Average Error: 2.8 → 0.3
Time: 10.5s
Precision: 64
\[\frac{x \cdot \frac{\sin y}{y}}{z}\]
↓
\[\begin{array}{l} \mathbf{if}\;z \le -6.556330221928381769630387918095839368079 \cdot 10^{49} \lor \neg \left(z \le 2.48803922824049036872437422192558118528 \cdot 10^{-43}\right):\\ \;\;\;\;\frac{\left(\sqrt{1} \cdot x\right) \cdot \left|\sqrt[3]{1}\right|}{z} \cdot \frac{\sqrt{\sqrt[3]{1}}}{\frac{1}{\frac{\sin y}{y}}}\\ \mathbf{else}:\\ \;\;\;\;\left(\sqrt{1} \cdot x\right) \cdot \frac{\sqrt{1}}{\frac{z}{\frac{\sin y}{y}}}\\ \end{array}\]
\frac{x \cdot \frac{\sin y}{y}}{z}
↓
\begin{array}{l}
\mathbf{if}\;z \le -6.556330221928381769630387918095839368079 \cdot 10^{49} \lor \neg \left(z \le 2.48803922824049036872437422192558118528 \cdot 10^{-43}\right):\\
\;\;\;\;\frac{\left(\sqrt{1} \cdot x\right) \cdot \left|\sqrt[3]{1}\right|}{z} \cdot \frac{\sqrt{\sqrt[3]{1}}}{\frac{1}{\frac{\sin y}{y}}}\\

\mathbf{else}:\\
\;\;\;\;\left(\sqrt{1} \cdot x\right) \cdot \frac{\sqrt{1}}{\frac{z}{\frac{\sin y}{y}}}\\

\end{array}
double f(double x, double y, double z) {
        double r436287 = x;
        double r436288 = y;
        double r436289 = sin(r436288);
        double r436290 = r436289 / r436288;
        double r436291 = r436287 * r436290;
        double r436292 = z;
        double r436293 = r436291 / r436292;
        return r436293;
}
↓
double f(double x, double y, double z) {
        double r436294 = z;
        double r436295 = -6.556330221928382e+49;
        bool r436296 = r436294 <= r436295;
        double r436297 = 2.4880392282404904e-43;
        bool r436298 = r436294 <= r436297;
        double r436299 = !r436298;
        bool r436300 = r436296 || r436299;
        double r436301 = 1.0;
        double r436302 = sqrt(r436301);
        double r436303 = x;
        double r436304 = r436302 * r436303;
        double r436305 = cbrt(r436301);
        double r436306 = fabs(r436305);
        double r436307 = r436304 * r436306;
        double r436308 = r436307 / r436294;
        double r436309 = sqrt(r436305);
        double r436310 = y;
        double r436311 = sin(r436310);
        double r436312 = r436311 / r436310;
        double r436313 = r436301 / r436312;
        double r436314 = r436309 / r436313;
        double r436315 = r436308 * r436314;
        double r436316 = r436294 / r436312;
        double r436317 = r436302 / r436316;
        double r436318 = r436304 * r436317;
        double r436319 = r436300 ? r436315 : r436318;
        return r436319;
}

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

Original2.8
Target0.3
Herbie0.3
\[\begin{array}{l} \mathbf{if}\;z \lt -4.217372020342714661850238929213415773451 \cdot 10^{-29}:\\ \;\;\;\;\frac{x \cdot \frac{1}{\frac{y}{\sin y}}}{z}\\ \mathbf{elif}\;z \lt 4.446702369113811028051510715777703865332 \cdot 10^{64}:\\ \;\;\;\;\frac{x}{z \cdot \frac{y}{\sin y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \frac{1}{\frac{y}{\sin y}}}{z}\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if z < -6.556330221928382e+49 or 2.4880392282404904e-43 < z

