Average Error: 23.8 → 10.7
Time: 16.4s
Precision: 64
\[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z}\]
↓
\[\begin{array}{l} \mathbf{if}\;a \le -2.145869478761536680500210929593317634387 \cdot 10^{-21} \lor \neg \left(a \le 5.909250579364137682050418316946687031018 \cdot 10^{-179}\right):\\ \;\;\;\;\frac{t - x}{\frac{a - z}{y - z}} + x\\ \mathbf{else}:\\ \;\;\;\;t + \left(\frac{y \cdot x}{z} - \frac{t}{\frac{z}{y}}\right)\\ \end{array}\]
x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z}
↓
\begin{array}{l}
\mathbf{if}\;a \le -2.145869478761536680500210929593317634387 \cdot 10^{-21} \lor \neg \left(a \le 5.909250579364137682050418316946687031018 \cdot 10^{-179}\right):\\
\;\;\;\;\frac{t - x}{\frac{a - z}{y - z}} + x\\

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

\end{array}
double f(double x, double y, double z, double t, double a) {
        double r514406 = x;
        double r514407 = y;
        double r514408 = z;
        double r514409 = r514407 - r514408;
        double r514410 = t;
        double r514411 = r514410 - r514406;
        double r514412 = r514409 * r514411;
        double r514413 = a;
        double r514414 = r514413 - r514408;
        double r514415 = r514412 / r514414;
        double r514416 = r514406 + r514415;
        return r514416;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r514417 = a;
        double r514418 = -2.1458694787615367e-21;
        bool r514419 = r514417 <= r514418;
        double r514420 = 5.909250579364138e-179;
        bool r514421 = r514417 <= r514420;
        double r514422 = !r514421;
        bool r514423 = r514419 || r514422;
        double r514424 = t;
        double r514425 = x;
        double r514426 = r514424 - r514425;
        double r514427 = z;
        double r514428 = r514417 - r514427;
        double r514429 = y;
        double r514430 = r514429 - r514427;
        double r514431 = r514428 / r514430;
        double r514432 = r514426 / r514431;
        double r514433 = r514432 + r514425;
        double r514434 = r514429 * r514425;
        double r514435 = r514434 / r514427;
        double r514436 = r514427 / r514429;
        double r514437 = r514424 / r514436;
        double r514438 = r514435 - r514437;
        double r514439 = r514424 + r514438;
        double r514440 = r514423 ? r514433 : r514439;
        return r514440;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original23.8
Target11.4
Herbie10.7
\[\begin{array}{l} \mathbf{if}\;z \lt -1.253613105609503593846459977496550767343 \cdot 10^{188}:\\ \;\;\;\;t - \frac{y}{z} \cdot \left(t - x\right)\\ \mathbf{elif}\;z \lt 4.446702369113811028051510715777703865332 \cdot 10^{64}:\\ \;\;\;\;x + \frac{y - z}{\frac{a - z}{t - x}}\\ \mathbf{else}:\\ \;\;\;\;t - \frac{y}{z} \cdot \left(t - x\right)\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if a < -2.1458694787615367e-21 or 5.909250579364138e-179 < a

    1. Initial program 21.8

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z}\]

    2. Simplified8.1

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

    4. Applied clear-num8.2

      \[\leadsto x + \color{blue}{\frac{1}{\frac{a - z}{y - z}}} \cdot \left(t - x\right)\]
    5. Using strategy rm

    6. Applied *-un-lft-identity8.2

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

    7. Applied add-cube-cbrt8.2

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

    8. Applied times-frac8.2

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

    9. Applied associate-*l*8.2

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

    10. Simplified8.1

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

    if -2.1458694787615367e-21 < a < 5.909250579364138e-179

    1. Initial program 28.3

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z}\]

    2. Simplified18.7

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

    3. Taylor expanded around inf 18.0

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

    4. Simplified16.4

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

  4. Final simplification10.7

    \[\leadsto \begin{array}{l} \mathbf{if}\;a \le -2.145869478761536680500210929593317634387 \cdot 10^{-21} \lor \neg \left(a \le 5.909250579364137682050418316946687031018 \cdot 10^{-179}\right):\\ \;\;\;\;\frac{t - x}{\frac{a - z}{y - z}} + x\\ \mathbf{else}:\\ \;\;\;\;t + \left(\frac{y \cdot x}{z} - \frac{t}{\frac{z}{y}}\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2019179 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Chart.Axis.Types:invLinMap from Chart-1.5.3"

  :herbie-target
  (if (< z -1.2536131056095036e+188) (- t (* (/ y z) (- t x))) (if (< z 4.446702369113811e+64) (+ x (/ (- y z) (/ (- a z) (- t x)))) (- t (* (/ y z) (- t x)))))

  (+ x (/ (* (- y z) (- t x)) (- a z))))