Average Error: 2.7 → 1.6
Time: 18.1s
Precision: 64
\[\frac{x \cdot \frac{\sin y}{y}}{z}\]
↓
\[\begin{array}{l} \mathbf{if}\;x \le 2.843405087967007653899124626840383149923 \cdot 10^{134}:\\ \;\;\;\;\frac{x}{z \cdot \frac{y}{\sin y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x \cdot \sin y}{y}}{z}\\ \end{array}\]
\frac{x \cdot \frac{\sin y}{y}}{z}
↓
\begin{array}{l}
\mathbf{if}\;x \le 2.843405087967007653899124626840383149923 \cdot 10^{134}:\\
\;\;\;\;\frac{x}{z \cdot \frac{y}{\sin y}}\\

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

\end{array}
double f(double x, double y, double z) {
        double r345442 = x;
        double r345443 = y;
        double r345444 = sin(r345443);
        double r345445 = r345444 / r345443;
        double r345446 = r345442 * r345445;
        double r345447 = z;
        double r345448 = r345446 / r345447;
        return r345448;
}
↓
double f(double x, double y, double z) {
        double r345449 = x;
        double r345450 = 2.8434050879670077e+134;
        bool r345451 = r345449 <= r345450;
        double r345452 = z;
        double r345453 = y;
        double r345454 = sin(r345453);
        double r345455 = r345453 / r345454;
        double r345456 = r345452 * r345455;
        double r345457 = r345449 / r345456;
        double r345458 = r345449 * r345454;
        double r345459 = r345458 / r345453;
        double r345460 = r345459 / r345452;
        double r345461 = r345451 ? r345457 : r345460;
        return r345461;
}

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

Original2.7
Target0.3
Herbie1.6
\[\begin{array}{l} \mathbf{if}\;z \lt -4.217372020342714661850238929213415773451 \cdot 10^{-29}:\\ \;\;\;\;\frac{x \cdot \frac{1}{\frac{y}{\sin y}}}{z}\\ \mathbf{elif}\;z \lt 4.446702369113811028051510715777703865332 \cdot 10^{64}:\\ \;\;\;\;\frac{x}{z \cdot \frac{y}{\sin y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \frac{1}{\frac{y}{\sin y}}}{z}\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if x < 2.8434050879670077e+134

    1. Initial program 3.0

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

    3. Applied associate-/l*1.8

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

    4. Simplified1.8

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

    if 2.8434050879670077e+134 < x

    1. Initial program 0.3

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

    3. Applied pow10.3

      \[\leadsto \frac{x \cdot \color{blue}{{\left(\frac{\sin y}{y}\right)}^{1}}}{z}\]

    4. Applied pow10.3

      \[\leadsto \frac{\color{blue}{{x}^{1}} \cdot {\left(\frac{\sin y}{y}\right)}^{1}}{z}\]

    5. Applied pow-prod-down0.3

      \[\leadsto \frac{\color{blue}{{\left(x \cdot \frac{\sin y}{y}\right)}^{1}}}{z}\]

    6. Simplified0.3

      \[\leadsto \frac{{\color{blue}{\left(\frac{x \cdot \sin y}{y}\right)}}^{1}}{z}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification1.6

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \le 2.843405087967007653899124626840383149923 \cdot 10^{134}:\\ \;\;\;\;\frac{x}{z \cdot \frac{y}{\sin y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x \cdot \sin y}{y}}{z}\\ \end{array}\]

Reproduce

herbie shell --seed 2019323 +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))