Average Error: 4.6 → 2.3
Time: 19.1s
Precision: 64
\[x + \left(y \cdot z\right) \cdot \left(\tanh \left(\frac{t}{y}\right) - \tanh \left(\frac{x}{y}\right)\right)\]
↓
\[x + \left(\sqrt[3]{y \cdot \left(z \cdot \left(\tanh \left(\frac{t}{y}\right) - \tanh \left(\frac{x}{y}\right)\right)\right)} \cdot \sqrt[3]{y \cdot \left(z \cdot \left(\tanh \left(\frac{t}{y}\right) - \tanh \left(\frac{x}{y}\right)\right)\right)}\right) \cdot \sqrt[3]{\left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) \cdot \left(\sqrt[3]{y} \cdot \left(z \cdot \left(\tanh \left(\frac{t}{y}\right) - \tanh \left(\frac{x}{y}\right)\right)\right)\right)}\]
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 \left(z \cdot \left(\tanh \left(\frac{t}{y}\right) - \tanh \left(\frac{x}{y}\right)\right)\right)} \cdot \sqrt[3]{y \cdot \left(z \cdot \left(\tanh \left(\frac{t}{y}\right) - \tanh \left(\frac{x}{y}\right)\right)\right)}\right) \cdot \sqrt[3]{\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)}
double f(double x, double y, double z, double t) {
        double r242627 = x;
        double r242628 = y;
        double r242629 = z;
        double r242630 = r242628 * r242629;
        double r242631 = t;
        double r242632 = r242631 / r242628;
        double r242633 = tanh(r242632);
        double r242634 = r242627 / r242628;
        double r242635 = tanh(r242634);
        double r242636 = r242633 - r242635;
        double r242637 = r242630 * r242636;
        double r242638 = r242627 + r242637;
        return r242638;
}
↓
double f(double x, double y, double z, double t) {
        double r242639 = x;
        double r242640 = y;
        double r242641 = z;
        double r242642 = t;
        double r242643 = r242642 / r242640;
        double r242644 = tanh(r242643);
        double r242645 = r242639 / r242640;
        double r242646 = tanh(r242645);
        double r242647 = r242644 - r242646;
        double r242648 = r242641 * r242647;
        double r242649 = r242640 * r242648;
        double r242650 = cbrt(r242649);
        double r242651 = r242650 * r242650;
        double r242652 = cbrt(r242640);
        double r242653 = r242652 * r242652;
        double r242654 = r242652 * r242648;
        double r242655 = r242653 * r242654;
        double r242656 = cbrt(r242655);
        double r242657 = r242651 * r242656;
        double r242658 = r242639 + r242657;
        return r242658;
}

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

Original4.6
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 4.6

    \[x + \left(y \cdot z\right) \cdot \left(\tanh \left(\frac{t}{y}\right) - \tanh \left(\frac{x}{y}\right)\right)\]
  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 add-cube-cbrt2.3

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

  7. Applied add-cube-cbrt2.3

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

  8. Applied associate-*l*2.3

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

  9. Final simplification2.3

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

Reproduce

herbie shell --seed 2019323 
(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))))))