Average Error: 4.6 → 1.5
Time: 6.3s
Precision: 64
\[x + \left(y \cdot z\right) \cdot \left(\tanh \left(\frac{t}{y}\right) - \tanh \left(\frac{x}{y}\right)\right)\]
↓
\[\left(y \cdot \tanh \left(\frac{t}{y}\right) + y \cdot \left(-\tanh \left(\frac{x}{y}\right)\right)\right) \cdot z + x\]
x + \left(y \cdot z\right) \cdot \left(\tanh \left(\frac{t}{y}\right) - \tanh \left(\frac{x}{y}\right)\right)
↓
\left(y \cdot \tanh \left(\frac{t}{y}\right) + y \cdot \left(-\tanh \left(\frac{x}{y}\right)\right)\right) \cdot z + x
double f(double x, double y, double z, double t) {
        double r243151 = x;
        double r243152 = y;
        double r243153 = z;
        double r243154 = r243152 * r243153;
        double r243155 = t;
        double r243156 = r243155 / r243152;
        double r243157 = tanh(r243156);
        double r243158 = r243151 / r243152;
        double r243159 = tanh(r243158);
        double r243160 = r243157 - r243159;
        double r243161 = r243154 * r243160;
        double r243162 = r243151 + r243161;
        return r243162;
}
↓
double f(double x, double y, double z, double t) {
        double r243163 = y;
        double r243164 = t;
        double r243165 = r243164 / r243163;
        double r243166 = tanh(r243165);
        double r243167 = r243163 * r243166;
        double r243168 = x;
        double r243169 = r243168 / r243163;
        double r243170 = tanh(r243169);
        double r243171 = -r243170;
        double r243172 = r243163 * r243171;
        double r243173 = r243167 + r243172;
        double r243174 = z;
        double r243175 = r243173 * r243174;
        double r243176 = r243175 + r243168;
        return r243176;
}

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
Target2.1
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. Simplified2.1

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

  4. Applied add-cube-cbrt2.5

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

  5. Applied associate-*l*2.5

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

  7. Applied fma-udef2.5

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

  8. Simplified1.5

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

  10. Applied sub-neg1.5

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

  11. Applied distribute-lft-in1.5

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

  12. Final simplification1.5

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

Reproduce

herbie shell --seed 2020089 +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))))))