Average Error: 24.6 → 10.4
Time: 21.1s
Precision: 64
\[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\]
↓
\[\begin{array}{l} \mathbf{if}\;a \le -4.911453117926138773931568290458543734291 \cdot 10^{-142}:\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;a \le 7.273457157218697182460513419680927492199 \cdot 10^{-223}:\\ \;\;\;\;\left(y + \frac{x \cdot z}{t}\right) - \frac{z \cdot y}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\frac{y - x}{\frac{\sqrt[3]{a - t}}{\sqrt[3]{z - t}} \cdot \frac{\sqrt[3]{a - t}}{\sqrt[3]{z - t}}}}{\frac{\sqrt[3]{a - t}}{\sqrt[3]{z - t}}}\\ \end{array}\]
x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}
↓
\begin{array}{l}
\mathbf{if}\;a \le -4.911453117926138773931568290458543734291 \cdot 10^{-142}:\\
\;\;\;\;x + \left(y - x\right) \cdot \frac{z - t}{a - t}\\

\mathbf{elif}\;a \le 7.273457157218697182460513419680927492199 \cdot 10^{-223}:\\
\;\;\;\;\left(y + \frac{x \cdot z}{t}\right) - \frac{z \cdot y}{t}\\

\mathbf{else}:\\
\;\;\;\;x + \frac{\frac{y - x}{\frac{\sqrt[3]{a - t}}{\sqrt[3]{z - t}} \cdot \frac{\sqrt[3]{a - t}}{\sqrt[3]{z - t}}}}{\frac{\sqrt[3]{a - t}}{\sqrt[3]{z - t}}}\\

\end{array}
double f(double x, double y, double z, double t, double a) {
        double r29251458 = x;
        double r29251459 = y;
        double r29251460 = r29251459 - r29251458;
        double r29251461 = z;
        double r29251462 = t;
        double r29251463 = r29251461 - r29251462;
        double r29251464 = r29251460 * r29251463;
        double r29251465 = a;
        double r29251466 = r29251465 - r29251462;
        double r29251467 = r29251464 / r29251466;
        double r29251468 = r29251458 + r29251467;
        return r29251468;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r29251469 = a;
        double r29251470 = -4.911453117926139e-142;
        bool r29251471 = r29251469 <= r29251470;
        double r29251472 = x;
        double r29251473 = y;
        double r29251474 = r29251473 - r29251472;
        double r29251475 = z;
        double r29251476 = t;
        double r29251477 = r29251475 - r29251476;
        double r29251478 = r29251469 - r29251476;
        double r29251479 = r29251477 / r29251478;
        double r29251480 = r29251474 * r29251479;
        double r29251481 = r29251472 + r29251480;
        double r29251482 = 7.273457157218697e-223;
        bool r29251483 = r29251469 <= r29251482;
        double r29251484 = r29251472 * r29251475;
        double r29251485 = r29251484 / r29251476;
        double r29251486 = r29251473 + r29251485;
        double r29251487 = r29251475 * r29251473;
        double r29251488 = r29251487 / r29251476;
        double r29251489 = r29251486 - r29251488;
        double r29251490 = cbrt(r29251478);
        double r29251491 = cbrt(r29251477);
        double r29251492 = r29251490 / r29251491;
        double r29251493 = r29251492 * r29251492;
        double r29251494 = r29251474 / r29251493;
        double r29251495 = r29251494 / r29251492;
        double r29251496 = r29251472 + r29251495;
        double r29251497 = r29251483 ? r29251489 : r29251496;
        double r29251498 = r29251471 ? r29251481 : r29251497;
        return r29251498;
}

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

Original24.6
Target9.4
Herbie10.4
\[\begin{array}{l} \mathbf{if}\;a \lt -1.615306284544257464183904494091872805513 \cdot 10^{-142}:\\ \;\;\;\;x + \frac{y - x}{1} \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;a \lt 3.774403170083174201868024161554637965035 \cdot 10^{-182}:\\ \;\;\;\;y - \frac{z}{t} \cdot \left(y - x\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{1} \cdot \frac{z - t}{a - t}\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if a < -4.911453117926139e-142

    1. Initial program 23.4

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

    3. Applied *-un-lft-identity23.4

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

    4. Applied times-frac9.4

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

    5. Simplified9.4

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

    if -4.911453117926139e-142 < a < 7.273457157218697e-223

    1. Initial program 30.3

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

    2. Taylor expanded around inf 13.4

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

    if 7.273457157218697e-223 < a

    1. Initial program 23.4

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

    3. Applied associate-/l*10.1

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

    5. Applied add-cube-cbrt10.8

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

    6. Applied add-cube-cbrt10.7

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

    7. Applied times-frac10.7

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

    8. Applied associate-/r*10.1

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

    9. Simplified10.1

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

  4. Final simplification10.4

    \[\leadsto \begin{array}{l} \mathbf{if}\;a \le -4.911453117926138773931568290458543734291 \cdot 10^{-142}:\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;a \le 7.273457157218697182460513419680927492199 \cdot 10^{-223}:\\ \;\;\;\;\left(y + \frac{x \cdot z}{t}\right) - \frac{z \cdot y}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\frac{y - x}{\frac{\sqrt[3]{a - t}}{\sqrt[3]{z - t}} \cdot \frac{\sqrt[3]{a - t}}{\sqrt[3]{z - t}}}}{\frac{\sqrt[3]{a - t}}{\sqrt[3]{z - t}}}\\ \end{array}\]

Reproduce

herbie shell --seed 2019170 
(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))))