Average Error: 4.8 → 1.6
Time: 20.2s
Precision: 64
\[x + \left(y \cdot z\right) \cdot \left(\tanh \left(\frac{t}{y}\right) - \tanh \left(\frac{x}{y}\right)\right)\]
↓
\[x + z \cdot \left(\left(\tanh \left(\frac{t}{y}\right) - \tanh \left(\frac{x}{y}\right)\right) \cdot y\right)\]
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 r233316 = x;
        double r233317 = y;
        double r233318 = z;
        double r233319 = r233317 * r233318;
        double r233320 = t;
        double r233321 = r233320 / r233317;
        double r233322 = tanh(r233321);
        double r233323 = r233316 / r233317;
        double r233324 = tanh(r233323);
        double r233325 = r233322 - r233324;
        double r233326 = r233319 * r233325;
        double r233327 = r233316 + r233326;
        return r233327;
}
↓
double f(double x, double y, double z, double t) {
        double r233328 = x;
        double r233329 = z;
        double r233330 = t;
        double r233331 = y;
        double r233332 = r233330 / r233331;
        double r233333 = tanh(r233332);
        double r233334 = r233328 / r233331;
        double r233335 = tanh(r233334);
        double r233336 = r233333 - r233335;
        double r233337 = r233336 * r233331;
        double r233338 = r233329 * r233337;
        double r233339 = r233328 + r233338;
        return r233339;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original4.8
Target2.1
Herbie1.6
\[x + y \cdot \left(z \cdot \left(\tanh \left(\frac{t}{y}\right) - \tanh \left(\frac{x}{y}\right)\right)\right)\]

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 associate-*l*2.1

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

  4. Simplified2.1

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

  6. Applied associate-*r*1.6

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

  7. Simplified1.6

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

  8. Final simplification1.6

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

Reproduce

herbie shell --seed 2019194 
(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))))))