Average Error: 4.6 → 1.6
Time: 6.1s
Precision: 64
\[x + \left(y \cdot z\right) \cdot \left(\tanh \left(\frac{t}{y}\right) - \tanh \left(\frac{x}{y}\right)\right)\]
↓
\[x + \left(\left(y \cdot \tanh \left(\frac{t}{y}\right)\right) \cdot z + \left(y \cdot \left(-\tanh \left(\frac{x}{y}\right)\right)\right) \cdot z\right)\]
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 + \left(y \cdot \left(-\tanh \left(\frac{x}{y}\right)\right)\right) \cdot z\right)
double f(double x, double y, double z, double t) {
        double r329970 = x;
        double r329971 = y;
        double r329972 = z;
        double r329973 = r329971 * r329972;
        double r329974 = t;
        double r329975 = r329974 / r329971;
        double r329976 = tanh(r329975);
        double r329977 = r329970 / r329971;
        double r329978 = tanh(r329977);
        double r329979 = r329976 - r329978;
        double r329980 = r329973 * r329979;
        double r329981 = r329970 + r329980;
        return r329981;
}
↓
double f(double x, double y, double z, double t) {
        double r329982 = x;
        double r329983 = y;
        double r329984 = t;
        double r329985 = r329984 / r329983;
        double r329986 = tanh(r329985);
        double r329987 = r329983 * r329986;
        double r329988 = z;
        double r329989 = r329987 * r329988;
        double r329990 = r329982 / r329983;
        double r329991 = tanh(r329990);
        double r329992 = -r329991;
        double r329993 = r329983 * r329992;
        double r329994 = r329993 * r329988;
        double r329995 = r329989 + r329994;
        double r329996 = r329982 + r329995;
        return r329996;
}

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
Herbie1.6
\[x + y \cdot \left(z \cdot \left(\tanh \left(\frac{t}{y}\right) - \tanh \left(\frac{x}{y}\right)\right)\right)\]

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 pow12.1

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

  7. Applied sub-neg2.1

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

  8. Applied distribute-lft-in2.1

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

  9. Applied distribute-lft-in2.3

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

  10. Simplified1.7

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

  11. Simplified1.7

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

  13. Applied associate-*r*1.6

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

  14. Final simplification1.6

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

Reproduce

herbie shell --seed 2020089 
(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))))))