Average Error: 24.3 → 10.3
Time: 29.8s
Precision: 64
\[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\]
↓
\[\begin{array}{l} \mathbf{if}\;a \le -1.903940587482351271448540463407352524949 \cdot 10^{-94}:\\ \;\;\;\;x + \frac{\frac{1}{\frac{\sqrt[3]{a - t}}{\sqrt[3]{y - x} \cdot \sqrt[3]{z - t}} \cdot \frac{\sqrt[3]{a - t}}{\left(\sqrt[3]{\sqrt[3]{y - x}} \cdot \sqrt[3]{\sqrt[3]{y - x} \cdot \sqrt[3]{y - x}}\right) \cdot \sqrt[3]{z - t}}}}{\frac{\frac{\sqrt[3]{a - t}}{\sqrt[3]{z - t}}}{\sqrt[3]{y - x}}}\\ \mathbf{elif}\;a \le 2.486579097351087244398754404400467109927 \cdot 10^{-154}:\\ \;\;\;\;\left(y + \frac{z \cdot x}{t}\right) - \frac{z \cdot y}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{\frac{a - t}{z - t}}{y - x}} + x\\ \end{array}\]
x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}
↓
\begin{array}{l}
\mathbf{if}\;a \le -1.903940587482351271448540463407352524949 \cdot 10^{-94}:\\
\;\;\;\;x + \frac{\frac{1}{\frac{\sqrt[3]{a - t}}{\sqrt[3]{y - x} \cdot \sqrt[3]{z - t}} \cdot \frac{\sqrt[3]{a - t}}{\left(\sqrt[3]{\sqrt[3]{y - x}} \cdot \sqrt[3]{\sqrt[3]{y - x} \cdot \sqrt[3]{y - x}}\right) \cdot \sqrt[3]{z - t}}}}{\frac{\frac{\sqrt[3]{a - t}}{\sqrt[3]{z - t}}}{\sqrt[3]{y - x}}}\\

\mathbf{elif}\;a \le 2.486579097351087244398754404400467109927 \cdot 10^{-154}:\\
\;\;\;\;\left(y + \frac{z \cdot x}{t}\right) - \frac{z \cdot y}{t}\\

\mathbf{else}:\\
\;\;\;\;\frac{1}{\frac{\frac{a - t}{z - t}}{y - x}} + x\\

\end{array}
double f(double x, double y, double z, double t, double a) {
        double r35484476 = x;
        double r35484477 = y;
        double r35484478 = r35484477 - r35484476;
        double r35484479 = z;
        double r35484480 = t;
        double r35484481 = r35484479 - r35484480;
        double r35484482 = r35484478 * r35484481;
        double r35484483 = a;
        double r35484484 = r35484483 - r35484480;
        double r35484485 = r35484482 / r35484484;
        double r35484486 = r35484476 + r35484485;
        return r35484486;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r35484487 = a;
        double r35484488 = -1.9039405874823513e-94;
        bool r35484489 = r35484487 <= r35484488;
        double r35484490 = x;
        double r35484491 = 1.0;
        double r35484492 = t;
        double r35484493 = r35484487 - r35484492;
        double r35484494 = cbrt(r35484493);
        double r35484495 = y;
        double r35484496 = r35484495 - r35484490;
        double r35484497 = cbrt(r35484496);
        double r35484498 = z;
        double r35484499 = r35484498 - r35484492;
        double r35484500 = cbrt(r35484499);
        double r35484501 = r35484497 * r35484500;
        double r35484502 = r35484494 / r35484501;
        double r35484503 = cbrt(r35484497);
        double r35484504 = r35484497 * r35484497;
        double r35484505 = cbrt(r35484504);
        double r35484506 = r35484503 * r35484505;
        double r35484507 = r35484506 * r35484500;
        double r35484508 = r35484494 / r35484507;
        double r35484509 = r35484502 * r35484508;
        double r35484510 = r35484491 / r35484509;
        double r35484511 = r35484494 / r35484500;
        double r35484512 = r35484511 / r35484497;
        double r35484513 = r35484510 / r35484512;
        double r35484514 = r35484490 + r35484513;
        double r35484515 = 2.4865790973510872e-154;
        bool r35484516 = r35484487 <= r35484515;
        double r35484517 = r35484498 * r35484490;
        double r35484518 = r35484517 / r35484492;
        double r35484519 = r35484495 + r35484518;
        double r35484520 = r35484498 * r35484495;
        double r35484521 = r35484520 / r35484492;
        double r35484522 = r35484519 - r35484521;
        double r35484523 = r35484493 / r35484499;
        double r35484524 = r35484523 / r35484496;
        double r35484525 = r35484491 / r35484524;
        double r35484526 = r35484525 + r35484490;
        double r35484527 = r35484516 ? r35484522 : r35484526;
        double r35484528 = r35484489 ? r35484514 : r35484527;
        return r35484528;
}

