Average Error: 2.9 → 1.8
Time: 45.8s
Precision: 64
\[\frac{x \cdot \frac{\sin y}{y}}{z}\]
↓
\[\begin{array}{l} \mathbf{if}\;x \le 3.564026261687553078497224150168067424455 \cdot 10^{114}:\\ \;\;\;\;\frac{x}{\frac{z}{\frac{\sin y}{y}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{z}{\frac{x}{\frac{y}{\sin y}}}}\\ \end{array}\]
\frac{x \cdot \frac{\sin y}{y}}{z}
↓
\begin{array}{l}
\mathbf{if}\;x \le 3.564026261687553078497224150168067424455 \cdot 10^{114}:\\
\;\;\;\;\frac{x}{\frac{z}{\frac{\sin y}{y}}}\\

\mathbf{else}:\\
\;\;\;\;\frac{1}{\frac{z}{\frac{x}{\frac{y}{\sin y}}}}\\

\end{array}
double f(double x, double y, double z) {
        double r20712197 = x;
        double r20712198 = y;
        double r20712199 = sin(r20712198);
        double r20712200 = r20712199 / r20712198;
        double r20712201 = r20712197 * r20712200;
        double r20712202 = z;
        double r20712203 = r20712201 / r20712202;
        return r20712203;
}
↓
double f(double x, double y, double z) {
        double r20712204 = x;
        double r20712205 = 3.564026261687553e+114;
        bool r20712206 = r20712204 <= r20712205;
        double r20712207 = z;
        double r20712208 = y;
        double r20712209 = sin(r20712208);
        double r20712210 = r20712209 / r20712208;
        double r20712211 = r20712207 / r20712210;
        double r20712212 = r20712204 / r20712211;
        double r20712213 = 1.0;
        double r20712214 = r20712208 / r20712209;
        double r20712215 = r20712204 / r20712214;
        double r20712216 = r20712207 / r20712215;
        double r20712217 = r20712213 / r20712216;
        double r20712218 = r20712206 ? r20712212 : r20712217;
        return r20712218;
}

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

Original2.9
Target0.3
Herbie1.8
\[\begin{array}{l} \mathbf{if}\;z \lt -4.217372020342714661850238929213415773451 \cdot 10^{-29}:\\ \;\;\;\;\frac{x \cdot \frac{1}{\frac{y}{\sin y}}}{z}\\ \mathbf{elif}\;z \lt 4.446702369113811028051510715777703865332 \cdot 10^{64}:\\ \;\;\;\;\frac{x}{z \cdot \frac{y}{\sin y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \frac{1}{\frac{y}{\sin y}}}{z}\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if x < 3.564026261687553e+114

    1. Initial program 3.3

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

    3. Applied associate-/l*2.0

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

    if 3.564026261687553e+114 < x

    1. Initial program 0.3

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

    3. Applied clear-num0.3

      \[\leadsto \frac{x \cdot \color{blue}{\frac{1}{\frac{y}{\sin y}}}}{z}\]
    4. Using strategy rm

    5. Applied clear-num0.5

      \[\leadsto \color{blue}{\frac{1}{\frac{z}{x \cdot \frac{1}{\frac{y}{\sin y}}}}}\]

    6. Simplified0.5

      \[\leadsto \frac{1}{\color{blue}{\frac{z}{\frac{x}{\frac{y}{\sin y}}}}}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification1.8

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \le 3.564026261687553078497224150168067424455 \cdot 10^{114}:\\ \;\;\;\;\frac{x}{\frac{z}{\frac{\sin y}{y}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{z}{\frac{x}{\frac{y}{\sin y}}}}\\ \end{array}\]

Reproduce

herbie shell --seed 2019168 +o rules:numerics
(FPCore (x y z)
  :name "Linear.Quaternion:$ctanh from linear-1.19.1.3"

  :herbie-target
  (if (< z -4.2173720203427147e-29) (/ (* x (/ 1.0 (/ y (sin y)))) z) (if (< z 4.446702369113811e+64) (/ x (* z (/ y (sin y)))) (/ (* x (/ 1.0 (/ y (sin y)))) z)))

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