Average Error: 24.7 → 9.6
Time: 20.6s
Precision: 64
\[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z}\]
↓
\[\begin{array}{l} \mathbf{if}\;a \le -2.810611023808398538063550912841564074447 \cdot 10^{-193} \lor \neg \left(a \le 3.465450532765299161045523535708764605591 \cdot 10^{-157}\right):\\ \;\;\;\;x + \frac{y - z}{a - z} \cdot \left(t - x\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{x}{\frac{z}{y}} - y \cdot \frac{t}{z}\right) + t\\ \end{array}\]
x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z}
↓
\begin{array}{l}
\mathbf{if}\;a \le -2.810611023808398538063550912841564074447 \cdot 10^{-193} \lor \neg \left(a \le 3.465450532765299161045523535708764605591 \cdot 10^{-157}\right):\\
\;\;\;\;x + \frac{y - z}{a - z} \cdot \left(t - x\right)\\

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

\end{array}
double f(double x, double y, double z, double t, double a) {
        double r530366 = x;
        double r530367 = y;
        double r530368 = z;
        double r530369 = r530367 - r530368;
        double r530370 = t;
        double r530371 = r530370 - r530366;
        double r530372 = r530369 * r530371;
        double r530373 = a;
        double r530374 = r530373 - r530368;
        double r530375 = r530372 / r530374;
        double r530376 = r530366 + r530375;
        return r530376;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r530377 = a;
        double r530378 = -2.8106110238083985e-193;
        bool r530379 = r530377 <= r530378;
        double r530380 = 3.465450532765299e-157;
        bool r530381 = r530377 <= r530380;
        double r530382 = !r530381;
        bool r530383 = r530379 || r530382;
        double r530384 = x;
        double r530385 = y;
        double r530386 = z;
        double r530387 = r530385 - r530386;
        double r530388 = r530377 - r530386;
        double r530389 = r530387 / r530388;
        double r530390 = t;
        double r530391 = r530390 - r530384;
        double r530392 = r530389 * r530391;
        double r530393 = r530384 + r530392;
        double r530394 = r530386 / r530385;
        double r530395 = r530384 / r530394;
        double r530396 = r530390 / r530386;
        double r530397 = r530385 * r530396;
        double r530398 = r530395 - r530397;
        double r530399 = r530398 + r530390;
        double r530400 = r530383 ? r530393 : r530399;
        return r530400;
}

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

Original24.7
Target11.8
Herbie9.6
\[\begin{array}{l} \mathbf{if}\;z \lt -1.253613105609503593846459977496550767343 \cdot 10^{188}:\\ \;\;\;\;t - \frac{y}{z} \cdot \left(t - x\right)\\ \mathbf{elif}\;z \lt 4.446702369113811028051510715777703865332 \cdot 10^{64}:\\ \;\;\;\;x + \frac{y - z}{\frac{a - z}{t - x}}\\ \mathbf{else}:\\ \;\;\;\;t - \frac{y}{z} \cdot \left(t - x\right)\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if a < -2.8106110238083985e-193 or 3.465450532765299e-157 < a

    1. Initial program 23.4

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

    2. Simplified9.5

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

    if -2.8106110238083985e-193 < a < 3.465450532765299e-157

    1. Initial program 30.4

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

    2. Simplified19.9

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

    3. Taylor expanded around inf 12.5

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

    4. Simplified10.2

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

  4. Final simplification9.6

    \[\leadsto \begin{array}{l} \mathbf{if}\;a \le -2.810611023808398538063550912841564074447 \cdot 10^{-193} \lor \neg \left(a \le 3.465450532765299161045523535708764605591 \cdot 10^{-157}\right):\\ \;\;\;\;x + \frac{y - z}{a - z} \cdot \left(t - x\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{x}{\frac{z}{y}} - y \cdot \frac{t}{z}\right) + t\\ \end{array}\]

Reproduce

herbie shell --seed 2019196 
(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))))