Average Error: 24.3 → 8.5
Time: 5.3s
Precision: 64
\[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\]
↓
\[\begin{array}{l} \mathbf{if}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \le -6.2666950177420879 \cdot 10^{-252}:\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \le 0.0:\\ \;\;\;\;\left(y + \frac{x \cdot z}{t}\right) - \frac{z \cdot y}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \left(\left(y - x\right) \cdot \frac{\sqrt[3]{z - t} \cdot \sqrt[3]{z - t}}{\left(\left(\sqrt[3]{\sqrt[3]{a - t}} \cdot \sqrt[3]{\sqrt[3]{a - t}}\right) \cdot \sqrt[3]{\sqrt[3]{a - t}}\right) \cdot \sqrt[3]{a - t}}\right) \cdot \frac{\sqrt[3]{z - t}}{\sqrt[3]{a - t}}\\ \end{array}\]
x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}
↓
\begin{array}{l}
\mathbf{if}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \le -6.2666950177420879 \cdot 10^{-252}:\\
\;\;\;\;x + \left(y - x\right) \cdot \frac{z - t}{a - t}\\

\mathbf{elif}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \le 0.0:\\
\;\;\;\;\left(y + \frac{x \cdot z}{t}\right) - \frac{z \cdot y}{t}\\

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

\end{array}
double f(double x, double y, double z, double t, double a) {
        double r667340 = x;
        double r667341 = y;
        double r667342 = r667341 - r667340;
        double r667343 = z;
        double r667344 = t;
        double r667345 = r667343 - r667344;
        double r667346 = r667342 * r667345;
        double r667347 = a;
        double r667348 = r667347 - r667344;
        double r667349 = r667346 / r667348;
        double r667350 = r667340 + r667349;
        return r667350;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r667351 = x;
        double r667352 = y;
        double r667353 = r667352 - r667351;
        double r667354 = z;
        double r667355 = t;
        double r667356 = r667354 - r667355;
        double r667357 = r667353 * r667356;
        double r667358 = a;
        double r667359 = r667358 - r667355;
        double r667360 = r667357 / r667359;
        double r667361 = r667351 + r667360;
        double r667362 = -6.266695017742088e-252;
        bool r667363 = r667361 <= r667362;
        double r667364 = r667356 / r667359;
        double r667365 = r667353 * r667364;
        double r667366 = r667351 + r667365;
        double r667367 = 0.0;
        bool r667368 = r667361 <= r667367;
        double r667369 = r667351 * r667354;
        double r667370 = r667369 / r667355;
        double r667371 = r667352 + r667370;
        double r667372 = r667354 * r667352;
        double r667373 = r667372 / r667355;
        double r667374 = r667371 - r667373;
        double r667375 = cbrt(r667356);
        double r667376 = r667375 * r667375;
        double r667377 = cbrt(r667359);
        double r667378 = cbrt(r667377);
        double r667379 = r667378 * r667378;
        double r667380 = r667379 * r667378;
        double r667381 = r667380 * r667377;
        double r667382 = r667376 / r667381;
        double r667383 = r667353 * r667382;
        double r667384 = r667375 / r667377;
        double r667385 = r667383 * r667384;
        double r667386 = r667351 + r667385;
        double r667387 = r667368 ? r667374 : r667386;
        double r667388 = r667363 ? r667366 : r667387;
        return r667388;
}

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
Target9.5
Herbie8.5
\[\begin{array}{l} \mathbf{if}\;a \lt -1.6153062845442575 \cdot 10^{-142}:\\ \;\;\;\;x + \frac{y - x}{1} \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;a \lt 3.7744031700831742 \cdot 10^{-182}:\\ \;\;\;\;y - \frac{z}{t} \cdot \left(y - x\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{1} \cdot \frac{z - t}{a - t}\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if (+ x (/ (* (- y x) (- z t)) (- a t))) < -6.266695017742088e-252

    1. Initial program 21.0

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

    3. Applied *-un-lft-identity21.0

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

    4. Applied times-frac7.2

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

    5. Simplified7.2

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

    if -6.266695017742088e-252 < (+ x (/ (* (- y x) (- z t)) (- a t))) < 0.0

    1. Initial program 56.9

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

    2. Taylor expanded around inf 20.5

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

    if 0.0 < (+ x (/ (* (- y x) (- z t)) (- a t)))

    1. Initial program 20.7

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

    3. Applied *-un-lft-identity20.7

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

    4. Applied times-frac7.1

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

    5. Simplified7.1

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

    7. Applied add-cube-cbrt7.9

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

    8. Applied add-cube-cbrt7.7

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

    9. Applied times-frac7.7

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

    10. Applied associate-*r*6.9

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

    12. Applied add-cube-cbrt7.3

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

  4. Final simplification8.5

    \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \le -6.2666950177420879 \cdot 10^{-252}:\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \le 0.0:\\ \;\;\;\;\left(y + \frac{x \cdot z}{t}\right) - \frac{z \cdot y}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \left(\left(y - x\right) \cdot \frac{\sqrt[3]{z - t} \cdot \sqrt[3]{z - t}}{\left(\left(\sqrt[3]{\sqrt[3]{a - t}} \cdot \sqrt[3]{\sqrt[3]{a - t}}\right) \cdot \sqrt[3]{\sqrt[3]{a - t}}\right) \cdot \sqrt[3]{a - t}}\right) \cdot \frac{\sqrt[3]{z - t}}{\sqrt[3]{a - t}}\\ \end{array}\]

Reproduce

herbie shell --seed 2020049 
(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))))