Average Error: 4.5 → 1.7
Time: 20.4s
Precision: 64
\[x + \left(y \cdot z\right) \cdot \left(\tanh \left(\frac{t}{y}\right) - \tanh \left(\frac{x}{y}\right)\right)\]
↓
\[\left(\left(y \cdot \tanh \left(\frac{t}{y}\right)\right) \cdot z + \left(z \cdot \tanh \left(\frac{x}{y}\right)\right) \cdot \left(-y\right)\right) + x\]
x + \left(y \cdot z\right) \cdot \left(\tanh \left(\frac{t}{y}\right) - \tanh \left(\frac{x}{y}\right)\right)
↓
\left(\left(y \cdot \tanh \left(\frac{t}{y}\right)\right) \cdot z + \left(z \cdot \tanh \left(\frac{x}{y}\right)\right) \cdot \left(-y\right)\right) + x
double f(double x, double y, double z, double t) {
        double r14713620 = x;
        double r14713621 = y;
        double r14713622 = z;
        double r14713623 = r14713621 * r14713622;
        double r14713624 = t;
        double r14713625 = r14713624 / r14713621;
        double r14713626 = tanh(r14713625);
        double r14713627 = r14713620 / r14713621;
        double r14713628 = tanh(r14713627);
        double r14713629 = r14713626 - r14713628;
        double r14713630 = r14713623 * r14713629;
        double r14713631 = r14713620 + r14713630;
        return r14713631;
}
↓
double f(double x, double y, double z, double t) {
        double r14713632 = y;
        double r14713633 = t;
        double r14713634 = r14713633 / r14713632;
        double r14713635 = tanh(r14713634);
        double r14713636 = r14713632 * r14713635;
        double r14713637 = z;
        double r14713638 = r14713636 * r14713637;
        double r14713639 = x;
        double r14713640 = r14713639 / r14713632;
        double r14713641 = tanh(r14713640);
        double r14713642 = r14713637 * r14713641;
        double r14713643 = -r14713632;
        double r14713644 = r14713642 * r14713643;
        double r14713645 = r14713638 + r14713644;
        double r14713646 = r14713645 + r14713639;
        return r14713646;
}

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

Original4.5
Target2.1
Herbie1.7
\[x + y \cdot \left(z \cdot \left(\tanh \left(\frac{t}{y}\right) - \tanh \left(\frac{x}{y}\right)\right)\right)\]

Derivation

  1. Initial program 4.5

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

  8. Applied sub-neg2.5

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

  9. Applied distribute-lft-in2.5

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

  10. Applied distribute-lft-in2.6

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

  11. Applied distribute-lft-in2.7

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

  12. Simplified3.1

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

  13. Simplified1.7

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

  14. Final simplification1.7

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

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))))))