Average Error: 4.8 → 2.0
Time: 15.7s
Precision: 64
\[x + \left(y \cdot z\right) \cdot \left(\tanh \left(\frac{t}{y}\right) - \tanh \left(\frac{x}{y}\right)\right)\]
↓
\[\left(\sqrt[3]{z} \cdot \sqrt[3]{z}\right) \cdot \left(\left(\left(\tanh \left(\frac{t}{y}\right) - \tanh \left(\frac{x}{y}\right)\right) \cdot y\right) \cdot \sqrt[3]{z}\right) + x\]
x + \left(y \cdot z\right) \cdot \left(\tanh \left(\frac{t}{y}\right) - \tanh \left(\frac{x}{y}\right)\right)
↓
\left(\sqrt[3]{z} \cdot \sqrt[3]{z}\right) \cdot \left(\left(\left(\tanh \left(\frac{t}{y}\right) - \tanh \left(\frac{x}{y}\right)\right) \cdot y\right) \cdot \sqrt[3]{z}\right) + x
double f(double x, double y, double z, double t) {
        double r269978 = x;
        double r269979 = y;
        double r269980 = z;
        double r269981 = r269979 * r269980;
        double r269982 = t;
        double r269983 = r269982 / r269979;
        double r269984 = tanh(r269983);
        double r269985 = r269978 / r269979;
        double r269986 = tanh(r269985);
        double r269987 = r269984 - r269986;
        double r269988 = r269981 * r269987;
        double r269989 = r269978 + r269988;
        return r269989;
}
↓
double f(double x, double y, double z, double t) {
        double r269990 = z;
        double r269991 = cbrt(r269990);
        double r269992 = r269991 * r269991;
        double r269993 = t;
        double r269994 = y;
        double r269995 = r269993 / r269994;
        double r269996 = tanh(r269995);
        double r269997 = x;
        double r269998 = r269997 / r269994;
        double r269999 = tanh(r269998);
        double r270000 = r269996 - r269999;
        double r270001 = r270000 * r269994;
        double r270002 = r270001 * r269991;
        double r270003 = r269992 * r270002;
        double r270004 = r270003 + r269997;
        return r270004;
}

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

Original4.8
Target2.1
Herbie2.0
\[x + y \cdot \left(z \cdot \left(\tanh \left(\frac{t}{y}\right) - \tanh \left(\frac{x}{y}\right)\right)\right)\]

Derivation

  1. Initial program 4.8

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

  2. Simplified4.8

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

  4. Applied fma-udef4.8

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

  5. Simplified1.6

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

  7. Applied add-cube-cbrt2.0

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

  8. Applied associate-*l*2.0

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

  9. Final simplification2.0

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

Reproduce

herbie shell --seed 2019194 +o rules:numerics
(FPCore (x y z t)
  :name "SynthBasics:moogVCF from YampaSynth-0.2"

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

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