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 r282593 = x;
        double r282594 = y;
        double r282595 = z;
        double r282596 = r282594 * r282595;
        double r282597 = t;
        double r282598 = r282597 / r282594;
        double r282599 = tanh(r282598);
        double r282600 = r282593 / r282594;
        double r282601 = tanh(r282600);
        double r282602 = r282599 - r282601;
        double r282603 = r282596 * r282602;
        double r282604 = r282593 + r282603;
        return r282604;
}
↓
double f(double x, double y, double z, double t) {
        double r282605 = x;
        double r282606 = z;
        double r282607 = t;
        double r282608 = y;
        double r282609 = r282607 / r282608;
        double r282610 = tanh(r282609);
        double r282611 = r282605 / r282608;
        double r282612 = tanh(r282611);
        double r282613 = r282610 - r282612;
        double r282614 = r282613 * r282608;
        double r282615 = r282606 * r282614;
        double r282616 = r282605 + r282615;
        return r282616;
}

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. 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))))))