Average Error: 6.9 → 2.4
Time: 9.4s
Precision: 64
\[\frac{x \cdot 2}{y \cdot z - t \cdot z}\]
↓
\[\begin{array}{l} \mathbf{if}\;z \le -2.302276795464792958697075142375509937409 \cdot 10^{-8} \lor \neg \left(z \le 6.74946915654484623003503662072569973222 \cdot 10^{-38}\right):\\ \;\;\;\;\frac{1}{\frac{y - t}{x \cdot 2}} \cdot \frac{1}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot 2}{y \cdot z + \left(-t\right) \cdot z}\\ \end{array}\]
\frac{x \cdot 2}{y \cdot z - t \cdot z}
↓
\begin{array}{l}
\mathbf{if}\;z \le -2.302276795464792958697075142375509937409 \cdot 10^{-8} \lor \neg \left(z \le 6.74946915654484623003503662072569973222 \cdot 10^{-38}\right):\\
\;\;\;\;\frac{1}{\frac{y - t}{x \cdot 2}} \cdot \frac{1}{z}\\

\mathbf{else}:\\
\;\;\;\;\frac{x \cdot 2}{y \cdot z + \left(-t\right) \cdot z}\\

\end{array}
double f(double x, double y, double z, double t) {
        double r396305 = x;
        double r396306 = 2.0;
        double r396307 = r396305 * r396306;
        double r396308 = y;
        double r396309 = z;
        double r396310 = r396308 * r396309;
        double r396311 = t;
        double r396312 = r396311 * r396309;
        double r396313 = r396310 - r396312;
        double r396314 = r396307 / r396313;
        return r396314;
}
↓
double f(double x, double y, double z, double t) {
        double r396315 = z;
        double r396316 = -2.302276795464793e-08;
        bool r396317 = r396315 <= r396316;
        double r396318 = 6.749469156544846e-38;
        bool r396319 = r396315 <= r396318;
        double r396320 = !r396319;
        bool r396321 = r396317 || r396320;
        double r396322 = 1.0;
        double r396323 = y;
        double r396324 = t;
        double r396325 = r396323 - r396324;
        double r396326 = x;
        double r396327 = 2.0;
        double r396328 = r396326 * r396327;
        double r396329 = r396325 / r396328;
        double r396330 = r396322 / r396329;
        double r396331 = r396322 / r396315;
        double r396332 = r396330 * r396331;
        double r396333 = r396323 * r396315;
        double r396334 = -r396324;
        double r396335 = r396334 * r396315;
        double r396336 = r396333 + r396335;
        double r396337 = r396328 / r396336;
        double r396338 = r396321 ? r396332 : r396337;
        return r396338;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original6.9
Target2.1
Herbie2.4
\[\begin{array}{l} \mathbf{if}\;\frac{x \cdot 2}{y \cdot z - t \cdot z} \lt -2.559141628295061113708240820439530037456 \cdot 10^{-13}:\\ \;\;\;\;\frac{x}{\left(y - t\right) \cdot z} \cdot 2\\ \mathbf{elif}\;\frac{x \cdot 2}{y \cdot z - t \cdot z} \lt 1.045027827330126029709547581125571222799 \cdot 10^{-269}:\\ \;\;\;\;\frac{\frac{x}{z} \cdot 2}{y - t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - t\right) \cdot z} \cdot 2\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if z < -2.302276795464793e-08 or 6.749469156544846e-38 < z

    1. Initial program 10.2

      \[\frac{x \cdot 2}{y \cdot z - t \cdot z}\]

    2. Simplified8.5

      \[\leadsto \color{blue}{\frac{x \cdot 2}{z \cdot \left(y - t\right)}}\]
    3. Using strategy rm

    4. Applied associate-/r*1.7

      \[\leadsto \color{blue}{\frac{\frac{x \cdot 2}{z}}{y - t}}\]
    5. Using strategy rm

    6. Applied clear-num2.2

      \[\leadsto \color{blue}{\frac{1}{\frac{y - t}{\frac{x \cdot 2}{z}}}}\]
    7. Using strategy rm

    8. Applied associate-/r/2.5

      \[\leadsto \frac{1}{\color{blue}{\frac{y - t}{x \cdot 2} \cdot z}}\]

    9. Applied add-cube-cbrt2.5

      \[\leadsto \frac{\color{blue}{\left(\sqrt[3]{1} \cdot \sqrt[3]{1}\right) \cdot \sqrt[3]{1}}}{\frac{y - t}{x \cdot 2} \cdot z}\]

    10. Applied times-frac2.3

      \[\leadsto \color{blue}{\frac{\sqrt[3]{1} \cdot \sqrt[3]{1}}{\frac{y - t}{x \cdot 2}} \cdot \frac{\sqrt[3]{1}}{z}}\]

    11. Simplified2.3

      \[\leadsto \color{blue}{\frac{1}{\frac{y - t}{x \cdot 2}}} \cdot \frac{\sqrt[3]{1}}{z}\]

    12. Simplified2.3

      \[\leadsto \frac{1}{\frac{y - t}{x \cdot 2}} \cdot \color{blue}{\frac{1}{z}}\]

    if -2.302276795464793e-08 < z < 6.749469156544846e-38

    1. Initial program 2.5

      \[\frac{x \cdot 2}{y \cdot z - t \cdot z}\]

    2. Simplified2.5

      \[\leadsto \color{blue}{\frac{x \cdot 2}{z \cdot \left(y - t\right)}}\]
    3. Using strategy rm

    4. Applied sub-neg2.5

      \[\leadsto \frac{x \cdot 2}{z \cdot \color{blue}{\left(y + \left(-t\right)\right)}}\]

    5. Applied distribute-lft-in2.5

      \[\leadsto \frac{x \cdot 2}{\color{blue}{z \cdot y + z \cdot \left(-t\right)}}\]

    6. Simplified2.5

      \[\leadsto \frac{x \cdot 2}{\color{blue}{y \cdot z} + z \cdot \left(-t\right)}\]

    7. Simplified2.5

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

  4. Final simplification2.4

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \le -2.302276795464792958697075142375509937409 \cdot 10^{-8} \lor \neg \left(z \le 6.74946915654484623003503662072569973222 \cdot 10^{-38}\right):\\ \;\;\;\;\frac{1}{\frac{y - t}{x \cdot 2}} \cdot \frac{1}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot 2}{y \cdot z + \left(-t\right) \cdot z}\\ \end{array}\]

Reproduce

herbie shell --seed 2019305 
(FPCore (x y z t)
  :name "Linear.Projection:infinitePerspective from linear-1.19.1.3, A"
  :precision binary64

  :herbie-target
  (if (< (/ (* x 2) (- (* y z) (* t z))) -2.559141628295061e-13) (* (/ x (* (- y t) z)) 2) (if (< (/ (* x 2) (- (* y z) (* t z))) 1.045027827330126e-269) (/ (* (/ x z) 2) (- y t)) (* (/ x (* (- y t) z)) 2)))

  (/ (* x 2) (- (* y z) (* t z))))