Average Error: 4.7 → 2.5
Time: 55.8s
Precision: 64
\[x + \left(y \cdot z\right) \cdot \left(\tanh \left(\frac{t}{y}\right) - \tanh \left(\frac{x}{y}\right)\right)\]
↓
\[\left(\left(z \cdot \left(\tanh \left(\frac{t}{y}\right) - \tanh \left(\frac{x}{y}\right)\right)\right) \cdot \sqrt[3]{y}\right) \cdot \left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) + x\]
x + \left(y \cdot z\right) \cdot \left(\tanh \left(\frac{t}{y}\right) - \tanh \left(\frac{x}{y}\right)\right)
↓
\left(\left(z \cdot \left(\tanh \left(\frac{t}{y}\right) - \tanh \left(\frac{x}{y}\right)\right)\right) \cdot \sqrt[3]{y}\right) \cdot \left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) + x
double f(double x, double y, double z, double t) {
        double r19600978 = x;
        double r19600979 = y;
        double r19600980 = z;
        double r19600981 = r19600979 * r19600980;
        double r19600982 = t;
        double r19600983 = r19600982 / r19600979;
        double r19600984 = tanh(r19600983);
        double r19600985 = r19600978 / r19600979;
        double r19600986 = tanh(r19600985);
        double r19600987 = r19600984 - r19600986;
        double r19600988 = r19600981 * r19600987;
        double r19600989 = r19600978 + r19600988;
        return r19600989;
}
↓
double f(double x, double y, double z, double t) {
        double r19600990 = z;
        double r19600991 = t;
        double r19600992 = y;
        double r19600993 = r19600991 / r19600992;
        double r19600994 = tanh(r19600993);
        double r19600995 = x;
        double r19600996 = r19600995 / r19600992;
        double r19600997 = tanh(r19600996);
        double r19600998 = r19600994 - r19600997;
        double r19600999 = r19600990 * r19600998;
        double r19601000 = cbrt(r19600992);
        double r19601001 = r19600999 * r19601000;
        double r19601002 = r19601000 * r19601000;
        double r19601003 = r19601001 * r19601002;
        double r19601004 = r19601003 + r19600995;
        return r19601004;
}

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

Original4.7
Target2.1
Herbie2.5
\[x + y \cdot \left(z \cdot \left(\tanh \left(\frac{t}{y}\right) - \tanh \left(\frac{x}{y}\right)\right)\right)\]

Derivation

  1. Initial program 4.7

    \[x + \left(y \cdot z\right) \cdot \left(\tanh \left(\frac{t}{y}\right) - \tanh \left(\frac{x}{y}\right)\right)\]
  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-cbrt2.5

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

  6. Applied associate-*l*2.5

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

  7. Final simplification2.5

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

Reproduce

herbie shell --seed 2019165 
(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))))))