Average Error: 2.6 → 0.5
Time: 4.4s
Precision: 64
\[\frac{x \cdot \frac{\sin y}{y}}{z}\]
↓
\[\begin{array}{l} \mathbf{if}\;x \le -1.74032442839244311 \cdot 10^{61} \lor \neg \left(x \le 1.06761205643968897 \cdot 10^{85}\right):\\ \;\;\;\;\frac{\frac{x \cdot \sin y}{y}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{\frac{\sin y}{y}}}\\ \end{array}\]
\frac{x \cdot \frac{\sin y}{y}}{z}
↓
\begin{array}{l}
\mathbf{if}\;x \le -1.74032442839244311 \cdot 10^{61} \lor \neg \left(x \le 1.06761205643968897 \cdot 10^{85}\right):\\
\;\;\;\;\frac{\frac{x \cdot \sin y}{y}}{z}\\

\mathbf{else}:\\
\;\;\;\;\frac{x}{\frac{z}{\frac{\sin y}{y}}}\\

\end{array}
double f(double x, double y, double z) {
        double r583440 = x;
        double r583441 = y;
        double r583442 = sin(r583441);
        double r583443 = r583442 / r583441;
        double r583444 = r583440 * r583443;
        double r583445 = z;
        double r583446 = r583444 / r583445;
        return r583446;
}
↓
double f(double x, double y, double z) {
        double r583447 = x;
        double r583448 = -1.740324428392443e+61;
        bool r583449 = r583447 <= r583448;
        double r583450 = 1.067612056439689e+85;
        bool r583451 = r583447 <= r583450;
        double r583452 = !r583451;
        bool r583453 = r583449 || r583452;
        double r583454 = y;
        double r583455 = sin(r583454);
        double r583456 = r583447 * r583455;
        double r583457 = r583456 / r583454;
        double r583458 = z;
        double r583459 = r583457 / r583458;
        double r583460 = r583455 / r583454;
        double r583461 = r583458 / r583460;
        double r583462 = r583447 / r583461;
        double r583463 = r583453 ? r583459 : r583462;
        return r583463;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original2.6
Target0.3
Herbie0.5
\[\begin{array}{l} \mathbf{if}\;z \lt -4.21737202034271466 \cdot 10^{-29}:\\ \;\;\;\;\frac{x \cdot \frac{1}{\frac{y}{\sin y}}}{z}\\ \mathbf{elif}\;z \lt 4.44670236911381103 \cdot 10^{64}:\\ \;\;\;\;\frac{x}{z \cdot \frac{y}{\sin y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \frac{1}{\frac{y}{\sin y}}}{z}\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if x < -1.740324428392443e+61 or 1.067612056439689e+85 < x

    1. Initial program 0.2

      \[\frac{x \cdot \frac{\sin y}{y}}{z}\]
    2. Using strategy rm

    3. Applied associate-*r/0.3

      \[\leadsto \frac{\color{blue}{\frac{x \cdot \sin y}{y}}}{z}\]

    if -1.740324428392443e+61 < x < 1.067612056439689e+85

    1. Initial program 3.8

      \[\frac{x \cdot \frac{\sin y}{y}}{z}\]
    2. Using strategy rm

    3. Applied associate-/l*0.5

      \[\leadsto \color{blue}{\frac{x}{\frac{z}{\frac{\sin y}{y}}}}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification0.5

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \le -1.74032442839244311 \cdot 10^{61} \lor \neg \left(x \le 1.06761205643968897 \cdot 10^{85}\right):\\ \;\;\;\;\frac{\frac{x \cdot \sin y}{y}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{\frac{\sin y}{y}}}\\ \end{array}\]

Reproduce

herbie shell --seed 2020057 +o rules:numerics
(FPCore (x y z)
  :name "Linear.Quaternion:$ctanh from linear-1.19.1.3"
  :precision binary64

  :herbie-target
  (if (< z -4.2173720203427147e-29) (/ (* x (/ 1 (/ y (sin y)))) z) (if (< z 4.446702369113811e+64) (/ x (* z (/ y (sin y)))) (/ (* x (/ 1 (/ y (sin y)))) z)))

  (/ (* x (/ (sin y) y)) z))