Average Error: 4.6 → 1.5
Time: 4.7s
Precision: 64
\[x + \left(y \cdot z\right) \cdot \left(\tanh \left(\frac{t}{y}\right) - \tanh \left(\frac{x}{y}\right)\right)\]
↓
\[x + \left(\left(y \cdot \tanh \left(\frac{t}{y}\right)\right) \cdot z + y \cdot \left(\left(-\tanh \left(\frac{x}{y}\right)\right) \cdot z\right)\right)\]
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 + y \cdot \left(\left(-\tanh \left(\frac{x}{y}\right)\right) \cdot z\right)\right)
double code(double x, double y, double z, double t) {
	return (x + ((y * z) * (tanh((t / y)) - tanh((x / y)))));
}
↓
double code(double x, double y, double z, double t) {
	return (x + (((y * tanh((t / y))) * z) + (y * (-tanh((x / y)) * z))));
}

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

Derivation

  1. Initial program 4.6

    \[x + \left(y \cdot z\right) \cdot \left(\tanh \left(\frac{t}{y}\right) - \tanh \left(\frac{x}{y}\right)\right)\]
  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-in2.0

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

  8. Simplified2.0

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

  9. Simplified2.0

    \[\leadsto x + \left(y \cdot \left(\tanh \left(\frac{t}{y}\right) \cdot z\right) + \color{blue}{y \cdot \left(\left(-\tanh \left(\frac{x}{y}\right)\right) \cdot z\right)}\right)\]
  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. Final simplification1.5

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

Reproduce

herbie shell --seed 2020092 
(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))))))