Average Error: 6.6 → 1.7
Time: 20.1s
Precision: 64
\[x + \frac{y \cdot \left(z - x\right)}{t}\]
↓
\[\begin{array}{l} \mathbf{if}\;t \le -5792166923042434167341056:\\ \;\;\;\;x + \frac{y}{\frac{t}{z - x}}\\ \mathbf{elif}\;t \le 1.313456436383683786127876557812595999187 \cdot 10^{-110}:\\ \;\;\;\;x + \frac{\left(z - x\right) \cdot y}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{t}{z - x}}\\ \end{array}\]
x + \frac{y \cdot \left(z - x\right)}{t}
↓
\begin{array}{l}
\mathbf{if}\;t \le -5792166923042434167341056:\\
\;\;\;\;x + \frac{y}{\frac{t}{z - x}}\\

\mathbf{elif}\;t \le 1.313456436383683786127876557812595999187 \cdot 10^{-110}:\\
\;\;\;\;x + \frac{\left(z - x\right) \cdot y}{t}\\

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

\end{array}
double f(double x, double y, double z, double t) {
        double r17493308 = x;
        double r17493309 = y;
        double r17493310 = z;
        double r17493311 = r17493310 - r17493308;
        double r17493312 = r17493309 * r17493311;
        double r17493313 = t;
        double r17493314 = r17493312 / r17493313;
        double r17493315 = r17493308 + r17493314;
        return r17493315;
}
↓
double f(double x, double y, double z, double t) {
        double r17493316 = t;
        double r17493317 = -5.792166923042434e+24;
        bool r17493318 = r17493316 <= r17493317;
        double r17493319 = x;
        double r17493320 = y;
        double r17493321 = z;
        double r17493322 = r17493321 - r17493319;
        double r17493323 = r17493316 / r17493322;
        double r17493324 = r17493320 / r17493323;
        double r17493325 = r17493319 + r17493324;
        double r17493326 = 1.3134564363836838e-110;
        bool r17493327 = r17493316 <= r17493326;
        double r17493328 = r17493322 * r17493320;
        double r17493329 = r17493328 / r17493316;
        double r17493330 = r17493319 + r17493329;
        double r17493331 = r17493327 ? r17493330 : r17493325;
        double r17493332 = r17493318 ? r17493325 : r17493331;
        return r17493332;
}

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

Original6.6
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 < -5.792166923042434e+24 or 1.3134564363836838e-110 < t

    1. Initial program 8.9

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

    3. Applied associate-/l*1.6

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

    if -5.792166923042434e+24 < t < 1.3134564363836838e-110

    1. Initial program 1.9

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

  4. Final simplification1.7

    \[\leadsto \begin{array}{l} \mathbf{if}\;t \le -5792166923042434167341056:\\ \;\;\;\;x + \frac{y}{\frac{t}{z - x}}\\ \mathbf{elif}\;t \le 1.313456436383683786127876557812595999187 \cdot 10^{-110}:\\ \;\;\;\;x + \frac{\left(z - x\right) \cdot y}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{t}{z - x}}\\ \end{array}\]

Reproduce

herbie shell --seed 2019171 
(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)))