Average Error: 6.1 → 2.1
Time: 5.6s
Precision: 64
\[x + \frac{y \cdot \left(z - x\right)}{t}\]
↓
\[\begin{array}{l} \mathbf{if}\;x \le -3.52279374725536558 \cdot 10^{-91} \lor \neg \left(x \le 8.1960799302122424 \cdot 10^{-188}\right):\\ \;\;\;\;x + \frac{\frac{y}{t}}{\frac{1}{z - x}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{t}{z - x}}\\ \end{array}\]
x + \frac{y \cdot \left(z - x\right)}{t}
↓
\begin{array}{l}
\mathbf{if}\;x \le -3.52279374725536558 \cdot 10^{-91} \lor \neg \left(x \le 8.1960799302122424 \cdot 10^{-188}\right):\\
\;\;\;\;x + \frac{\frac{y}{t}}{\frac{1}{z - x}}\\

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

\end{array}
double f(double x, double y, double z, double t) {
        double r438508 = x;
        double r438509 = y;
        double r438510 = z;
        double r438511 = r438510 - r438508;
        double r438512 = r438509 * r438511;
        double r438513 = t;
        double r438514 = r438512 / r438513;
        double r438515 = r438508 + r438514;
        return r438515;
}
↓
double f(double x, double y, double z, double t) {
        double r438516 = x;
        double r438517 = -3.5227937472553656e-91;
        bool r438518 = r438516 <= r438517;
        double r438519 = 8.196079930212242e-188;
        bool r438520 = r438516 <= r438519;
        double r438521 = !r438520;
        bool r438522 = r438518 || r438521;
        double r438523 = y;
        double r438524 = t;
        double r438525 = r438523 / r438524;
        double r438526 = 1.0;
        double r438527 = z;
        double r438528 = r438527 - r438516;
        double r438529 = r438526 / r438528;
        double r438530 = r438525 / r438529;
        double r438531 = r438516 + r438530;
        double r438532 = r438524 / r438528;
        double r438533 = r438523 / r438532;
        double r438534 = r438516 + r438533;
        double r438535 = r438522 ? r438531 : r438534;
        return r438535;
}

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

Original6.1
Target2.2
Herbie2.1
\[x - \left(x \cdot \frac{y}{t} + \left(-z\right) \cdot \frac{y}{t}\right)\]

Derivation

  1. Split input into 2 regimes

  2. if x < -3.5227937472553656e-91 or 8.196079930212242e-188 < x

    1. Initial program 6.9

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

    3. Applied associate-/l*5.9

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

    5. Applied div-inv6.0

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

    6. Applied associate-/r*1.0

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

    if -3.5227937472553656e-91 < x < 8.196079930212242e-188

    1. Initial program 4.2

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

    3. Applied associate-/l*4.7

      \[\leadsto x + \color{blue}{\frac{y}{\frac{t}{z - x}}}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification2.1

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \le -3.52279374725536558 \cdot 10^{-91} \lor \neg \left(x \le 8.1960799302122424 \cdot 10^{-188}\right):\\ \;\;\;\;x + \frac{\frac{y}{t}}{\frac{1}{z - x}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{t}{z - x}}\\ \end{array}\]

Reproduce

herbie shell --seed 2020089 
(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)))