Average Error: 24.8 → 9.9
Time: 20.4s
Precision: 64
\[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z}\]
↓
\[\begin{array}{l} \mathbf{if}\;a \le -2.303115495338194376941539756876286948596 \cdot 10^{-89} \lor \neg \left(a \le 9.399741012957091794694252310132614356479 \cdot 10^{-155}\right):\\ \;\;\;\;x + \left(t - x\right) \cdot \left(\frac{y}{a - z} - \frac{z}{a - z}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{x}{\frac{z}{y}} - y \cdot \frac{t}{z}\right) + t\\ \end{array}\]
x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z}
↓
\begin{array}{l}
\mathbf{if}\;a \le -2.303115495338194376941539756876286948596 \cdot 10^{-89} \lor \neg \left(a \le 9.399741012957091794694252310132614356479 \cdot 10^{-155}\right):\\
\;\;\;\;x + \left(t - x\right) \cdot \left(\frac{y}{a - z} - \frac{z}{a - z}\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 r474756 = x;
        double r474757 = y;
        double r474758 = z;
        double r474759 = r474757 - r474758;
        double r474760 = t;
        double r474761 = r474760 - r474756;
        double r474762 = r474759 * r474761;
        double r474763 = a;
        double r474764 = r474763 - r474758;
        double r474765 = r474762 / r474764;
        double r474766 = r474756 + r474765;
        return r474766;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r474767 = a;
        double r474768 = -2.3031154953381944e-89;
        bool r474769 = r474767 <= r474768;
        double r474770 = 9.399741012957092e-155;
        bool r474771 = r474767 <= r474770;
        double r474772 = !r474771;
        bool r474773 = r474769 || r474772;
        double r474774 = x;
        double r474775 = t;
        double r474776 = r474775 - r474774;
        double r474777 = y;
        double r474778 = z;
        double r474779 = r474767 - r474778;
        double r474780 = r474777 / r474779;
        double r474781 = r474778 / r474779;
        double r474782 = r474780 - r474781;
        double r474783 = r474776 * r474782;
        double r474784 = r474774 + r474783;
        double r474785 = r474778 / r474777;
        double r474786 = r474774 / r474785;
        double r474787 = r474775 / r474778;
        double r474788 = r474777 * r474787;
        double r474789 = r474786 - r474788;
        double r474790 = r474789 + r474775;
        double r474791 = r474773 ? r474784 : r474790;
        return r474791;
}

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

Original24.8
Target12.1
Herbie9.9
\[\begin{array}{l} \mathbf{if}\;z \lt -1.253613105609503593846459977496550767343 \cdot 10^{188}:\\ \;\;\;\;t - \frac{y}{z} \cdot \left(t - x\right)\\ \mathbf{elif}\;z \lt 4.446702369113811028051510715777703865332 \cdot 10^{64}:\\ \;\;\;\;x + \frac{y - z}{\frac{a - z}{t - x}}\\ \mathbf{else}:\\ \;\;\;\;t - \frac{y}{z} \cdot \left(t - x\right)\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if a < -2.3031154953381944e-89 or 9.399741012957092e-155 < a

    1. Initial program 23.0

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

    2. Simplified8.6

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

    4. Applied div-sub8.6

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

    if -2.3031154953381944e-89 < a < 9.399741012957092e-155

    1. Initial program 29.7

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

    2. Simplified20.0

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

    3. Taylor expanded around inf 15.7

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

    4. Simplified13.1

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

  4. Final simplification9.9

    \[\leadsto \begin{array}{l} \mathbf{if}\;a \le -2.303115495338194376941539756876286948596 \cdot 10^{-89} \lor \neg \left(a \le 9.399741012957091794694252310132614356479 \cdot 10^{-155}\right):\\ \;\;\;\;x + \left(t - x\right) \cdot \left(\frac{y}{a - z} - \frac{z}{a - z}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{x}{\frac{z}{y}} - y \cdot \frac{t}{z}\right) + t\\ \end{array}\]

Reproduce

herbie shell --seed 2019195 
(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))))