Average Error: 6.2 → 1.7
Time: 3.6s
Precision: 64
\[x + \frac{y \cdot \left(z - x\right)}{t}\]
↓
\[\begin{array}{l} \mathbf{if}\;y \le -1.135513131207627854220763512156247298535 \cdot 10^{-100}:\\ \;\;\;\;x + \frac{\sqrt[3]{y} \cdot \sqrt[3]{y}}{1} \cdot \left(\frac{\sqrt[3]{y}}{t} \cdot \left(z - x\right)\right)\\ \mathbf{elif}\;y \le 1.679711245375942250255279733473869160103 \cdot 10^{-30}:\\ \;\;\;\;x + \left(y \cdot \left(z - x\right)\right) \cdot \frac{1}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{t}{z - x}}\\ \end{array}\]
x + \frac{y \cdot \left(z - x\right)}{t}
↓
\begin{array}{l}
\mathbf{if}\;y \le -1.135513131207627854220763512156247298535 \cdot 10^{-100}:\\
\;\;\;\;x + \frac{\sqrt[3]{y} \cdot \sqrt[3]{y}}{1} \cdot \left(\frac{\sqrt[3]{y}}{t} \cdot \left(z - x\right)\right)\\

\mathbf{elif}\;y \le 1.679711245375942250255279733473869160103 \cdot 10^{-30}:\\
\;\;\;\;x + \left(y \cdot \left(z - x\right)\right) \cdot \frac{1}{t}\\

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

\end{array}
double f(double x, double y, double z, double t) {
        double r338379 = x;
        double r338380 = y;
        double r338381 = z;
        double r338382 = r338381 - r338379;
        double r338383 = r338380 * r338382;
        double r338384 = t;
        double r338385 = r338383 / r338384;
        double r338386 = r338379 + r338385;
        return r338386;
}
↓
double f(double x, double y, double z, double t) {
        double r338387 = y;
        double r338388 = -1.1355131312076279e-100;
        bool r338389 = r338387 <= r338388;
        double r338390 = x;
        double r338391 = cbrt(r338387);
        double r338392 = r338391 * r338391;
        double r338393 = 1.0;
        double r338394 = r338392 / r338393;
        double r338395 = t;
        double r338396 = r338391 / r338395;
        double r338397 = z;
        double r338398 = r338397 - r338390;
        double r338399 = r338396 * r338398;
        double r338400 = r338394 * r338399;
        double r338401 = r338390 + r338400;
        double r338402 = 1.6797112453759423e-30;
        bool r338403 = r338387 <= r338402;
        double r338404 = r338387 * r338398;
        double r338405 = r338393 / r338395;
        double r338406 = r338404 * r338405;
        double r338407 = r338390 + r338406;
        double r338408 = r338395 / r338398;
        double r338409 = r338387 / r338408;
        double r338410 = r338390 + r338409;
        double r338411 = r338403 ? r338407 : r338410;
        double r338412 = r338389 ? r338401 : r338411;
        return r338412;
}

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

Original6.2
Target2.2
Herbie1.7
\[x - \left(x \cdot \frac{y}{t} + \left(-z\right) \cdot \frac{y}{t}\right)\]

Derivation

  1. Split input into 3 regimes

  2. if y < -1.1355131312076279e-100

    1. Initial program 10.1

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

    3. Applied associate-/l*2.8

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

    5. Applied associate-/r/2.8

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

    7. Applied *-un-lft-identity2.8

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

    8. Applied add-cube-cbrt3.5

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

    9. Applied times-frac3.4

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

    10. Applied associate-*l*2.5

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

    if -1.1355131312076279e-100 < y < 1.6797112453759423e-30

    1. Initial program 1.3

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

    3. Applied div-inv1.4

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

    if 1.6797112453759423e-30 < y

    1. Initial program 12.7

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

    3. Applied associate-/l*1.4

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

  4. Final simplification1.7

    \[\leadsto \begin{array}{l} \mathbf{if}\;y \le -1.135513131207627854220763512156247298535 \cdot 10^{-100}:\\ \;\;\;\;x + \frac{\sqrt[3]{y} \cdot \sqrt[3]{y}}{1} \cdot \left(\frac{\sqrt[3]{y}}{t} \cdot \left(z - x\right)\right)\\ \mathbf{elif}\;y \le 1.679711245375942250255279733473869160103 \cdot 10^{-30}:\\ \;\;\;\;x + \left(y \cdot \left(z - x\right)\right) \cdot \frac{1}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{t}{z - x}}\\ \end{array}\]

Reproduce

herbie shell --seed 2019362 
(FPCore (x y z t)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, D"
  :precision binary64

  :herbie-target
  (- x (+ (* x (/ y t)) (* (- z) (/ y t))))

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