Average Error: 4.8 → 1.5
Time: 20.5s
Precision: 64
\[x + \left(y \cdot z\right) \cdot \left(\tanh \left(\frac{t}{y}\right) - \tanh \left(\frac{x}{y}\right)\right)\]
↓
\[x + z \cdot \left(\left(\tanh \left(\frac{t}{y}\right) - \tanh \left(\frac{x}{y}\right)\right) \cdot y\right)\]
x + \left(y \cdot z\right) \cdot \left(\tanh \left(\frac{t}{y}\right) - \tanh \left(\frac{x}{y}\right)\right)
↓
x + z \cdot \left(\left(\tanh \left(\frac{t}{y}\right) - \tanh \left(\frac{x}{y}\right)\right) \cdot y\right)
double f(double x, double y, double z, double t) {
        double r213243 = x;
        double r213244 = y;
        double r213245 = z;
        double r213246 = r213244 * r213245;
        double r213247 = t;
        double r213248 = r213247 / r213244;
        double r213249 = tanh(r213248);
        double r213250 = r213243 / r213244;
        double r213251 = tanh(r213250);
        double r213252 = r213249 - r213251;
        double r213253 = r213246 * r213252;
        double r213254 = r213243 + r213253;
        return r213254;
}
↓
double f(double x, double y, double z, double t) {
        double r213255 = x;
        double r213256 = z;
        double r213257 = t;
        double r213258 = y;
        double r213259 = r213257 / r213258;
        double r213260 = tanh(r213259);
        double r213261 = r213255 / r213258;
        double r213262 = tanh(r213261);
        double r213263 = r213260 - r213262;
        double r213264 = r213263 * r213258;
        double r213265 = r213256 * r213264;
        double r213266 = r213255 + r213265;
        return r213266;
}

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
Target2.0
Herbie1.5
\[x + y \cdot \left(z \cdot \left(\tanh \left(\frac{t}{y}\right) - \tanh \left(\frac{x}{y}\right)\right)\right)\]

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. Using strategy rm

  3. Applied pow14.8

    \[\leadsto x + \left(y \cdot z\right) \cdot \color{blue}{{\left(\tanh \left(\frac{t}{y}\right) - \tanh \left(\frac{x}{y}\right)\right)}^{1}}\]

  4. Applied pow14.8

    \[\leadsto x + \left(y \cdot \color{blue}{{z}^{1}}\right) \cdot {\left(\tanh \left(\frac{t}{y}\right) - \tanh \left(\frac{x}{y}\right)\right)}^{1}\]

  5. Applied pow14.8

    \[\leadsto x + \left(\color{blue}{{y}^{1}} \cdot {z}^{1}\right) \cdot {\left(\tanh \left(\frac{t}{y}\right) - \tanh \left(\frac{x}{y}\right)\right)}^{1}\]

  6. Applied pow-prod-down4.8

    \[\leadsto x + \color{blue}{{\left(y \cdot z\right)}^{1}} \cdot {\left(\tanh \left(\frac{t}{y}\right) - \tanh \left(\frac{x}{y}\right)\right)}^{1}\]

  7. Applied pow-prod-down4.8

    \[\leadsto x + \color{blue}{{\left(\left(y \cdot z\right) \cdot \left(\tanh \left(\frac{t}{y}\right) - \tanh \left(\frac{x}{y}\right)\right)\right)}^{1}}\]

  8. Simplified1.5

    \[\leadsto x + {\color{blue}{\left(z \cdot \left(\left(\tanh \left(\frac{t}{y}\right) - \tanh \left(\frac{x}{y}\right)\right) \cdot y\right)\right)}}^{1}\]

  9. Final simplification1.5

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

Reproduce

herbie shell --seed 2019347 +o rules:numerics
(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))))))