Average Error: 4.8 → 1.6
Time: 20.3s
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 r237382 = x;
        double r237383 = y;
        double r237384 = z;
        double r237385 = r237383 * r237384;
        double r237386 = t;
        double r237387 = r237386 / r237383;
        double r237388 = tanh(r237387);
        double r237389 = r237382 / r237383;
        double r237390 = tanh(r237389);
        double r237391 = r237388 - r237390;
        double r237392 = r237385 * r237391;
        double r237393 = r237382 + r237392;
        return r237393;
}
↓
double f(double x, double y, double z, double t) {
        double r237394 = x;
        double r237395 = z;
        double r237396 = t;
        double r237397 = y;
        double r237398 = r237396 / r237397;
        double r237399 = tanh(r237398);
        double r237400 = r237394 / r237397;
        double r237401 = tanh(r237400);
        double r237402 = r237399 - r237401;
        double r237403 = r237402 * r237397;
        double r237404 = r237395 * r237403;
        double r237405 = r237394 + r237404;
        return r237405;
}

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
Target2.1
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. Using strategy rm

  5. Applied add-cube-cbrt2.4

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

  6. Applied associate-*l*2.4

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

  8. Applied *-un-lft-identity2.4

    \[\leadsto x + \color{blue}{\left(1 \cdot y\right)} \cdot \left(\left(\sqrt[3]{z} \cdot \sqrt[3]{z}\right) \cdot \left(\sqrt[3]{z} \cdot \left(\tanh \left(\frac{t}{y}\right) - \tanh \left(\frac{x}{y}\right)\right)\right)\right)\]

  9. Applied associate-*l*2.4

    \[\leadsto x + \color{blue}{1 \cdot \left(y \cdot \left(\left(\sqrt[3]{z} \cdot \sqrt[3]{z}\right) \cdot \left(\sqrt[3]{z} \cdot \left(\tanh \left(\frac{t}{y}\right) - \tanh \left(\frac{x}{y}\right)\right)\right)\right)\right)}\]

  10. Simplified1.6

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

  11. 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 2019235 
(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))))))