SynthBasics:moogVCF from YampaSynth-0.2

Average Error: 4.8 → 2.0

Time: 25.9s

Precision: 64

Math

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

↓

\[\mathsf{fma}\left(y, z \cdot \left(\tanh \left(\frac{t}{y}\right) - \tanh \left(\frac{x}{y}\right)\right), x\right)\]

C

double f(double x, double y, double z, double t) {
        double r431603 = x;
        double r431604 = y;
        double r431605 = z;
        double r431606 = r431604 * r431605;
        double r431607 = t;
        double r431608 = r431607 / r431604;
        double r431609 = tanh(r431608);
        double r431610 = r431603 / r431604;
        double r431611 = tanh(r431610);
        double r431612 = r431609 - r431611;
        double r431613 = r431606 * r431612;
        double r431614 = r431603 + r431613;
        return r431614;
}

↓

double f(double x, double y, double z, double t) {
        double r431615 = y;
        double r431616 = z;
        double r431617 = t;
        double r431618 = r431617 / r431615;
        double r431619 = tanh(r431618);
        double r431620 = x;
        double r431621 = r431620 / r431615;
        double r431622 = tanh(r431621);
        double r431623 = r431619 - r431622;
        double r431624 = r431616 * r431623;
        double r431625 = fma(r431615, r431624, r431620);
        return r431625;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Target

Original	4.8
Target	2.0
Herbie	2.0

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

Derivation

1. Initial program 4.8

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

2. Simplified 2.0

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

3. Final simplification 2.0

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

Reproduce

herbie shell --seed 2020057 +o rules:numerics
(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))))))