Average Error: 23.5 → 12.0
Time: 21.0s
Precision: 64
\[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\]
↓
\[\begin{array}{l} \mathbf{if}\;t \le -8.356995228214703 \cdot 10^{+200}:\\ \;\;\;\;\left(y + \frac{x \cdot z}{t}\right) - \frac{y \cdot z}{t}\\ \mathbf{elif}\;t \le 1.0761632607426357 \cdot 10^{+182}:\\ \;\;\;\;x + \frac{y - x}{\frac{a}{z - t} - \frac{\frac{t}{\sqrt[3]{z - t} \cdot \sqrt[3]{z - t}}}{\sqrt[3]{z - t}}}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array}\]
x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}
↓
\begin{array}{l}
\mathbf{if}\;t \le -8.356995228214703 \cdot 10^{+200}:\\
\;\;\;\;\left(y + \frac{x \cdot z}{t}\right) - \frac{y \cdot z}{t}\\

\mathbf{elif}\;t \le 1.0761632607426357 \cdot 10^{+182}:\\
\;\;\;\;x + \frac{y - x}{\frac{a}{z - t} - \frac{\frac{t}{\sqrt[3]{z - t} \cdot \sqrt[3]{z - t}}}{\sqrt[3]{z - t}}}\\

\mathbf{else}:\\
\;\;\;\;y\\

\end{array}
double f(double x, double y, double z, double t, double a) {
        double r33459507 = x;
        double r33459508 = y;
        double r33459509 = r33459508 - r33459507;
        double r33459510 = z;
        double r33459511 = t;
        double r33459512 = r33459510 - r33459511;
        double r33459513 = r33459509 * r33459512;
        double r33459514 = a;
        double r33459515 = r33459514 - r33459511;
        double r33459516 = r33459513 / r33459515;
        double r33459517 = r33459507 + r33459516;
        return r33459517;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r33459518 = t;
        double r33459519 = -8.356995228214703e+200;
        bool r33459520 = r33459518 <= r33459519;
        double r33459521 = y;
        double r33459522 = x;
        double r33459523 = z;
        double r33459524 = r33459522 * r33459523;
        double r33459525 = r33459524 / r33459518;
        double r33459526 = r33459521 + r33459525;
        double r33459527 = r33459521 * r33459523;
        double r33459528 = r33459527 / r33459518;
        double r33459529 = r33459526 - r33459528;
        double r33459530 = 1.0761632607426357e+182;
        bool r33459531 = r33459518 <= r33459530;
        double r33459532 = r33459521 - r33459522;
        double r33459533 = a;
        double r33459534 = r33459523 - r33459518;
        double r33459535 = r33459533 / r33459534;
        double r33459536 = cbrt(r33459534);
        double r33459537 = r33459536 * r33459536;
        double r33459538 = r33459518 / r33459537;
        double r33459539 = r33459538 / r33459536;
        double r33459540 = r33459535 - r33459539;
        double r33459541 = r33459532 / r33459540;
        double r33459542 = r33459522 + r33459541;
        double r33459543 = r33459531 ? r33459542 : r33459521;
        double r33459544 = r33459520 ? r33459529 : r33459543;
        return r33459544;
}

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

Original23.5
Target9.5
Herbie12.0
\[\begin{array}{l} \mathbf{if}\;a \lt -1.6153062845442575 \cdot 10^{-142}:\\ \;\;\;\;x + \frac{y - x}{1} \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;a \lt 3.774403170083174 \cdot 10^{-182}:\\ \;\;\;\;y - \frac{z}{t} \cdot \left(y - x\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{1} \cdot \frac{z - t}{a - t}\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if t < -8.356995228214703e+200

    1. Initial program 48.8

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

    2. Taylor expanded around inf 22.6

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

    if -8.356995228214703e+200 < t < 1.0761632607426357e+182

    1. Initial program 16.8

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

    3. Applied associate-/l*8.4

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

    5. Applied div-sub8.4

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

    7. Applied add-cube-cbrt8.7

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

    8. Applied associate-/r*8.7

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

    if 1.0761632607426357e+182 < t

    1. Initial program 47.6

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

    3. Applied associate-/l*24.0

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

    4. Taylor expanded around 0 25.4

      \[\leadsto \color{blue}{y}\]
  3. Recombined 3 regimes into one program.

  4. Final simplification12.0

    \[\leadsto \begin{array}{l} \mathbf{if}\;t \le -8.356995228214703 \cdot 10^{+200}:\\ \;\;\;\;\left(y + \frac{x \cdot z}{t}\right) - \frac{y \cdot z}{t}\\ \mathbf{elif}\;t \le 1.0761632607426357 \cdot 10^{+182}:\\ \;\;\;\;x + \frac{y - x}{\frac{a}{z - t} - \frac{\frac{t}{\sqrt[3]{z - t} \cdot \sqrt[3]{z - t}}}{\sqrt[3]{z - t}}}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array}\]

Reproduce

herbie shell --seed 2019164 
(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) (/ (- 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))))