Average Error: 4.6 → 2.3
Time: 21.0s
Precision: 64
\[x + \left(y \cdot z\right) \cdot \left(\tanh \left(\frac{t}{y}\right) - \tanh \left(\frac{x}{y}\right)\right)\]
↓
\[x + \left(\sqrt[3]{y \cdot \left(z \cdot \left(\tanh \left(\frac{t}{y}\right) - \tanh \left(\frac{x}{y}\right)\right)\right)} \cdot \sqrt[3]{y \cdot \left(z \cdot \left(\tanh \left(\frac{t}{y}\right) - \tanh \left(\frac{x}{y}\right)\right)\right)}\right) \cdot \sqrt[3]{\left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) \cdot \left(\sqrt[3]{y} \cdot \left(z \cdot \left(\tanh \left(\frac{t}{y}\right) - \tanh \left(\frac{x}{y}\right)\right)\right)\right)}\]
x + \left(y \cdot z\right) \cdot \left(\tanh \left(\frac{t}{y}\right) - \tanh \left(\frac{x}{y}\right)\right)
↓
x + \left(\sqrt[3]{y \cdot \left(z \cdot \left(\tanh \left(\frac{t}{y}\right) - \tanh \left(\frac{x}{y}\right)\right)\right)} \cdot \sqrt[3]{y \cdot \left(z \cdot \left(\tanh \left(\frac{t}{y}\right) - \tanh \left(\frac{x}{y}\right)\right)\right)}\right) \cdot \sqrt[3]{\left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) \cdot \left(\sqrt[3]{y} \cdot \left(z \cdot \left(\tanh \left(\frac{t}{y}\right) - \tanh \left(\frac{x}{y}\right)\right)\right)\right)}
double f(double x, double y, double z, double t) {
        double r204908 = x;
        double r204909 = y;
        double r204910 = z;
        double r204911 = r204909 * r204910;
        double r204912 = t;
        double r204913 = r204912 / r204909;
        double r204914 = tanh(r204913);
        double r204915 = r204908 / r204909;
        double r204916 = tanh(r204915);
        double r204917 = r204914 - r204916;
        double r204918 = r204911 * r204917;
        double r204919 = r204908 + r204918;
        return r204919;
}
↓
double f(double x, double y, double z, double t) {
        double r204920 = x;
        double r204921 = y;
        double r204922 = z;
        double r204923 = t;
        double r204924 = r204923 / r204921;
        double r204925 = tanh(r204924);
        double r204926 = r204920 / r204921;
        double r204927 = tanh(r204926);
        double r204928 = r204925 - r204927;
        double r204929 = r204922 * r204928;
        double r204930 = r204921 * r204929;
        double r204931 = cbrt(r204930);
        double r204932 = r204931 * r204931;
        double r204933 = cbrt(r204921);
        double r204934 = r204933 * r204933;
        double r204935 = r204933 * r204929;
        double r204936 = r204934 * r204935;
        double r204937 = cbrt(r204936);
        double r204938 = r204932 * r204937;
        double r204939 = r204920 + r204938;
        return r204939;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original4.6
Target1.9
Herbie2.3
\[x + y \cdot \left(z \cdot \left(\tanh \left(\frac{t}{y}\right) - \tanh \left(\frac{x}{y}\right)\right)\right)\]

Derivation

  1. Initial program 4.6

    \[x + \left(y \cdot z\right) \cdot \left(\tanh \left(\frac{t}{y}\right) - \tanh \left(\frac{x}{y}\right)\right)\]
  2. Using strategy rm

  3. Applied associate-*l*1.9

    \[\leadsto x + \color{blue}{y \cdot \left(z \cdot \left(\tanh \left(\frac{t}{y}\right) - \tanh \left(\frac{x}{y}\right)\right)\right)}\]
  4. Using strategy rm

  5. Applied add-cube-cbrt2.3

    \[\leadsto x + \color{blue}{\left(\sqrt[3]{y \cdot \left(z \cdot \left(\tanh \left(\frac{t}{y}\right) - \tanh \left(\frac{x}{y}\right)\right)\right)} \cdot \sqrt[3]{y \cdot \left(z \cdot \left(\tanh \left(\frac{t}{y}\right) - \tanh \left(\frac{x}{y}\right)\right)\right)}\right) \cdot \sqrt[3]{y \cdot \left(z \cdot \left(\tanh \left(\frac{t}{y}\right) - \tanh \left(\frac{x}{y}\right)\right)\right)}}\]
  6. Using strategy rm

  7. Applied add-cube-cbrt2.3

    \[\leadsto x + \left(\sqrt[3]{y \cdot \left(z \cdot \left(\tanh \left(\frac{t}{y}\right) - \tanh \left(\frac{x}{y}\right)\right)\right)} \cdot \sqrt[3]{y \cdot \left(z \cdot \left(\tanh \left(\frac{t}{y}\right) - \tanh \left(\frac{x}{y}\right)\right)\right)}\right) \cdot \sqrt[3]{\color{blue}{\left(\left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) \cdot \sqrt[3]{y}\right)} \cdot \left(z \cdot \left(\tanh \left(\frac{t}{y}\right) - \tanh \left(\frac{x}{y}\right)\right)\right)}\]

  8. Applied associate-*l*2.3

    \[\leadsto x + \left(\sqrt[3]{y \cdot \left(z \cdot \left(\tanh \left(\frac{t}{y}\right) - \tanh \left(\frac{x}{y}\right)\right)\right)} \cdot \sqrt[3]{y \cdot \left(z \cdot \left(\tanh \left(\frac{t}{y}\right) - \tanh \left(\frac{x}{y}\right)\right)\right)}\right) \cdot \sqrt[3]{\color{blue}{\left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) \cdot \left(\sqrt[3]{y} \cdot \left(z \cdot \left(\tanh \left(\frac{t}{y}\right) - \tanh \left(\frac{x}{y}\right)\right)\right)\right)}}\]

  9. Final simplification2.3

    \[\leadsto x + \left(\sqrt[3]{y \cdot \left(z \cdot \left(\tanh \left(\frac{t}{y}\right) - \tanh \left(\frac{x}{y}\right)\right)\right)} \cdot \sqrt[3]{y \cdot \left(z \cdot \left(\tanh \left(\frac{t}{y}\right) - \tanh \left(\frac{x}{y}\right)\right)\right)}\right) \cdot \sqrt[3]{\left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) \cdot \left(\sqrt[3]{y} \cdot \left(z \cdot \left(\tanh \left(\frac{t}{y}\right) - \tanh \left(\frac{x}{y}\right)\right)\right)\right)}\]

Reproduce

herbie shell --seed 2019323 
(FPCore (x y z t)
  :name "SynthBasics:moogVCF from YampaSynth-0.2"
  :precision binary64

  :herbie-target
  (+ x (* y (* z (- (tanh (/ t y)) (tanh (/ x y))))))

  (+ x (* (* y z) (- (tanh (/ t y)) (tanh (/ x y))))))