Average Error: 6.3 → 1.7
Time: 10.0s
Precision: 64
\[x + \frac{y \cdot \left(z - x\right)}{t}\]
↓
\[\begin{array}{l} \mathbf{if}\;t \le -8.363664958439672667278554160764100153889 \cdot 10^{69} \lor \neg \left(t \le 7.486542709900388243398285213925344255536 \cdot 10^{-169}\right):\\ \;\;\;\;\left(z - x\right) \cdot \frac{y}{t} + x\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot \left(z - x\right)}{t} + x\\ \end{array}\]
x + \frac{y \cdot \left(z - x\right)}{t}
↓
\begin{array}{l}
\mathbf{if}\;t \le -8.363664958439672667278554160764100153889 \cdot 10^{69} \lor \neg \left(t \le 7.486542709900388243398285213925344255536 \cdot 10^{-169}\right):\\
\;\;\;\;\left(z - x\right) \cdot \frac{y}{t} + x\\

\mathbf{else}:\\
\;\;\;\;\frac{y \cdot \left(z - x\right)}{t} + x\\

\end{array}
double f(double x, double y, double z, double t) {
        double r269358 = x;
        double r269359 = y;
        double r269360 = z;
        double r269361 = r269360 - r269358;
        double r269362 = r269359 * r269361;
        double r269363 = t;
        double r269364 = r269362 / r269363;
        double r269365 = r269358 + r269364;
        return r269365;
}
↓
double f(double x, double y, double z, double t) {
        double r269366 = t;
        double r269367 = -8.363664958439673e+69;
        bool r269368 = r269366 <= r269367;
        double r269369 = 7.486542709900388e-169;
        bool r269370 = r269366 <= r269369;
        double r269371 = !r269370;
        bool r269372 = r269368 || r269371;
        double r269373 = z;
        double r269374 = x;
        double r269375 = r269373 - r269374;
        double r269376 = y;
        double r269377 = r269376 / r269366;
        double r269378 = r269375 * r269377;
        double r269379 = r269378 + r269374;
        double r269380 = r269376 * r269375;
        double r269381 = r269380 / r269366;
        double r269382 = r269381 + r269374;
        double r269383 = r269372 ? r269379 : r269382;
        return r269383;
}

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

Original6.3
Target2.0
Herbie1.7
\[x - \left(x \cdot \frac{y}{t} + \left(-z\right) \cdot \frac{y}{t}\right)\]

Derivation

  1. Split input into 2 regimes

  2. if t < -8.363664958439673e+69 or 7.486542709900388e-169 < t

    1. Initial program 8.1

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

    3. Applied associate-/l*2.4

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

    5. Applied *-un-lft-identity2.4

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

    6. Applied *-un-lft-identity2.4

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

    7. Applied distribute-lft-out2.4

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

    8. Simplified1.3

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

    if -8.363664958439673e+69 < t < 7.486542709900388e-169

    1. Initial program 2.7

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

  4. Final simplification1.7

    \[\leadsto \begin{array}{l} \mathbf{if}\;t \le -8.363664958439672667278554160764100153889 \cdot 10^{69} \lor \neg \left(t \le 7.486542709900388243398285213925344255536 \cdot 10^{-169}\right):\\ \;\;\;\;\left(z - x\right) \cdot \frac{y}{t} + x\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot \left(z - x\right)}{t} + x\\ \end{array}\]

Reproduce

herbie shell --seed 2019179 
(FPCore (x y z t)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, D"

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

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