Average Error: 4.5 → 1.4
Time: 22.1s
Precision: 64
\[x + \left(y \cdot z\right) \cdot \left(\tanh \left(\frac{t}{y}\right) - \tanh \left(\frac{x}{y}\right)\right)\]
↓
\[x + z \cdot \left(\left(\tanh \left(\frac{t}{y}\right) - \tanh \left(\frac{x}{y}\right)\right) \cdot y\right)\]
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 r219483 = x;
        double r219484 = y;
        double r219485 = z;
        double r219486 = r219484 * r219485;
        double r219487 = t;
        double r219488 = r219487 / r219484;
        double r219489 = tanh(r219488);
        double r219490 = r219483 / r219484;
        double r219491 = tanh(r219490);
        double r219492 = r219489 - r219491;
        double r219493 = r219486 * r219492;
        double r219494 = r219483 + r219493;
        return r219494;
}
↓
double f(double x, double y, double z, double t) {
        double r219495 = x;
        double r219496 = z;
        double r219497 = t;
        double r219498 = y;
        double r219499 = r219497 / r219498;
        double r219500 = tanh(r219499);
        double r219501 = r219495 / r219498;
        double r219502 = tanh(r219501);
        double r219503 = r219500 - r219502;
        double r219504 = r219503 * r219498;
        double r219505 = r219496 * r219504;
        double r219506 = r219495 + r219505;
        return r219506;
}

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
Target2.0
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 4.5

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

  3. Applied associate-*l*2.0

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

  5. Applied add-cube-cbrt2.4

    \[\leadsto x + y \cdot \left(\color{blue}{\left(\left(\sqrt[3]{z} \cdot \sqrt[3]{z}\right) \cdot \sqrt[3]{z}\right)} \cdot \left(\tanh \left(\frac{t}{y}\right) - \tanh \left(\frac{x}{y}\right)\right)\right)\]

  6. Applied associate-*l*2.4

    \[\leadsto x + y \cdot \color{blue}{\left(\left(\sqrt[3]{z} \cdot \sqrt[3]{z}\right) \cdot \left(\sqrt[3]{z} \cdot \left(\tanh \left(\frac{t}{y}\right) - \tanh \left(\frac{x}{y}\right)\right)\right)\right)}\]
  7. Using strategy rm

  8. Applied *-un-lft-identity2.4

    \[\leadsto x + \color{blue}{\left(1 \cdot y\right)} \cdot \left(\left(\sqrt[3]{z} \cdot \sqrt[3]{z}\right) \cdot \left(\sqrt[3]{z} \cdot \left(\tanh \left(\frac{t}{y}\right) - \tanh \left(\frac{x}{y}\right)\right)\right)\right)\]

  9. Applied associate-*l*2.4

    \[\leadsto x + \color{blue}{1 \cdot \left(y \cdot \left(\left(\sqrt[3]{z} \cdot \sqrt[3]{z}\right) \cdot \left(\sqrt[3]{z} \cdot \left(\tanh \left(\frac{t}{y}\right) - \tanh \left(\frac{x}{y}\right)\right)\right)\right)\right)}\]

  10. Simplified1.4

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

  11. Final simplification1.4

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

Reproduce

herbie shell --seed 2019212 
(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))))))