Average Error: 0.1 → 0.6
Time: 19.7s
Precision: 64
\[x \cdot \cos y + z \cdot \sin y\]
↓
\[x \cdot \cos y + \sqrt[3]{\sin y \cdot z} \cdot \left(\left(\sqrt[3]{\sin y} \cdot \sqrt[3]{\sin y}\right) \cdot \left(\sqrt[3]{z} \cdot \sqrt[3]{z}\right)\right)\]
x \cdot \cos y + z \cdot \sin y
↓
x \cdot \cos y + \sqrt[3]{\sin y \cdot z} \cdot \left(\left(\sqrt[3]{\sin y} \cdot \sqrt[3]{\sin y}\right) \cdot \left(\sqrt[3]{z} \cdot \sqrt[3]{z}\right)\right)
double f(double x, double y, double z) {
        double r12578139 = x;
        double r12578140 = y;
        double r12578141 = cos(r12578140);
        double r12578142 = r12578139 * r12578141;
        double r12578143 = z;
        double r12578144 = sin(r12578140);
        double r12578145 = r12578143 * r12578144;
        double r12578146 = r12578142 + r12578145;
        return r12578146;
}
↓
double f(double x, double y, double z) {
        double r12578147 = x;
        double r12578148 = y;
        double r12578149 = cos(r12578148);
        double r12578150 = r12578147 * r12578149;
        double r12578151 = sin(r12578148);
        double r12578152 = z;
        double r12578153 = r12578151 * r12578152;
        double r12578154 = cbrt(r12578153);
        double r12578155 = cbrt(r12578151);
        double r12578156 = r12578155 * r12578155;
        double r12578157 = cbrt(r12578152);
        double r12578158 = r12578157 * r12578157;
        double r12578159 = r12578156 * r12578158;
        double r12578160 = r12578154 * r12578159;
        double r12578161 = r12578150 + r12578160;
        return r12578161;
}

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-cbrt0.6

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

  5. Applied cbrt-prod0.5

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

  6. Applied cbrt-prod0.6

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

  7. Applied swap-sqr0.6

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

  8. Final simplification0.6

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

Reproduce

herbie shell --seed 2019162 
(FPCore (x y z)
  :name "Diagrams.ThreeD.Transform:aboutY from diagrams-lib-1.3.0.3"
  (+ (* x (cos y)) (* z (sin y))))