Average Error: 4.4 → 2.3
Time: 22.8s
Precision: 64
\[x + \left(y \cdot z\right) \cdot \left(\tanh \left(\frac{t}{y}\right) - \tanh \left(\frac{x}{y}\right)\right)\]
↓
\[\sqrt[3]{\tanh \left(\frac{x}{y}\right) \cdot \left(-z\right) + z \cdot \tanh \left(\frac{t}{y}\right)} \cdot \left(y \cdot \left(\sqrt[3]{\tanh \left(\frac{x}{y}\right) \cdot \left(-z\right) + z \cdot \tanh \left(\frac{t}{y}\right)} \cdot \sqrt[3]{\tanh \left(\frac{x}{y}\right) \cdot \left(-z\right) + z \cdot \tanh \left(\frac{t}{y}\right)}\right)\right) + x\]
x + \left(y \cdot z\right) \cdot \left(\tanh \left(\frac{t}{y}\right) - \tanh \left(\frac{x}{y}\right)\right)
↓
\sqrt[3]{\tanh \left(\frac{x}{y}\right) \cdot \left(-z\right) + z \cdot \tanh \left(\frac{t}{y}\right)} \cdot \left(y \cdot \left(\sqrt[3]{\tanh \left(\frac{x}{y}\right) \cdot \left(-z\right) + z \cdot \tanh \left(\frac{t}{y}\right)} \cdot \sqrt[3]{\tanh \left(\frac{x}{y}\right) \cdot \left(-z\right) + z \cdot \tanh \left(\frac{t}{y}\right)}\right)\right) + x
double f(double x, double y, double z, double t) {
        double r14131748 = x;
        double r14131749 = y;
        double r14131750 = z;
        double r14131751 = r14131749 * r14131750;
        double r14131752 = t;
        double r14131753 = r14131752 / r14131749;
        double r14131754 = tanh(r14131753);
        double r14131755 = r14131748 / r14131749;
        double r14131756 = tanh(r14131755);
        double r14131757 = r14131754 - r14131756;
        double r14131758 = r14131751 * r14131757;
        double r14131759 = r14131748 + r14131758;
        return r14131759;
}
↓
double f(double x, double y, double z, double t) {
        double r14131760 = x;
        double r14131761 = y;
        double r14131762 = r14131760 / r14131761;
        double r14131763 = tanh(r14131762);
        double r14131764 = z;
        double r14131765 = -r14131764;
        double r14131766 = r14131763 * r14131765;
        double r14131767 = t;
        double r14131768 = r14131767 / r14131761;
        double r14131769 = tanh(r14131768);
        double r14131770 = r14131764 * r14131769;
        double r14131771 = r14131766 + r14131770;
        double r14131772 = cbrt(r14131771);
        double r14131773 = r14131772 * r14131772;
        double r14131774 = r14131761 * r14131773;
        double r14131775 = r14131772 * r14131774;
        double r14131776 = r14131775 + r14131760;
        return r14131776;
}

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

Original4.4
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 4.4

    \[x + \left(y \cdot z\right) \cdot \left(\tanh \left(\frac{t}{y}\right) - \tanh \left(\frac{x}{y}\right)\right)\]
  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 sub-neg1.9

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

  6. Applied distribute-lft-in1.9

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

  8. Applied add-cube-cbrt2.3

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

  9. Applied associate-*r*2.3

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

  10. Final simplification2.3

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

Reproduce

herbie shell --seed 2019163 
(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))))))