Average Error: 4.6 → 1.4
Time: 5.3s
Precision: 64
\[x + \left(y \cdot z\right) \cdot \left(\tanh \left(\frac{t}{y}\right) - \tanh \left(\frac{x}{y}\right)\right)\]
↓
\[x + \left(\left(y \cdot \tanh \left(\frac{t}{y}\right)\right) \cdot z + \left(y \cdot \left(-\tanh \left(\frac{x}{y}\right)\right)\right) \cdot z\right)\]
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 r349361 = x;
        double r349362 = y;
        double r349363 = z;
        double r349364 = r349362 * r349363;
        double r349365 = t;
        double r349366 = r349365 / r349362;
        double r349367 = tanh(r349366);
        double r349368 = r349361 / r349362;
        double r349369 = tanh(r349368);
        double r349370 = r349367 - r349369;
        double r349371 = r349364 * r349370;
        double r349372 = r349361 + r349371;
        return r349372;
}
↓
double f(double x, double y, double z, double t) {
        double r349373 = x;
        double r349374 = y;
        double r349375 = t;
        double r349376 = r349375 / r349374;
        double r349377 = tanh(r349376);
        double r349378 = r349374 * r349377;
        double r349379 = z;
        double r349380 = r349378 * r349379;
        double r349381 = r349373 / r349374;
        double r349382 = tanh(r349381);
        double r349383 = -r349382;
        double r349384 = r349374 * r349383;
        double r349385 = r349384 * r349379;
        double r349386 = r349380 + r349385;
        double r349387 = r349373 + r349386;
        return r349387;
}

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
Target1.8
Herbie1.4
\[x + y \cdot \left(z \cdot \left(\tanh \left(\frac{t}{y}\right) - \tanh \left(\frac{x}{y}\right)\right)\right)\]

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*1.8

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

  5. Applied sub-neg1.8

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

  6. Applied distribute-lft-in1.8

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

  7. Applied distribute-lft-in1.9

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

  8. Simplified1.9

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

  9. Simplified1.9

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

  11. Applied associate-*r*1.5

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

  13. Applied associate-*r*1.4

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

  14. Final simplification1.4

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

Reproduce

herbie shell --seed 2020036 
(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))))))