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

Original24.3
Target9.0
Herbie10.3
\[\begin{array}{l} \mathbf{if}\;a \lt -1.615306284544257464183904494091872805513 \cdot 10^{-142}:\\ \;\;\;\;x + \frac{y - x}{1} \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;a \lt 3.774403170083174201868024161554637965035 \cdot 10^{-182}:\\ \;\;\;\;y - \frac{z}{t} \cdot \left(y - x\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{1} \cdot \frac{z - t}{a - t}\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if a < -1.9039405874823513e-94

    1. Initial program 22.0

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

    3. Applied associate-/l*7.8

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

    5. Applied clear-num7.9

      \[\leadsto x + \color{blue}{\frac{1}{\frac{\frac{a - t}{z - t}}{y - x}}}\]
    6. Using strategy rm

    7. Applied add-cube-cbrt8.4

      \[\leadsto x + \frac{1}{\frac{\frac{a - t}{z - t}}{\color{blue}{\left(\sqrt[3]{y - x} \cdot \sqrt[3]{y - x}\right) \cdot \sqrt[3]{y - x}}}}\]

    8. Applied add-cube-cbrt8.5

      \[\leadsto x + \frac{1}{\frac{\frac{a - t}{\color{blue}{\left(\sqrt[3]{z - t} \cdot \sqrt[3]{z - t}\right) \cdot \sqrt[3]{z - t}}}}{\left(\sqrt[3]{y - x} \cdot \sqrt[3]{y - x}\right) \cdot \sqrt[3]{y - x}}}\]

    9. Applied add-cube-cbrt8.5

      \[\leadsto x + \frac{1}{\frac{\frac{\color{blue}{\left(\sqrt[3]{a - t} \cdot \sqrt[3]{a - t}\right) \cdot \sqrt[3]{a - t}}}{\left(\sqrt[3]{z - t} \cdot \sqrt[3]{z - t}\right) \cdot \sqrt[3]{z - t}}}{\left(\sqrt[3]{y - x} \cdot \sqrt[3]{y - x}\right) \cdot \sqrt[3]{y - x}}}\]

    10. Applied times-frac8.5

      \[\leadsto x + \frac{1}{\frac{\color{blue}{\frac{\sqrt[3]{a - t} \cdot \sqrt[3]{a - t}}{\sqrt[3]{z - t} \cdot \sqrt[3]{z - t}} \cdot \frac{\sqrt[3]{a - t}}{\sqrt[3]{z - t}}}}{\left(\sqrt[3]{y - x} \cdot \sqrt[3]{y - x}\right) \cdot \sqrt[3]{y - x}}}\]

    11. Applied times-frac8.1

      \[\leadsto x + \frac{1}{\color{blue}{\frac{\frac{\sqrt[3]{a - t} \cdot \sqrt[3]{a - t}}{\sqrt[3]{z - t} \cdot \sqrt[3]{z - t}}}{\sqrt[3]{y - x} \cdot \sqrt[3]{y - x}} \cdot \frac{\frac{\sqrt[3]{a - t}}{\sqrt[3]{z - t}}}{\sqrt[3]{y - x}}}}\]

