Average Error: 4.7 → 1.4
Time: 5.4s
Precision: 64
\[x + \left(y \cdot z\right) \cdot \left(\tanh \left(\frac{t}{y}\right) - \tanh \left(\frac{x}{y}\right)\right)\]
↓
\[\left(y \cdot \left(\tanh \left(\frac{t}{y}\right) - \tanh \left(\frac{x}{y}\right)\right)\right) \cdot z + x\]
x + \left(y \cdot z\right) \cdot \left(\tanh \left(\frac{t}{y}\right) - \tanh \left(\frac{x}{y}\right)\right)
↓
\left(y \cdot \left(\tanh \left(\frac{t}{y}\right) - \tanh \left(\frac{x}{y}\right)\right)\right) \cdot z + x
double code(double x, double y, double z, double t) {
	return ((double) (x + ((double) (((double) (y * z)) * ((double) (((double) tanh(((double) (t / y)))) - ((double) tanh(((double) (x / y))))))))));
}
↓
double code(double x, double y, double z, double t) {
	return ((double) (((double) (((double) (y * ((double) (((double) tanh(((double) (t / y)))) - ((double) tanh(((double) (x / y)))))))) * z)) + x));
}

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

Original4.7
Target1.9
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 4.7

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

  3. Applied add-log-exp7.0

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

  5. Applied pow17.0

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

  6. Applied pow17.0

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

  7. Applied pow17.0

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

  8. Applied pow-prod-down7.0

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

  9. Applied pow-prod-down7.0

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

  10. Simplified1.4

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

  11. Final simplification1.4

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

Reproduce

herbie shell --seed 2020121 
(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))))))