Average Error: 6.7 → 2.3
Time: 24.2s
Precision: 64
\[x + \frac{y \cdot \left(z - x\right)}{t}\]
↓
\[\begin{array}{l} \mathbf{if}\;t \le -1.57808943454970652 \cdot 10^{-307}:\\ \;\;\;\;x + \left(\frac{y}{\sqrt[3]{t}} \cdot \frac{\sqrt[3]{\frac{z - x}{\sqrt[3]{t}}} \cdot \sqrt[3]{\frac{z - x}{\sqrt[3]{t}}}}{{\left(\sqrt[3]{\sqrt[3]{t}}\right)}^{3}}\right) \cdot \sqrt[3]{\frac{z - x}{\sqrt[3]{t}}}\\ \mathbf{elif}\;t \le 4.22353994051715781 \cdot 10^{104}:\\ \;\;\;\;x + \frac{y \cdot z + \left(-x\right) \cdot y}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\sqrt[3]{t} \cdot \sqrt[3]{t}} \cdot \frac{z - x}{\sqrt[3]{t}}\\ \end{array}\]
x + \frac{y \cdot \left(z - x\right)}{t}
↓
\begin{array}{l}
\mathbf{if}\;t \le -1.57808943454970652 \cdot 10^{-307}:\\
\;\;\;\;x + \left(\frac{y}{\sqrt[3]{t}} \cdot \frac{\sqrt[3]{\frac{z - x}{\sqrt[3]{t}}} \cdot \sqrt[3]{\frac{z - x}{\sqrt[3]{t}}}}{{\left(\sqrt[3]{\sqrt[3]{t}}\right)}^{3}}\right) \cdot \sqrt[3]{\frac{z - x}{\sqrt[3]{t}}}\\

\mathbf{elif}\;t \le 4.22353994051715781 \cdot 10^{104}:\\
\;\;\;\;x + \frac{y \cdot z + \left(-x\right) \cdot y}{t}\\

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

\end{array}
double f(double x, double y, double z, double t) {
        double r1053444 = x;
        double r1053445 = y;
        double r1053446 = z;
        double r1053447 = r1053446 - r1053444;
        double r1053448 = r1053445 * r1053447;
        double r1053449 = t;
        double r1053450 = r1053448 / r1053449;
        double r1053451 = r1053444 + r1053450;
        return r1053451;
}
↓
double f(double x, double y, double z, double t) {
        double r1053452 = t;
        double r1053453 = -1.5780894345497065e-307;
        bool r1053454 = r1053452 <= r1053453;
        double r1053455 = x;
        double r1053456 = y;
        double r1053457 = cbrt(r1053452);
        double r1053458 = r1053456 / r1053457;
        double r1053459 = z;
        double r1053460 = r1053459 - r1053455;
        double r1053461 = r1053460 / r1053457;
        double r1053462 = cbrt(r1053461);
        double r1053463 = r1053462 * r1053462;
        double r1053464 = cbrt(r1053457);
        double r1053465 = 3.0;
        double r1053466 = pow(r1053464, r1053465);
        double r1053467 = r1053463 / r1053466;
        double r1053468 = r1053458 * r1053467;
        double r1053469 = r1053468 * r1053462;
        double r1053470 = r1053455 + r1053469;
        double r1053471 = 4.223539940517158e+104;
        bool r1053472 = r1053452 <= r1053471;
        double r1053473 = r1053456 * r1053459;
        double r1053474 = -r1053455;
        double r1053475 = r1053474 * r1053456;
        double r1053476 = r1053473 + r1053475;
        double r1053477 = r1053476 / r1053452;
        double r1053478 = r1053455 + r1053477;
        double r1053479 = r1053457 * r1053457;
        double r1053480 = r1053456 / r1053479;
        double r1053481 = r1053480 * r1053461;
        double r1053482 = r1053455 + r1053481;
        double r1053483 = r1053472 ? r1053478 : r1053482;
        double r1053484 = r1053454 ? r1053470 : r1053483;
        return r1053484;
}

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

Original6.7
Target2.0
Herbie2.3
\[x - \left(x \cdot \frac{y}{t} + \left(-z\right) \cdot \frac{y}{t}\right)\]

Derivation

  1. Split input into 3 regimes

  2. if t < -1.5780894345497065e-307

    1. Initial program 6.8

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

    3. Applied add-cube-cbrt7.3

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

    4. Applied times-frac3.1

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

    6. Applied add-cube-cbrt3.3

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

    8. Applied add-cube-cbrt3.3

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

    9. Applied associate-*r*3.3

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

    10. Simplified2.7

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

    if -1.5780894345497065e-307 < t < 4.223539940517158e+104

    1. Initial program 2.7

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

    3. Applied sub-neg2.7

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

    4. Applied distribute-lft-in2.7

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

    5. Simplified2.7

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

    if 4.223539940517158e+104 < t

    1. Initial program 12.3

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

    3. Applied add-cube-cbrt12.5

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

    4. Applied times-frac0.8

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

  4. Final simplification2.3

    \[\leadsto \begin{array}{l} \mathbf{if}\;t \le -1.57808943454970652 \cdot 10^{-307}:\\ \;\;\;\;x + \left(\frac{y}{\sqrt[3]{t}} \cdot \frac{\sqrt[3]{\frac{z - x}{\sqrt[3]{t}}} \cdot \sqrt[3]{\frac{z - x}{\sqrt[3]{t}}}}{{\left(\sqrt[3]{\sqrt[3]{t}}\right)}^{3}}\right) \cdot \sqrt[3]{\frac{z - x}{\sqrt[3]{t}}}\\ \mathbf{elif}\;t \le 4.22353994051715781 \cdot 10^{104}:\\ \;\;\;\;x + \frac{y \cdot z + \left(-x\right) \cdot y}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\sqrt[3]{t} \cdot \sqrt[3]{t}} \cdot \frac{z - x}{\sqrt[3]{t}}\\ \end{array}\]

Reproduce

herbie shell --seed 2020047 
(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)))