Average Error: 5.0 → 2.8
Time: 6.7s
Precision: 64
\[x + \left(y \cdot z\right) \cdot \left(\tanh \left(\frac{t}{y}\right) - \tanh \left(\frac{x}{y}\right)\right)\]
↓
\[x + \left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) \cdot \left(\left(\sqrt[3]{y} \cdot z\right) \cdot \left(\tanh \left(\frac{t}{y}\right) - \tanh \left(\frac{x}{y}\right)\right)\right)\]
x + \left(y \cdot z\right) \cdot \left(\tanh \left(\frac{t}{y}\right) - \tanh \left(\frac{x}{y}\right)\right)
↓
x + \left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) \cdot \left(\left(\sqrt[3]{y} \cdot z\right) \cdot \left(\tanh \left(\frac{t}{y}\right) - \tanh \left(\frac{x}{y}\right)\right)\right)
double f(double x, double y, double z, double t) {
        double r353522 = x;
        double r353523 = y;
        double r353524 = z;
        double r353525 = r353523 * r353524;
        double r353526 = t;
        double r353527 = r353526 / r353523;
        double r353528 = tanh(r353527);
        double r353529 = r353522 / r353523;
        double r353530 = tanh(r353529);
        double r353531 = r353528 - r353530;
        double r353532 = r353525 * r353531;
        double r353533 = r353522 + r353532;
        return r353533;
}
↓
double f(double x, double y, double z, double t) {
        double r353534 = x;
        double r353535 = y;
        double r353536 = cbrt(r353535);
        double r353537 = r353536 * r353536;
        double r353538 = z;
        double r353539 = r353536 * r353538;
        double r353540 = t;
        double r353541 = r353540 / r353535;
        double r353542 = tanh(r353541);
        double r353543 = r353534 / r353535;
        double r353544 = tanh(r353543);
        double r353545 = r353542 - r353544;
        double r353546 = r353539 * r353545;
        double r353547 = r353537 * r353546;
        double r353548 = r353534 + r353547;
        return r353548;
}

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

Original5.0
Target2.1
Herbie2.8
\[x + y \cdot \left(z \cdot \left(\tanh \left(\frac{t}{y}\right) - \tanh \left(\frac{x}{y}\right)\right)\right)\]

Derivation

  1. Initial program 5.0

    \[x + \left(y \cdot z\right) \cdot \left(\tanh \left(\frac{t}{y}\right) - \tanh \left(\frac{x}{y}\right)\right)\]
  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 sub-neg2.1

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

  6. Applied distribute-lft-in2.1

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

  8. Applied add-cube-cbrt2.5

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

  9. Applied associate-*l*2.5

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

  10. Simplified2.8

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

  11. Final simplification2.8

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

Reproduce

herbie shell --seed 2020083 
(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))))))