓
double f(double x, double y, double z) {
        double r7806211 = y;
        double r7806212 = cos(r7806211);
        double r7806213 = r7806212 * r7806212;
        double r7806214 = cbrt(r7806213);
        double r7806215 = x;
        double r7806216 = r7806214 * r7806215;
        double r7806217 = cbrt(r7806212);
        double r7806218 = r7806216 * r7806217;
        double r7806219 = sin(r7806211);
        double r7806220 = z;
        double r7806221 = r7806219 * r7806220;
        double r7806222 = r7806218 - r7806221;
        return r7806222;
}

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 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. Final simplification0.3

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

Reproduce

herbie shell --seed 2019164 +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))))