Average Error: 4.4 → 2.3
Time: 21.1s
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 r18714087 = x;
        double r18714088 = y;
        double r18714089 = z;
        double r18714090 = r18714088 * r18714089;
        double r18714091 = t;
        double r18714092 = r18714091 / r18714088;
        double r18714093 = tanh(r18714092);
        double r18714094 = r18714087 / r18714088;
        double r18714095 = tanh(r18714094);
        double r18714096 = r18714093 - r18714095;
        double r18714097 = r18714090 * r18714096;
        double r18714098 = r18714087 + r18714097;
        return r18714098;
}
↓
double f(double x, double y, double z, double t) {
        double r18714099 = x;
        double r18714100 = y;
        double r18714101 = r18714099 / r18714100;
        double r18714102 = tanh(r18714101);
        double r18714103 = z;
        double r18714104 = -r18714103;
        double r18714105 = r18714102 * r18714104;
        double r18714106 = t;
        double r18714107 = r18714106 / r18714100;
        double r18714108 = tanh(r18714107);
        double r18714109 = r18714103 * r18714108;
        double r18714110 = r18714105 + r18714109;
        double r18714111 = cbrt(r18714110);
        double r18714112 = r18714111 * r18714111;
        double r18714113 = r18714100 * r18714112;
        double r18714114 = r18714111 * r18714113;
        double r18714115 = r18714114 + r18714099;
        return r18714115;
}

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))))))