Diagrams.ThreeD.Transform:aboutX from diagrams-lib-1.3.0.3, B

Average Error: 0.1 → 0.6

Time: 19.8s

Precision: 64

Math

\[x \cdot \sin y + z \cdot \cos y\]

↓

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

C

double f(double x, double y, double z) {
        double r11343147 = x;
        double r11343148 = y;
        double r11343149 = sin(r11343148);
        double r11343150 = r11343147 * r11343149;
        double r11343151 = z;
        double r11343152 = cos(r11343148);
        double r11343153 = r11343151 * r11343152;
        double r11343154 = r11343150 + r11343153;
        return r11343154;
}

↓

double f(double x, double y, double z) {
        double r11343155 = x;
        double r11343156 = y;
        double r11343157 = sin(r11343156);
        double r11343158 = r11343155 * r11343157;
        double r11343159 = cbrt(r11343158);
        double r11343160 = r11343159 * r11343159;
        double r11343161 = r11343159 * r11343160;
        double r11343162 = z;
        double r11343163 = cos(r11343156);
        double r11343164 = r11343162 * r11343163;
        double r11343165 = r11343161 + r11343164;
        return r11343165;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Derivation

1. Initial program 0.1

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

3. Applied add-cube-cbrt 0.6

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

4. Final simplification 0.6

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

Reproduce

herbie shell --seed 2019169 
(FPCore (x y z)
  :name "Diagrams.ThreeD.Transform:aboutX from diagrams-lib-1.3.0.3, B"
  (+ (* x (sin y)) (* z (cos y))))