Average Error: 24.2 → 10.5
Time: 19.2s
Precision: 64
\[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\]
↓
\[\begin{array}{l} \mathbf{if}\;t \le -1.211070029229014479879246350183570546634 \cdot 10^{94} \lor \neg \left(t \le 1.341691777691101249586801592888631911931 \cdot 10^{125}\right):\\ \;\;\;\;y + \left(\frac{x}{\frac{t}{z}} - z \cdot \frac{y}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z - t}{a - t}\\ \end{array}\]
x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}
↓
\begin{array}{l}
\mathbf{if}\;t \le -1.211070029229014479879246350183570546634 \cdot 10^{94} \lor \neg \left(t \le 1.341691777691101249586801592888631911931 \cdot 10^{125}\right):\\
\;\;\;\;y + \left(\frac{x}{\frac{t}{z}} - z \cdot \frac{y}{t}\right)\\

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

\end{array}
double f(double x, double y, double z, double t, double a) {
        double r603050 = x;
        double r603051 = y;
        double r603052 = r603051 - r603050;
        double r603053 = z;
        double r603054 = t;
        double r603055 = r603053 - r603054;
        double r603056 = r603052 * r603055;
        double r603057 = a;
        double r603058 = r603057 - r603054;
        double r603059 = r603056 / r603058;
        double r603060 = r603050 + r603059;
        return r603060;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r603061 = t;
        double r603062 = -1.2110700292290145e+94;
        bool r603063 = r603061 <= r603062;
        double r603064 = 1.3416917776911012e+125;
        bool r603065 = r603061 <= r603064;
        double r603066 = !r603065;
        bool r603067 = r603063 || r603066;
        double r603068 = y;
        double r603069 = x;
        double r603070 = z;
        double r603071 = r603061 / r603070;
        double r603072 = r603069 / r603071;
        double r603073 = r603068 / r603061;
        double r603074 = r603070 * r603073;
        double r603075 = r603072 - r603074;
        double r603076 = r603068 + r603075;
        double r603077 = r603068 - r603069;
        double r603078 = r603070 - r603061;
        double r603079 = a;
        double r603080 = r603079 - r603061;
        double r603081 = r603078 / r603080;
        double r603082 = r603077 * r603081;
        double r603083 = r603069 + r603082;
        double r603084 = r603067 ? r603076 : r603083;
        return r603084;
}

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

Original24.2
Target8.9
Herbie10.5
\[\begin{array}{l} \mathbf{if}\;a \lt -1.615306284544257464183904494091872805513 \cdot 10^{-142}:\\ \;\;\;\;x + \frac{y - x}{1} \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;a \lt 3.774403170083174201868024161554637965035 \cdot 10^{-182}:\\ \;\;\;\;y - \frac{z}{t} \cdot \left(y - x\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{1} \cdot \frac{z - t}{a - t}\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if t < -1.2110700292290145e+94 or 1.3416917776911012e+125 < t

    1. Initial program 44.7

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

    2. Simplified24.8

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

    4. Applied div-inv24.9

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

    5. Applied associate-*l*20.7

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

    6. Simplified20.6

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

    8. Applied add-cube-cbrt20.9

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

    9. Taylor expanded around inf 26.4

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

    10. Simplified18.2

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

    if -1.2110700292290145e+94 < t < 1.3416917776911012e+125

    1. Initial program 12.7

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

    2. Simplified8.4

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

    4. Applied div-inv8.4

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

    5. Applied associate-*l*6.2

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

    6. Simplified6.2

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

  4. Final simplification10.5

    \[\leadsto \begin{array}{l} \mathbf{if}\;t \le -1.211070029229014479879246350183570546634 \cdot 10^{94} \lor \neg \left(t \le 1.341691777691101249586801592888631911931 \cdot 10^{125}\right):\\ \;\;\;\;y + \left(\frac{x}{\frac{t}{z}} - z \cdot \frac{y}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z - t}{a - t}\\ \end{array}\]

Reproduce

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

  :herbie-target
  (if (< a -1.6153062845442575e-142) (+ x (* (/ (- y x) 1.0) (/ (- z t) (- a t)))) (if (< a 3.774403170083174e-182) (- y (* (/ z t) (- y x))) (+ x (* (/ (- y x) 1.0) (/ (- z t) (- a t))))))

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