Average Error: 25.0 → 10.5
Time: 5.5s
Precision: 64
\[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\]
↓
\[\begin{array}{l} \mathbf{if}\;a \le -7.8100462476949922 \cdot 10^{-192} \lor \neg \left(a \le 6.9127787409822648 \cdot 10^{-128}\right):\\ \;\;\;\;x + \frac{y - x}{\left(a - t\right) \cdot \frac{1}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;\left(y + \frac{x \cdot z}{t}\right) - \frac{z \cdot y}{t}\\ \end{array}\]
x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}
↓
\begin{array}{l}
\mathbf{if}\;a \le -7.8100462476949922 \cdot 10^{-192} \lor \neg \left(a \le 6.9127787409822648 \cdot 10^{-128}\right):\\
\;\;\;\;x + \frac{y - x}{\left(a - t\right) \cdot \frac{1}{z - t}}\\

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

\end{array}
double f(double x, double y, double z, double t, double a) {
        double r636391 = x;
        double r636392 = y;
        double r636393 = r636392 - r636391;
        double r636394 = z;
        double r636395 = t;
        double r636396 = r636394 - r636395;
        double r636397 = r636393 * r636396;
        double r636398 = a;
        double r636399 = r636398 - r636395;
        double r636400 = r636397 / r636399;
        double r636401 = r636391 + r636400;
        return r636401;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r636402 = a;
        double r636403 = -7.810046247694992e-192;
        bool r636404 = r636402 <= r636403;
        double r636405 = 6.912778740982265e-128;
        bool r636406 = r636402 <= r636405;
        double r636407 = !r636406;
        bool r636408 = r636404 || r636407;
        double r636409 = x;
        double r636410 = y;
        double r636411 = r636410 - r636409;
        double r636412 = t;
        double r636413 = r636402 - r636412;
        double r636414 = 1.0;
        double r636415 = z;
        double r636416 = r636415 - r636412;
        double r636417 = r636414 / r636416;
        double r636418 = r636413 * r636417;
        double r636419 = r636411 / r636418;
        double r636420 = r636409 + r636419;
        double r636421 = r636409 * r636415;
        double r636422 = r636421 / r636412;
        double r636423 = r636410 + r636422;
        double r636424 = r636415 * r636410;
        double r636425 = r636424 / r636412;
        double r636426 = r636423 - r636425;
        double r636427 = r636408 ? r636420 : r636426;
        return r636427;
}

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

Original25.0
Target9.5
Herbie10.5
\[\begin{array}{l} \mathbf{if}\;a \lt -1.6153062845442575 \cdot 10^{-142}:\\ \;\;\;\;x + \frac{y - x}{1} \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;a \lt 3.7744031700831742 \cdot 10^{-182}:\\ \;\;\;\;y - \frac{z}{t} \cdot \left(y - x\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{1} \cdot \frac{z - t}{a - t}\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if a < -7.810046247694992e-192 or 6.912778740982265e-128 < a

    1. Initial program 23.8

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

    3. Applied associate-/l*9.6

      \[\leadsto x + \color{blue}{\frac{y - x}{\frac{a - t}{z - t}}}\]
    4. Using strategy rm

    5. Applied div-inv9.7

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

    if -7.810046247694992e-192 < a < 6.912778740982265e-128

    1. Initial program 29.6

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

    2. Taylor expanded around inf 13.5

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

  4. Final simplification10.5

    \[\leadsto \begin{array}{l} \mathbf{if}\;a \le -7.8100462476949922 \cdot 10^{-192} \lor \neg \left(a \le 6.9127787409822648 \cdot 10^{-128}\right):\\ \;\;\;\;x + \frac{y - x}{\left(a - t\right) \cdot \frac{1}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;\left(y + \frac{x \cdot z}{t}\right) - \frac{z \cdot y}{t}\\ \end{array}\]

Reproduce

herbie shell --seed 2020039 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Chart.Axis.Types:linMap from Chart-1.5.3"
  :precision binary64

  :herbie-target
  (if (< a -1.6153062845442575e-142) (+ x (* (/ (- y x) 1) (/ (- z t) (- a t)))) (if (< a 3.774403170083174e-182) (- y (* (/ z t) (- y x))) (+ x (* (/ (- y x) 1) (/ (- z t) (- a t))))))

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