Average Error: 2.7 → 1.8
Time: 14.9s
Precision: 64
\[\frac{x \cdot \frac{\sin y}{y}}{z}\]
↓
\[\begin{array}{l} \mathbf{if}\;x \le 3.883506706037952 \cdot 10^{-64}:\\ \;\;\;\;\frac{x}{\frac{z}{\frac{\sin y}{y}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{z}{x \cdot \frac{\sin y}{y}}}\\ \end{array}\]
\frac{x \cdot \frac{\sin y}{y}}{z}
↓
\begin{array}{l}
\mathbf{if}\;x \le 3.883506706037952 \cdot 10^{-64}:\\
\;\;\;\;\frac{x}{\frac{z}{\frac{\sin y}{y}}}\\

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

\end{array}
double f(double x, double y, double z) {
        double r25067189 = x;
        double r25067190 = y;
        double r25067191 = sin(r25067190);
        double r25067192 = r25067191 / r25067190;
        double r25067193 = r25067189 * r25067192;
        double r25067194 = z;
        double r25067195 = r25067193 / r25067194;
        return r25067195;
}
↓
double f(double x, double y, double z) {
        double r25067196 = x;
        double r25067197 = 3.883506706037952e-64;
        bool r25067198 = r25067196 <= r25067197;
        double r25067199 = z;
        double r25067200 = y;
        double r25067201 = sin(r25067200);
        double r25067202 = r25067201 / r25067200;
        double r25067203 = r25067199 / r25067202;
        double r25067204 = r25067196 / r25067203;
        double r25067205 = 1.0;
        double r25067206 = r25067196 * r25067202;
        double r25067207 = r25067199 / r25067206;
        double r25067208 = r25067205 / r25067207;
        double r25067209 = r25067198 ? r25067204 : r25067208;
        return r25067209;
}

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
Herbie1.8
\[\begin{array}{l} \mathbf{if}\;z \lt -4.2173720203427147 \cdot 10^{-29}:\\ \;\;\;\;\frac{x \cdot \frac{1}{\frac{y}{\sin y}}}{z}\\ \mathbf{elif}\;z \lt 4.446702369113811 \cdot 10^{+64}:\\ \;\;\;\;\frac{x}{z \cdot \frac{y}{\sin y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \frac{1}{\frac{y}{\sin y}}}{z}\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if x < 3.883506706037952e-64

    1. Initial program 3.7

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

    3. Applied associate-/l*2.1

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

    if 3.883506706037952e-64 < x

    1. Initial program 0.5

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

    3. Applied clear-num0.9

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

  4. Final simplification1.8

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \le 3.883506706037952 \cdot 10^{-64}:\\ \;\;\;\;\frac{x}{\frac{z}{\frac{\sin y}{y}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{z}{x \cdot \frac{\sin y}{y}}}\\ \end{array}\]

Reproduce

herbie shell --seed 2019163 
(FPCore (x y z)
  :name "Linear.Quaternion:$ctanh from linear-1.19.1.3"

  :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))