Average Error: 4.7 → 2.4
Time: 3.0m
Precision: 64
\[x + \left(y \cdot z\right) \cdot \left(\tanh \left(\frac{t}{y}\right) - \tanh \left(\frac{x}{y}\right)\right)\]
↓
\[\sqrt[3]{\left(z \cdot \left(\tanh \left(\frac{t}{y}\right) - \tanh \left(\frac{x}{y}\right)\right)\right) \cdot y} \cdot \left(\sqrt[3]{\left(z \cdot \left(\tanh \left(\frac{t}{y}\right) - \tanh \left(\frac{x}{y}\right)\right)\right) \cdot y} \cdot \sqrt[3]{\left(z \cdot \left(\tanh \left(\frac{t}{y}\right) - \tanh \left(\frac{x}{y}\right)\right)\right) \cdot y}\right) + x\]
x + \left(y \cdot z\right) \cdot \left(\tanh \left(\frac{t}{y}\right) - \tanh \left(\frac{x}{y}\right)\right)
↓
\sqrt[3]{\left(z \cdot \left(\tanh \left(\frac{t}{y}\right) - \tanh \left(\frac{x}{y}\right)\right)\right) \cdot y} \cdot \left(\sqrt[3]{\left(z \cdot \left(\tanh \left(\frac{t}{y}\right) - \tanh \left(\frac{x}{y}\right)\right)\right) \cdot y} \cdot \sqrt[3]{\left(z \cdot \left(\tanh \left(\frac{t}{y}\right) - \tanh \left(\frac{x}{y}\right)\right)\right) \cdot y}\right) + x
double f(double x, double y, double z, double t) {
        double r17867075 = x;
        double r17867076 = y;
        double r17867077 = z;
        double r17867078 = r17867076 * r17867077;
        double r17867079 = t;
        double r17867080 = r17867079 / r17867076;
        double r17867081 = tanh(r17867080);
        double r17867082 = r17867075 / r17867076;
        double r17867083 = tanh(r17867082);
        double r17867084 = r17867081 - r17867083;
        double r17867085 = r17867078 * r17867084;
        double r17867086 = r17867075 + r17867085;
        return r17867086;
}
↓
double f(double x, double y, double z, double t) {
        double r17867087 = z;
        double r17867088 = t;
        double r17867089 = y;
        double r17867090 = r17867088 / r17867089;
        double r17867091 = tanh(r17867090);
        double r17867092 = x;
        double r17867093 = r17867092 / r17867089;
        double r17867094 = tanh(r17867093);
        double r17867095 = r17867091 - r17867094;
        double r17867096 = r17867087 * r17867095;
        double r17867097 = r17867096 * r17867089;
        double r17867098 = cbrt(r17867097);
        double r17867099 = r17867098 * r17867098;
        double r17867100 = r17867098 * r17867099;
        double r17867101 = r17867100 + r17867092;
        return r17867101;
}

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

Original4.7
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 4.7

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

  3. Applied associate-*l*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

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

  6. Final simplification2.4

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

Reproduce

herbie shell --seed 2019200 
(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))))))