Average Error: 4.4 → 2.4
Time: 33.2s
Precision: 64
\[x + \left(y \cdot z\right) \cdot \left(\tanh \left(\frac{t}{y}\right) - \tanh \left(\frac{x}{y}\right)\right)\]
↓
\[x + y \cdot \left(\left(\sqrt[3]{z \cdot \left(\tanh \left(\frac{t}{y}\right) - \tanh \left(\frac{x}{y}\right)\right)} \cdot \sqrt[3]{z \cdot \left(\tanh \left(\frac{t}{y}\right) - \tanh \left(\frac{x}{y}\right)\right)}\right) \cdot \sqrt[3]{z \cdot \left(\tanh \left(\frac{t}{y}\right) - \tanh \left(\frac{x}{y}\right)\right)}\right)\]
x + \left(y \cdot z\right) \cdot \left(\tanh \left(\frac{t}{y}\right) - \tanh \left(\frac{x}{y}\right)\right)
↓
x + y \cdot \left(\left(\sqrt[3]{z \cdot \left(\tanh \left(\frac{t}{y}\right) - \tanh \left(\frac{x}{y}\right)\right)} \cdot \sqrt[3]{z \cdot \left(\tanh \left(\frac{t}{y}\right) - \tanh \left(\frac{x}{y}\right)\right)}\right) \cdot \sqrt[3]{z \cdot \left(\tanh \left(\frac{t}{y}\right) - \tanh \left(\frac{x}{y}\right)\right)}\right)
double f(double x, double y, double z, double t) {
        double r445137 = x;
        double r445138 = y;
        double r445139 = z;
        double r445140 = r445138 * r445139;
        double r445141 = t;
        double r445142 = r445141 / r445138;
        double r445143 = tanh(r445142);
        double r445144 = r445137 / r445138;
        double r445145 = tanh(r445144);
        double r445146 = r445143 - r445145;
        double r445147 = r445140 * r445146;
        double r445148 = r445137 + r445147;
        return r445148;
}
↓
double f(double x, double y, double z, double t) {
        double r445149 = x;
        double r445150 = y;
        double r445151 = z;
        double r445152 = t;
        double r445153 = r445152 / r445150;
        double r445154 = tanh(r445153);
        double r445155 = r445149 / r445150;
        double r445156 = tanh(r445155);
        double r445157 = r445154 - r445156;
        double r445158 = r445151 * r445157;
        double r445159 = cbrt(r445158);
        double r445160 = r445159 * r445159;
        double r445161 = r445160 * r445159;
        double r445162 = r445150 * r445161;
        double r445163 = r445149 + r445162;
        return r445163;
}

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

Original4.4
Target2.0
Herbie2.4
\[x + y \cdot \left(z \cdot \left(\tanh \left(\frac{t}{y}\right) - \tanh \left(\frac{x}{y}\right)\right)\right)\]

Derivation

  1. Initial program 4.4

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

  3. Applied associate-*l*2.0

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

  5. Applied add-cube-cbrt2.4

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

  6. Final simplification2.4

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

Reproduce

herbie shell --seed 2020047 
(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))))))