Average Error: 4.6 → 1.7
Time: 18.3s
Precision: 64
\[x + \left(y \cdot z\right) \cdot \left(\tanh \left(\frac{t}{y}\right) - \tanh \left(\frac{x}{y}\right)\right)\]
↓
\[x + \left(\left(y \cdot \tanh \left(\frac{t}{y}\right)\right) \cdot z + z \cdot \left(\left(-\tanh \left(\frac{x}{y}\right)\right) \cdot y\right)\right)\]
x + \left(y \cdot z\right) \cdot \left(\tanh \left(\frac{t}{y}\right) - \tanh \left(\frac{x}{y}\right)\right)
↓
x + \left(\left(y \cdot \tanh \left(\frac{t}{y}\right)\right) \cdot z + z \cdot \left(\left(-\tanh \left(\frac{x}{y}\right)\right) \cdot y\right)\right)
double f(double x, double y, double z, double t) {
        double r246240 = x;
        double r246241 = y;
        double r246242 = z;
        double r246243 = r246241 * r246242;
        double r246244 = t;
        double r246245 = r246244 / r246241;
        double r246246 = tanh(r246245);
        double r246247 = r246240 / r246241;
        double r246248 = tanh(r246247);
        double r246249 = r246246 - r246248;
        double r246250 = r246243 * r246249;
        double r246251 = r246240 + r246250;
        return r246251;
}
↓
double f(double x, double y, double z, double t) {
        double r246252 = x;
        double r246253 = y;
        double r246254 = t;
        double r246255 = r246254 / r246253;
        double r246256 = tanh(r246255);
        double r246257 = r246253 * r246256;
        double r246258 = z;
        double r246259 = r246257 * r246258;
        double r246260 = r246252 / r246253;
        double r246261 = tanh(r246260);
        double r246262 = -r246261;
        double r246263 = r246262 * r246253;
        double r246264 = r246258 * r246263;
        double r246265 = r246259 + r246264;
        double r246266 = r246252 + r246265;
        return r246266;
}

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
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 4.6

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

  3. Applied associate-*l*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-cbrt2.4

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

  6. Applied associate-*l*2.4

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

  8. Applied sub-neg2.4

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

  9. Applied distribute-lft-in2.4

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

  10. Applied distribute-lft-in2.5

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

  11. Applied distribute-lft-in2.6

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

  12. Simplified3.6

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

  13. Simplified2.2

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

  15. Applied associate-*r*1.7

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

  16. Final simplification1.7

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

Reproduce

herbie shell --seed 2019305 
(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))))))