Average Error: 4.5 → 1.5
Time: 22.2s
Precision: 64
\[x + \left(y \cdot z\right) \cdot \left(\tanh \left(\frac{t}{y}\right) - \tanh \left(\frac{x}{y}\right)\right)\]
↓
\[x + z \cdot \left(\left(\tanh \left(\frac{t}{y}\right) - \tanh \left(\frac{x}{y}\right)\right) \cdot y\right)\]
x + \left(y \cdot z\right) \cdot \left(\tanh \left(\frac{t}{y}\right) - \tanh \left(\frac{x}{y}\right)\right)
↓
x + z \cdot \left(\left(\tanh \left(\frac{t}{y}\right) - \tanh \left(\frac{x}{y}\right)\right) \cdot y\right)
double f(double x, double y, double z, double t) {
        double r233262 = x;
        double r233263 = y;
        double r233264 = z;
        double r233265 = r233263 * r233264;
        double r233266 = t;
        double r233267 = r233266 / r233263;
        double r233268 = tanh(r233267);
        double r233269 = r233262 / r233263;
        double r233270 = tanh(r233269);
        double r233271 = r233268 - r233270;
        double r233272 = r233265 * r233271;
        double r233273 = r233262 + r233272;
        return r233273;
}
↓
double f(double x, double y, double z, double t) {
        double r233274 = x;
        double r233275 = z;
        double r233276 = t;
        double r233277 = y;
        double r233278 = r233276 / r233277;
        double r233279 = tanh(r233278);
        double r233280 = r233274 / r233277;
        double r233281 = tanh(r233280);
        double r233282 = r233279 - r233281;
        double r233283 = r233282 * r233277;
        double r233284 = r233275 * r233283;
        double r233285 = r233274 + r233284;
        return r233285;
}

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
Target1.9
Herbie1.5
\[x + y \cdot \left(z \cdot \left(\tanh \left(\frac{t}{y}\right) - \tanh \left(\frac{x}{y}\right)\right)\right)\]

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 pow14.5

    \[\leadsto x + \left(y \cdot z\right) \cdot \color{blue}{{\left(\tanh \left(\frac{t}{y}\right) - \tanh \left(\frac{x}{y}\right)\right)}^{1}}\]

  4. Applied pow14.5

    \[\leadsto x + \left(y \cdot \color{blue}{{z}^{1}}\right) \cdot {\left(\tanh \left(\frac{t}{y}\right) - \tanh \left(\frac{x}{y}\right)\right)}^{1}\]

  5. Applied pow14.5

    \[\leadsto x + \left(\color{blue}{{y}^{1}} \cdot {z}^{1}\right) \cdot {\left(\tanh \left(\frac{t}{y}\right) - \tanh \left(\frac{x}{y}\right)\right)}^{1}\]

  6. Applied pow-prod-down4.5

    \[\leadsto x + \color{blue}{{\left(y \cdot z\right)}^{1}} \cdot {\left(\tanh \left(\frac{t}{y}\right) - \tanh \left(\frac{x}{y}\right)\right)}^{1}\]

  7. Applied pow-prod-down4.5

    \[\leadsto x + \color{blue}{{\left(\left(y \cdot z\right) \cdot \left(\tanh \left(\frac{t}{y}\right) - \tanh \left(\frac{x}{y}\right)\right)\right)}^{1}}\]

  8. Simplified1.5

    \[\leadsto x + {\color{blue}{\left(z \cdot \left(\left(\tanh \left(\frac{t}{y}\right) - \tanh \left(\frac{x}{y}\right)\right) \cdot y\right)\right)}}^{1}\]

  9. Final simplification1.5

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

Reproduce

herbie shell --seed 2019209 +o rules:numerics
(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))))))