Average Error: 2.0 → 1.5
Time: 4.7s
Precision: 64
\[x + \left(y - x\right) \cdot \frac{z}{t}\]
↓
\[\begin{array}{l} \mathbf{if}\;t \le -1.77199671097553032 \cdot 10^{-221} \lor \neg \left(t \le 1.4493129888661283 \cdot 10^{-108}\right):\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot \left(\left(\sqrt[3]{1} \cdot \sqrt[3]{\frac{z}{\sqrt[3]{t}}}\right) \cdot \sqrt[3]{z}\right)}{\sqrt[3]{\sqrt[3]{t} \cdot \sqrt[3]{t}} \cdot \sqrt[3]{t}} \cdot \frac{\sqrt[3]{z}}{\sqrt[3]{t}}\\ \end{array}\]
x + \left(y - x\right) \cdot \frac{z}{t}
↓
\begin{array}{l}
\mathbf{if}\;t \le -1.77199671097553032 \cdot 10^{-221} \lor \neg \left(t \le 1.4493129888661283 \cdot 10^{-108}\right):\\
\;\;\;\;x + \left(y - x\right) \cdot \frac{z}{t}\\

\mathbf{else}:\\
\;\;\;\;x + \frac{\left(y - x\right) \cdot \left(\left(\sqrt[3]{1} \cdot \sqrt[3]{\frac{z}{\sqrt[3]{t}}}\right) \cdot \sqrt[3]{z}\right)}{\sqrt[3]{\sqrt[3]{t} \cdot \sqrt[3]{t}} \cdot \sqrt[3]{t}} \cdot \frac{\sqrt[3]{z}}{\sqrt[3]{t}}\\

\end{array}
double f(double x, double y, double z, double t) {
        double r500205 = x;
        double r500206 = y;
        double r500207 = r500206 - r500205;
        double r500208 = z;
        double r500209 = t;
        double r500210 = r500208 / r500209;
        double r500211 = r500207 * r500210;
        double r500212 = r500205 + r500211;
        return r500212;
}
↓
double f(double x, double y, double z, double t) {
        double r500213 = t;
        double r500214 = -1.7719967109755303e-221;
        bool r500215 = r500213 <= r500214;
        double r500216 = 1.4493129888661283e-108;
        bool r500217 = r500213 <= r500216;
        double r500218 = !r500217;
        bool r500219 = r500215 || r500218;
        double r500220 = x;
        double r500221 = y;
        double r500222 = r500221 - r500220;
        double r500223 = z;
        double r500224 = r500223 / r500213;
        double r500225 = r500222 * r500224;
        double r500226 = r500220 + r500225;
        double r500227 = 1.0;
        double r500228 = cbrt(r500227);
        double r500229 = cbrt(r500213);
        double r500230 = r500223 / r500229;
        double r500231 = cbrt(r500230);
        double r500232 = r500228 * r500231;
        double r500233 = cbrt(r500223);
        double r500234 = r500232 * r500233;
        double r500235 = r500222 * r500234;
        double r500236 = r500229 * r500229;
        double r500237 = cbrt(r500236);
        double r500238 = r500237 * r500229;
        double r500239 = r500235 / r500238;
        double r500240 = r500233 / r500229;
        double r500241 = r500239 * r500240;
        double r500242 = r500220 + r500241;
        double r500243 = r500219 ? r500226 : r500242;
        return r500243;
}

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

Original2.0
Target2.0
Herbie1.5
\[\begin{array}{l} \mathbf{if}\;\left(y - x\right) \cdot \frac{z}{t} \lt -1013646692435.887:\\ \;\;\;\;x + \frac{y - x}{\frac{t}{z}}\\ \mathbf{elif}\;\left(y - x\right) \cdot \frac{z}{t} \lt -0.0:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{\frac{t}{z}}\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if t < -1.7719967109755303e-221 or 1.4493129888661283e-108 < t

    1. Initial program 1.4

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

    if -1.7719967109755303e-221 < t < 1.4493129888661283e-108

    1. Initial program 5.3

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

    3. Applied add-cube-cbrt6.0

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

    4. Applied associate-*r*6.1

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

    6. Applied cbrt-div6.0

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

    8. Applied add-cube-cbrt6.1

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

    9. Applied *-un-lft-identity6.1

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

    10. Applied times-frac6.1

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

    11. Applied cbrt-prod6.1

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

    13. Applied cbrt-div1.6

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

    14. Applied cbrt-div1.7

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

    15. Applied associate-*l/1.6

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

    16. Applied frac-times1.6

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

    17. Applied associate-*r/2.2

      \[\leadsto x + \color{blue}{\frac{\left(y - x\right) \cdot \left(\left(\sqrt[3]{1} \cdot \sqrt[3]{\frac{z}{\sqrt[3]{t}}}\right) \cdot \sqrt[3]{z}\right)}{\sqrt[3]{\sqrt[3]{t} \cdot \sqrt[3]{t}} \cdot \sqrt[3]{t}}} \cdot \frac{\sqrt[3]{z}}{\sqrt[3]{t}}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification1.5

    \[\leadsto \begin{array}{l} \mathbf{if}\;t \le -1.77199671097553032 \cdot 10^{-221} \lor \neg \left(t \le 1.4493129888661283 \cdot 10^{-108}\right):\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot \left(\left(\sqrt[3]{1} \cdot \sqrt[3]{\frac{z}{\sqrt[3]{t}}}\right) \cdot \sqrt[3]{z}\right)}{\sqrt[3]{\sqrt[3]{t} \cdot \sqrt[3]{t}} \cdot \sqrt[3]{t}} \cdot \frac{\sqrt[3]{z}}{\sqrt[3]{t}}\\ \end{array}\]

Reproduce

herbie shell --seed 2020064 
(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))))