Average Error: 4.6 → 1.8
Time: 6.1s
Precision: 64
\[x + \left(y \cdot z\right) \cdot \left(\tanh \left(\frac{t}{y}\right) - \tanh \left(\frac{x}{y}\right)\right)\]
↓
\[\begin{array}{l} \mathbf{if}\;x + \left(y \cdot z\right) \cdot \left(\tanh \left(\frac{t}{y}\right) - \tanh \left(\frac{x}{y}\right)\right) = -\infty \lor \neg \left(x + \left(y \cdot z\right) \cdot \left(\tanh \left(\frac{t}{y}\right) - \tanh \left(\frac{x}{y}\right)\right) \le 9.69418639124574765 \cdot 10^{292}\right):\\ \;\;\;\;x + \left(\left(\sqrt[3]{y \cdot \left(\tanh \left(\frac{t}{y}\right) \cdot z\right)} \cdot \sqrt[3]{y \cdot \left(\tanh \left(\frac{t}{y}\right) \cdot z\right)}\right) \cdot \sqrt[3]{y \cdot \left(\tanh \left(\frac{t}{y}\right) \cdot z\right)} + y \cdot \left(\left(-\tanh \left(\frac{x}{y}\right)\right) \cdot z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(y \cdot z\right) \cdot \left(\tanh \left(\frac{t}{y}\right) - \tanh \left(\frac{x}{y}\right)\right)\\ \end{array}\]
x + \left(y \cdot z\right) \cdot \left(\tanh \left(\frac{t}{y}\right) - \tanh \left(\frac{x}{y}\right)\right)
↓
\begin{array}{l}
\mathbf{if}\;x + \left(y \cdot z\right) \cdot \left(\tanh \left(\frac{t}{y}\right) - \tanh \left(\frac{x}{y}\right)\right) = -\infty \lor \neg \left(x + \left(y \cdot z\right) \cdot \left(\tanh \left(\frac{t}{y}\right) - \tanh \left(\frac{x}{y}\right)\right) \le 9.69418639124574765 \cdot 10^{292}\right):\\
\;\;\;\;x + \left(\left(\sqrt[3]{y \cdot \left(\tanh \left(\frac{t}{y}\right) \cdot z\right)} \cdot \sqrt[3]{y \cdot \left(\tanh \left(\frac{t}{y}\right) \cdot z\right)}\right) \cdot \sqrt[3]{y \cdot \left(\tanh \left(\frac{t}{y}\right) \cdot z\right)} + y \cdot \left(\left(-\tanh \left(\frac{x}{y}\right)\right) \cdot z\right)\right)\\

\mathbf{else}:\\
\;\;\;\;x + \left(y \cdot z\right) \cdot \left(\tanh \left(\frac{t}{y}\right) - \tanh \left(\frac{x}{y}\right)\right)\\

\end{array}
double f(double x, double y, double z, double t) {
        double r310075 = x;
        double r310076 = y;
        double r310077 = z;
        double r310078 = r310076 * r310077;
        double r310079 = t;
        double r310080 = r310079 / r310076;
        double r310081 = tanh(r310080);
        double r310082 = r310075 / r310076;
        double r310083 = tanh(r310082);
        double r310084 = r310081 - r310083;
        double r310085 = r310078 * r310084;
        double r310086 = r310075 + r310085;
        return r310086;
}
↓
double f(double x, double y, double z, double t) {
        double r310087 = x;
        double r310088 = y;
        double r310089 = z;
        double r310090 = r310088 * r310089;
        double r310091 = t;
        double r310092 = r310091 / r310088;
        double r310093 = tanh(r310092);
        double r310094 = r310087 / r310088;
        double r310095 = tanh(r310094);
        double r310096 = r310093 - r310095;
        double r310097 = r310090 * r310096;
        double r310098 = r310087 + r310097;
        double r310099 = -inf.0;
        bool r310100 = r310098 <= r310099;
        double r310101 = 9.694186391245748e+292;
        bool r310102 = r310098 <= r310101;
        double r310103 = !r310102;
        bool r310104 = r310100 || r310103;
        double r310105 = r310093 * r310089;
        double r310106 = r310088 * r310105;
        double r310107 = cbrt(r310106);
        double r310108 = r310107 * r310107;
        double r310109 = r310108 * r310107;
        double r310110 = -r310095;
        double r310111 = r310110 * r310089;
        double r310112 = r310088 * r310111;
        double r310113 = r310109 + r310112;
        double r310114 = r310087 + r310113;
        double r310115 = r310104 ? r310114 : r310098;
        return r310115;
}

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
Target2.0
Herbie1.8
\[x + y \cdot \left(z \cdot \left(\tanh \left(\frac{t}{y}\right) - \tanh \left(\frac{x}{y}\right)\right)\right)\]

Derivation

  1. Split input into 2 regimes

  2. if (+ x (* (* y z) (- (tanh (/ t y)) (tanh (/ x y))))) < -inf.0 or 9.694186391245748e+292 < (+ x (* (* y z) (- (tanh (/ t y)) (tanh (/ x y)))))

    1. Initial program 52.7

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

    3. Applied associate-*l*13.1

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

    5. Applied sub-neg13.1

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

    6. Applied distribute-lft-in13.1

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

    7. Applied distribute-lft-in15.4

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

    8. Simplified15.4

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

    9. Simplified15.4

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

    11. Applied add-cube-cbrt15.7

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

    if -inf.0 < (+ x (* (* y z) (- (tanh (/ t y)) (tanh (/ x y))))) < 9.694186391245748e+292

    1. Initial program 0.6

      \[x + \left(y \cdot z\right) \cdot \left(\tanh \left(\frac{t}{y}\right) - \tanh \left(\frac{x}{y}\right)\right)\]
  3. Recombined 2 regimes into one program.

  4. Final simplification1.8

    \[\leadsto \begin{array}{l} \mathbf{if}\;x + \left(y \cdot z\right) \cdot \left(\tanh \left(\frac{t}{y}\right) - \tanh \left(\frac{x}{y}\right)\right) = -\infty \lor \neg \left(x + \left(y \cdot z\right) \cdot \left(\tanh \left(\frac{t}{y}\right) - \tanh \left(\frac{x}{y}\right)\right) \le 9.69418639124574765 \cdot 10^{292}\right):\\ \;\;\;\;x + \left(\left(\sqrt[3]{y \cdot \left(\tanh \left(\frac{t}{y}\right) \cdot z\right)} \cdot \sqrt[3]{y \cdot \left(\tanh \left(\frac{t}{y}\right) \cdot z\right)}\right) \cdot \sqrt[3]{y \cdot \left(\tanh \left(\frac{t}{y}\right) \cdot z\right)} + y \cdot \left(\left(-\tanh \left(\frac{x}{y}\right)\right) \cdot z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(y \cdot z\right) \cdot \left(\tanh \left(\frac{t}{y}\right) - \tanh \left(\frac{x}{y}\right)\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2020100 
(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))))))