Average Error: 6.7 → 2.1
Time: 4.6s
Precision: 64
\[x + \frac{y \cdot \left(z - x\right)}{t}\]
↓
\[\begin{array}{l} \mathbf{if}\;x \le -1.324378283502526917772059572052329230767 \cdot 10^{-242} \lor \neg \left(x \le 1.042776901272343168104863784399005429514 \cdot 10^{-127}\right):\\ \;\;\;\;x + \frac{1}{\frac{\frac{t}{y}}{z - x}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{t}{z - x}}\\ \end{array}\]
x + \frac{y \cdot \left(z - x\right)}{t}
↓
\begin{array}{l}
\mathbf{if}\;x \le -1.324378283502526917772059572052329230767 \cdot 10^{-242} \lor \neg \left(x \le 1.042776901272343168104863784399005429514 \cdot 10^{-127}\right):\\
\;\;\;\;x + \frac{1}{\frac{\frac{t}{y}}{z - x}}\\

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

\end{array}
double f(double x, double y, double z, double t) {
        double r350366 = x;
        double r350367 = y;
        double r350368 = z;
        double r350369 = r350368 - r350366;
        double r350370 = r350367 * r350369;
        double r350371 = t;
        double r350372 = r350370 / r350371;
        double r350373 = r350366 + r350372;
        return r350373;
}
↓
double f(double x, double y, double z, double t) {
        double r350374 = x;
        double r350375 = -1.324378283502527e-242;
        bool r350376 = r350374 <= r350375;
        double r350377 = 1.0427769012723432e-127;
        bool r350378 = r350374 <= r350377;
        double r350379 = !r350378;
        bool r350380 = r350376 || r350379;
        double r350381 = 1.0;
        double r350382 = t;
        double r350383 = y;
        double r350384 = r350382 / r350383;
        double r350385 = z;
        double r350386 = r350385 - r350374;
        double r350387 = r350384 / r350386;
        double r350388 = r350381 / r350387;
        double r350389 = r350374 + r350388;
        double r350390 = r350382 / r350386;
        double r350391 = r350383 / r350390;
        double r350392 = r350374 + r350391;
        double r350393 = r350380 ? r350389 : r350392;
        return r350393;
}

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

Derivation

  1. Split input into 2 regimes

  2. if x < -1.324378283502527e-242 or 1.0427769012723432e-127 < x

    1. Initial program 7.1

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

    3. Applied clear-num7.1

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

    5. Applied associate-/r*1.1

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

    if -1.324378283502527e-242 < x < 1.0427769012723432e-127

    1. Initial program 5.5

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

    3. Applied associate-/l*5.7

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

  4. Final simplification2.1

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \le -1.324378283502526917772059572052329230767 \cdot 10^{-242} \lor \neg \left(x \le 1.042776901272343168104863784399005429514 \cdot 10^{-127}\right):\\ \;\;\;\;x + \frac{1}{\frac{\frac{t}{y}}{z - x}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{t}{z - x}}\\ \end{array}\]

Reproduce

herbie shell --seed 2019322 
(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)))