    1. Initial program 0.1

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

    3. Applied clear-num0.9

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

    5. Applied *-un-lft-identity0.9

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

    6. Applied times-frac6.0

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

    7. Applied add-sqr-sqrt6.0

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

    8. Applied times-frac5.7

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

    9. Simplified5.6

      \[\leadsto \color{blue}{\left(\sqrt{1} \cdot x\right)} \cdot \frac{\sqrt{1}}{\frac{z}{\frac{\sin y}{y}}}\]
    10. Using strategy rm

    11. Applied div-inv5.6

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

    12. Applied add-cube-cbrt5.6

      \[\leadsto \left(\sqrt{1} \cdot x\right) \cdot \frac{\sqrt{\color{blue}{\left(\sqrt[3]{1} \cdot \sqrt[3]{1}\right) \cdot \sqrt[3]{1}}}}{z \cdot \frac{1}{\frac{\sin y}{y}}}\]

    13. Applied sqrt-prod5.6

      \[\leadsto \left(\sqrt{1} \cdot x\right) \cdot \frac{\color{blue}{\sqrt{\sqrt[3]{1} \cdot \sqrt[3]{1}} \cdot \sqrt{\sqrt[3]{1}}}}{z \cdot \frac{1}{\frac{\sin y}{y}}}\]

    14. Applied times-frac5.2

      \[\leadsto \left(\sqrt{1} \cdot x\right) \cdot \color{blue}{\left(\frac{\sqrt{\sqrt[3]{1} \cdot \sqrt[3]{1}}}{z} \cdot \frac{\sqrt{\sqrt[3]{1}}}{\frac{1}{\frac{\sin y}{y}}}\right)}\]

    15. Applied associate-*r*0.3

      \[\leadsto \color{blue}{\left(\left(\sqrt{1} \cdot x\right) \cdot \frac{\sqrt{\sqrt[3]{1} \cdot \sqrt[3]{1}}}{z}\right) \cdot \frac{\sqrt{\sqrt[3]{1}}}{\frac{1}{\frac{\sin y}{y}}}}\]

    16. Simplified0.2

      \[\leadsto \color{blue}{\frac{\left(\sqrt{1} \cdot x\right) \cdot \left|\sqrt[3]{1}\right|}{z}} \cdot \frac{\sqrt{\sqrt[3]{1}}}{\frac{1}{\frac{\sin y}{y}}}\]

    if -6.556330221928382e+49 < z < 2.4880392282404904e-43

    1. Initial program 5.9

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

    3. Applied clear-num6.2

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

    5. Applied *-un-lft-identity6.2

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

    6. Applied times-frac0.7

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

    7. Applied add-sqr-sqrt0.7

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

    8. Applied times-frac0.5

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

    9. Simplified0.4

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

  4. Final simplification0.3

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \le -6.556330221928381769630387918095839368079 \cdot 10^{49} \lor \neg \left(z \le 2.48803922824049036872437422192558118528 \cdot 10^{-43}\right):\\ \;\;\;\;\frac{\left(\sqrt{1} \cdot x\right) \cdot \left|\sqrt[3]{1}\right|}{z} \cdot \frac{\sqrt{\sqrt[3]{1}}}{\frac{1}{\frac{\sin y}{y}}}\\ \mathbf{else}:\\ \;\;\;\;\left(\sqrt{1} \cdot x\right) \cdot \frac{\sqrt{1}}{\frac{z}{\frac{\sin y}{y}}}\\ \end{array}\]

Reproduce

herbie shell --seed 1978988140 
(FPCore (x y z)
  :name "Linear.Quaternion:$ctanh from linear-1.19.1.3"
  :precision binary64

  :herbie-target
  (if (< z -4.21737202034271466e-29) (/ (* x (/ 1 (/ y (sin y)))) z) (if (< z 4.44670236911381103e64) (/ x (* z (/ y (sin y)))) (/ (* x (/ 1 (/ y (sin y)))) z)))

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