Average Error: 4.7 → 2.5
Time: 19.5s
Precision: 64
\[x + \left(y \cdot z\right) \cdot \left(\tanh \left(\frac{t}{y}\right) - \tanh \left(\frac{x}{y}\right)\right)\]
↓
\[x + \left(\sqrt[3]{z \cdot \left(\tanh \left(\frac{t}{y}\right) - \tanh \left(\frac{x}{y}\right)\right)} \cdot \left(\sqrt[3]{z \cdot \left(\tanh \left(\frac{t}{y}\right) - \tanh \left(\frac{x}{y}\right)\right)} \cdot y\right)\right) \cdot \sqrt[3]{\tanh \left(\frac{t}{y}\right) \cdot z + \left(-\tanh \left(\frac{x}{y}\right)\right) \cdot z}\]
x + \left(y \cdot z\right) \cdot \left(\tanh \left(\frac{t}{y}\right) - \tanh \left(\frac{x}{y}\right)\right)
↓
x + \left(\sqrt[3]{z \cdot \left(\tanh \left(\frac{t}{y}\right) - \tanh \left(\frac{x}{y}\right)\right)} \cdot \left(\sqrt[3]{z \cdot \left(\tanh \left(\frac{t}{y}\right) - \tanh \left(\frac{x}{y}\right)\right)} \cdot y\right)\right) \cdot \sqrt[3]{\tanh \left(\frac{t}{y}\right) \cdot z + \left(-\tanh \left(\frac{x}{y}\right)\right) \cdot z}
double f(double x, double y, double z, double t) {
        double r217487 = x;
        double r217488 = y;
        double r217489 = z;
        double r217490 = r217488 * r217489;
        double r217491 = t;
        double r217492 = r217491 / r217488;
        double r217493 = tanh(r217492);
        double r217494 = r217487 / r217488;
        double r217495 = tanh(r217494);
        double r217496 = r217493 - r217495;
        double r217497 = r217490 * r217496;
        double r217498 = r217487 + r217497;
        return r217498;
}
↓
double f(double x, double y, double z, double t) {
        double r217499 = x;
        double r217500 = z;
        double r217501 = t;
        double r217502 = y;
        double r217503 = r217501 / r217502;
        double r217504 = tanh(r217503);
        double r217505 = r217499 / r217502;
        double r217506 = tanh(r217505);
        double r217507 = r217504 - r217506;
        double r217508 = r217500 * r217507;
        double r217509 = cbrt(r217508);
        double r217510 = r217509 * r217502;
        double r217511 = r217509 * r217510;
        double r217512 = r217504 * r217500;
        double r217513 = -r217506;
        double r217514 = r217513 * r217500;
        double r217515 = r217512 + r217514;
        double r217516 = cbrt(r217515);
        double r217517 = r217511 * r217516;
        double r217518 = r217499 + r217517;
        return r217518;
}

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
Target2.2
Herbie2.5
\[x + y \cdot \left(z \cdot \left(\tanh \left(\frac{t}{y}\right) - \tanh \left(\frac{x}{y}\right)\right)\right)\]

Derivation

  1. Initial program 4.7

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

  3. Applied associate-*l*2.2

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

  5. Applied sub-neg2.2

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

  6. Applied distribute-lft-in2.2

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

  7. Simplified2.2

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

  8. Simplified2.2

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

  10. Applied add-cube-cbrt2.5

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

  11. Applied associate-*r*2.5

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

  12. Simplified2.5

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

  13. Final simplification2.5

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

Reproduce

herbie shell --seed 2019325 
(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))))))