Average Error: 0.1 → 0.2
Time: 16.3s
Precision: 64
\[\left(\left(x \cdot x + y \cdot y\right) + y \cdot y\right) + y \cdot y\]
↓
\[x \cdot x + \left(\left(\sqrt{\sqrt[3]{3}} \cdot \left(\sqrt{\sqrt[3]{3}} \cdot y\right)\right) \cdot y\right) \cdot \left(\sqrt[3]{3} \cdot \sqrt[3]{3}\right)\]
\left(\left(x \cdot x + y \cdot y\right) + y \cdot y\right) + y \cdot y
↓
x \cdot x + \left(\left(\sqrt{\sqrt[3]{3}} \cdot \left(\sqrt{\sqrt[3]{3}} \cdot y\right)\right) \cdot y\right) \cdot \left(\sqrt[3]{3} \cdot \sqrt[3]{3}\right)
double f(double x, double y) {
        double r36490160 = x;
        double r36490161 = r36490160 * r36490160;
        double r36490162 = y;
        double r36490163 = r36490162 * r36490162;
        double r36490164 = r36490161 + r36490163;
        double r36490165 = r36490164 + r36490163;
        double r36490166 = r36490165 + r36490163;
        return r36490166;
}
↓
double f(double x, double y) {
        double r36490167 = x;
        double r36490168 = r36490167 * r36490167;
        double r36490169 = 3.0;
        double r36490170 = cbrt(r36490169);
        double r36490171 = sqrt(r36490170);
        double r36490172 = y;
        double r36490173 = r36490171 * r36490172;
        double r36490174 = r36490171 * r36490173;
        double r36490175 = r36490174 * r36490172;
        double r36490176 = r36490170 * r36490170;
        double r36490177 = r36490175 * r36490176;
        double r36490178 = r36490168 + r36490177;
        return r36490178;
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original0.1
Target0.1
Herbie0.2
\[x \cdot x + y \cdot \left(y + \left(y + y\right)\right)\]

Derivation

  1. Initial program 0.1

    \[\left(\left(x \cdot x + y \cdot y\right) + y \cdot y\right) + y \cdot y\]

  2. Simplified0.1

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

  4. Applied associate-*r*0.1

    \[\leadsto \color{blue}{\left(3 \cdot y\right) \cdot y} + x \cdot x\]
  5. Using strategy rm

  6. Applied add-cube-cbrt0.1

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

  7. Applied associate-*l*0.2

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

  8. Applied associate-*l*0.2

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

  10. Applied add-sqr-sqrt0.3

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

  11. Applied associate-*l*0.2

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

  12. Final simplification0.2

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

Reproduce

herbie shell --seed 2019158 
(FPCore (x y)
  :name "Linear.Quaternion:$c/ from linear-1.19.1.3, E"

  :herbie-target
  (+ (* x x) (* y (+ y (+ y y))))

  (+ (+ (+ (* x x) (* y y)) (* y y)) (* y y)))