    12. Applied associate-/r*8.1

      \[\leadsto x + \color{blue}{\frac{\frac{1}{\frac{\frac{\sqrt[3]{a - t} \cdot \sqrt[3]{a - t}}{\sqrt[3]{z - t} \cdot \sqrt[3]{z - t}}}{\sqrt[3]{y - x} \cdot \sqrt[3]{y - x}}}}{\frac{\frac{\sqrt[3]{a - t}}{\sqrt[3]{z - t}}}{\sqrt[3]{y - x}}}}\]

    13. Simplified8.1

      \[\leadsto x + \frac{\color{blue}{\frac{1}{\frac{\sqrt[3]{a - t}}{\sqrt[3]{y - x} \cdot \sqrt[3]{z - t}} \cdot \frac{\sqrt[3]{a - t}}{\sqrt[3]{y - x} \cdot \sqrt[3]{z - t}}}}}{\frac{\frac{\sqrt[3]{a - t}}{\sqrt[3]{z - t}}}{\sqrt[3]{y - x}}}\]
    14. Using strategy rm

    15. Applied add-cube-cbrt8.2

      \[\leadsto x + \frac{\frac{1}{\frac{\sqrt[3]{a - t}}{\sqrt[3]{\color{blue}{\left(\sqrt[3]{y - x} \cdot \sqrt[3]{y - x}\right) \cdot \sqrt[3]{y - x}}} \cdot \sqrt[3]{z - t}} \cdot \frac{\sqrt[3]{a - t}}{\sqrt[3]{y - x} \cdot \sqrt[3]{z - t}}}}{\frac{\frac{\sqrt[3]{a - t}}{\sqrt[3]{z - t}}}{\sqrt[3]{y - x}}}\]

    16. Applied cbrt-prod8.2

      \[\leadsto x + \frac{\frac{1}{\frac{\sqrt[3]{a - t}}{\color{blue}{\left(\sqrt[3]{\sqrt[3]{y - x} \cdot \sqrt[3]{y - x}} \cdot \sqrt[3]{\sqrt[3]{y - x}}\right)} \cdot \sqrt[3]{z - t}} \cdot \frac{\sqrt[3]{a - t}}{\sqrt[3]{y - x} \cdot \sqrt[3]{z - t}}}}{\frac{\frac{\sqrt[3]{a - t}}{\sqrt[3]{z - t}}}{\sqrt[3]{y - x}}}\]

    if -1.9039405874823513e-94 < a < 2.4865790973510872e-154

    1. Initial program 29.5

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

    2. Taylor expanded around inf 14.5

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

    if 2.4865790973510872e-154 < a

    1. Initial program 22.9

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

    3. Applied associate-/l*9.3

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

    5. Applied clear-num9.4

      \[\leadsto x + \color{blue}{\frac{1}{\frac{\frac{a - t}{z - t}}{y - x}}}\]
  3. Recombined 3 regimes into one program.

  4. Final simplification10.3

    \[\leadsto \begin{array}{l} \mathbf{if}\;a \le -1.903940587482351271448540463407352524949 \cdot 10^{-94}:\\ \;\;\;\;x + \frac{\frac{1}{\frac{\sqrt[3]{a - t}}{\sqrt[3]{y - x} \cdot \sqrt[3]{z - t}} \cdot \frac{\sqrt[3]{a - t}}{\left(\sqrt[3]{\sqrt[3]{y - x}} \cdot \sqrt[3]{\sqrt[3]{y - x} \cdot \sqrt[3]{y - x}}\right) \cdot \sqrt[3]{z - t}}}}{\frac{\frac{\sqrt[3]{a - t}}{\sqrt[3]{z - t}}}{\sqrt[3]{y - x}}}\\ \mathbf{elif}\;a \le 2.486579097351087244398754404400467109927 \cdot 10^{-154}:\\ \;\;\;\;\left(y + \frac{z \cdot x}{t}\right) - \frac{z \cdot y}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{\frac{a - t}{z - t}}{y - x}} + x\\ \end{array}\]

Reproduce

herbie shell --seed 2019171 
(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))))