Average Error: 4.6 → 2.3
Time: 18.5s
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 r232218 = x;
        double r232219 = y;
        double r232220 = z;
        double r232221 = r232219 * r232220;
        double r232222 = t;
        double r232223 = r232222 / r232219;
        double r232224 = tanh(r232223);
        double r232225 = r232218 / r232219;
        double r232226 = tanh(r232225);
        double r232227 = r232224 - r232226;
        double r232228 = r232221 * r232227;
        double r232229 = r232218 + r232228;
        return r232229;
}
↓
double f(double x, double y, double z, double t) {
        double r232230 = x;
        double r232231 = y;
        double r232232 = z;
        double r232233 = t;
        double r232234 = r232233 / r232231;
        double r232235 = tanh(r232234);
        double r232236 = r232230 / r232231;
        double r232237 = tanh(r232236);
        double r232238 = r232235 - r232237;
        double r232239 = r232232 * r232238;
        double r232240 = r232231 * r232239;
        double r232241 = cbrt(r232240);
        double r232242 = r232241 * r232241;
        double r232243 = cbrt(r232231);
        double r232244 = r232243 * r232243;
        double r232245 = r232243 * r232239;
        double r232246 = r232244 * r232245;
        double r232247 = cbrt(r232246);
        double r232248 = r232242 * r232247;
        double r232249 = r232230 + r232248;
        return r232249;
}

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))))))