Average Error: 1.9 → 1.3
Time: 24.1s
Precision: 64
\[x + \left(y - x\right) \cdot \frac{z}{t}\]
↓
\[\begin{array}{l} \mathbf{if}\;t \le -1.642352366428419672760218965734387145992 \cdot 10^{49}:\\ \;\;\;\;x + \frac{y - x}{\sqrt[3]{t} \cdot \sqrt[3]{t}} \cdot \frac{z}{\sqrt[3]{t}}\\ \mathbf{elif}\;t \le 9.000444220027358670760165371832293801472 \cdot 10^{57}:\\ \;\;\;\;x + \left(\frac{z \cdot y}{t} - \frac{x \cdot z}{t}\right)\\ \mathbf{elif}\;t \le 3.879050157548418050555246632767665715378 \cdot 10^{258}:\\ \;\;\;\;x + \frac{y - x}{\sqrt[3]{t} \cdot \sqrt[3]{t}} \cdot \frac{z}{\sqrt[3]{t}}\\ \mathbf{else}:\\ \;\;\;\;x + \left(\frac{\sqrt[3]{z} \cdot \sqrt[3]{z}}{\sqrt{t}} \cdot \left(y - x\right)\right) \cdot \frac{\sqrt[3]{z}}{\sqrt{t}}\\ \end{array}\]
x + \left(y - x\right) \cdot \frac{z}{t}
↓
\begin{array}{l}
\mathbf{if}\;t \le -1.642352366428419672760218965734387145992 \cdot 10^{49}:\\
\;\;\;\;x + \frac{y - x}{\sqrt[3]{t} \cdot \sqrt[3]{t}} \cdot \frac{z}{\sqrt[3]{t}}\\

\mathbf{elif}\;t \le 9.000444220027358670760165371832293801472 \cdot 10^{57}:\\
\;\;\;\;x + \left(\frac{z \cdot y}{t} - \frac{x \cdot z}{t}\right)\\

\mathbf{elif}\;t \le 3.879050157548418050555246632767665715378 \cdot 10^{258}:\\
\;\;\;\;x + \frac{y - x}{\sqrt[3]{t} \cdot \sqrt[3]{t}} \cdot \frac{z}{\sqrt[3]{t}}\\

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

\end{array}
double f(double x, double y, double z, double t) {
        double r435509 = x;
        double r435510 = y;
        double r435511 = r435510 - r435509;
        double r435512 = z;
        double r435513 = t;
        double r435514 = r435512 / r435513;
        double r435515 = r435511 * r435514;
        double r435516 = r435509 + r435515;
        return r435516;
}
↓
double f(double x, double y, double z, double t) {
        double r435517 = t;
        double r435518 = -1.6423523664284197e+49;
        bool r435519 = r435517 <= r435518;
        double r435520 = x;
        double r435521 = y;
        double r435522 = r435521 - r435520;
        double r435523 = cbrt(r435517);
        double r435524 = r435523 * r435523;
        double r435525 = r435522 / r435524;
        double r435526 = z;
        double r435527 = r435526 / r435523;
        double r435528 = r435525 * r435527;
        double r435529 = r435520 + r435528;
        double r435530 = 9.000444220027359e+57;
        bool r435531 = r435517 <= r435530;
        double r435532 = r435526 * r435521;
        double r435533 = r435532 / r435517;
        double r435534 = r435520 * r435526;
        double r435535 = r435534 / r435517;
        double r435536 = r435533 - r435535;
        double r435537 = r435520 + r435536;
        double r435538 = 3.879050157548418e+258;
        bool r435539 = r435517 <= r435538;
        double r435540 = cbrt(r435526);
        double r435541 = r435540 * r435540;
        double r435542 = sqrt(r435517);
        double r435543 = r435541 / r435542;
        double r435544 = r435543 * r435522;
        double r435545 = r435540 / r435542;
        double r435546 = r435544 * r435545;
        double r435547 = r435520 + r435546;
        double r435548 = r435539 ? r435529 : r435547;
        double r435549 = r435531 ? r435537 : r435548;
        double r435550 = r435519 ? r435529 : r435549;
        return r435550;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original1.9
Target2.0
Herbie1.3
\[\begin{array}{l} \mathbf{if}\;\left(y - x\right) \cdot \frac{z}{t} \lt -1013646692435.88671875:\\ \;\;\;\;x + \frac{y - x}{\frac{t}{z}}\\ \mathbf{elif}\;\left(y - x\right) \cdot \frac{z}{t} \lt -0.0:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{\frac{t}{z}}\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if t < -1.6423523664284197e+49 or 9.000444220027359e+57 < t < 3.879050157548418e+258

    1. Initial program 1.0

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

    3. Applied add-cube-cbrt1.3

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

    4. Applied *-un-lft-identity1.3

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

    5. Applied times-frac1.4

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

    6. Applied associate-*r*1.0

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

    7. Simplified1.0

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

    if -1.6423523664284197e+49 < t < 9.000444220027359e+57

    1. Initial program 2.8

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

    3. Applied add-cube-cbrt3.5

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

    4. Applied associate-*l*3.5

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

    5. Taylor expanded around 0 1.6

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

    if 3.879050157548418e+258 < t

    1. Initial program 1.2

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

    3. Applied add-sqr-sqrt1.3

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

    4. Applied add-cube-cbrt1.4

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

    5. Applied times-frac1.4

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

    6. Applied associate-*r*1.0

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

    7. Simplified1.0

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

  4. Final simplification1.3

    \[\leadsto \begin{array}{l} \mathbf{if}\;t \le -1.642352366428419672760218965734387145992 \cdot 10^{49}:\\ \;\;\;\;x + \frac{y - x}{\sqrt[3]{t} \cdot \sqrt[3]{t}} \cdot \frac{z}{\sqrt[3]{t}}\\ \mathbf{elif}\;t \le 9.000444220027358670760165371832293801472 \cdot 10^{57}:\\ \;\;\;\;x + \left(\frac{z \cdot y}{t} - \frac{x \cdot z}{t}\right)\\ \mathbf{elif}\;t \le 3.879050157548418050555246632767665715378 \cdot 10^{258}:\\ \;\;\;\;x + \frac{y - x}{\sqrt[3]{t} \cdot \sqrt[3]{t}} \cdot \frac{z}{\sqrt[3]{t}}\\ \mathbf{else}:\\ \;\;\;\;x + \left(\frac{\sqrt[3]{z} \cdot \sqrt[3]{z}}{\sqrt{t}} \cdot \left(y - x\right)\right) \cdot \frac{\sqrt[3]{z}}{\sqrt{t}}\\ \end{array}\]

Reproduce

herbie shell --seed 2019208 
(FPCore (x y z t)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:tickPosition from plot-0.2.3.4"
  :precision binary64

  :herbie-target
  (if (< (* (- y x) (/ z t)) -1013646692435.887) (+ x (/ (- y x) (/ t z))) (if (< (* (- y x) (/ z t)) -0.0) (+ x (/ (* (- y x) z) t)) (+ x (/ (- y x) (/ t z)))))

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