Average Error: 0.1 → 0.9
Time: 6.1s
Precision: 64
\[x \cdot \sin y + z \cdot \cos y\]
↓
\[x \cdot \sin y + \left(\sqrt[3]{z} \cdot \sqrt[3]{z}\right) \cdot \left(\sqrt[3]{z} \cdot \cos y\right)\]
x \cdot \sin y + z \cdot \cos y
↓
x \cdot \sin y + \left(\sqrt[3]{z} \cdot \sqrt[3]{z}\right) \cdot \left(\sqrt[3]{z} \cdot \cos y\right)
double f(double x, double y, double z) {
        double r183307 = x;
        double r183308 = y;
        double r183309 = sin(r183308);
        double r183310 = r183307 * r183309;
        double r183311 = z;
        double r183312 = cos(r183308);
        double r183313 = r183311 * r183312;
        double r183314 = r183310 + r183313;
        return r183314;
}
↓
double f(double x, double y, double z) {
        double r183315 = x;
        double r183316 = y;
        double r183317 = sin(r183316);
        double r183318 = r183315 * r183317;
        double r183319 = z;
        double r183320 = cbrt(r183319);
        double r183321 = r183320 * r183320;
        double r183322 = cos(r183316);
        double r183323 = r183320 * r183322;
        double r183324 = r183321 * r183323;
        double r183325 = r183318 + r183324;
        return r183325;
}

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

    \[x \cdot \sin y + z \cdot \cos y\]
  2. Using strategy rm

  3. Applied add-cube-cbrt0.9

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

  4. Applied associate-*l*0.9

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

  5. Final simplification0.9

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

Reproduce

herbie shell --seed 2020060 +o rules:numerics
(FPCore (x y z)
  :name "Diagrams.ThreeD.Transform:aboutX from diagrams-lib-1.3.0.3, B"
  :precision binary64
  (+ (* x (sin y)) (* z (cos y))))