Average Error: 6.7 → 0.9
Time: 19.6s
Precision: 64
\[x + \frac{y \cdot \left(z - x\right)}{t}\]
↓
\[\begin{array}{l} \mathbf{if}\;x + \frac{\left(z - x\right) \cdot y}{t} \le -4.015242760717319860347263184406053785305 \cdot 10^{305}:\\ \;\;\;\;x + \frac{y}{\frac{t}{z - x}}\\ \mathbf{elif}\;x + \frac{\left(z - x\right) \cdot y}{t} \le 2.038097847986346269413799617144504707187 \cdot 10^{304}:\\ \;\;\;\;x + \frac{\left(z - x\right) \cdot y}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{t}{z - x}}\\ \end{array}\]
x + \frac{y \cdot \left(z - x\right)}{t}
↓
\begin{array}{l}
\mathbf{if}\;x + \frac{\left(z - x\right) \cdot y}{t} \le -4.015242760717319860347263184406053785305 \cdot 10^{305}:\\
\;\;\;\;x + \frac{y}{\frac{t}{z - x}}\\

\mathbf{elif}\;x + \frac{\left(z - x\right) \cdot y}{t} \le 2.038097847986346269413799617144504707187 \cdot 10^{304}:\\
\;\;\;\;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 r13411699 = x;
        double r13411700 = y;
        double r13411701 = z;
        double r13411702 = r13411701 - r13411699;
        double r13411703 = r13411700 * r13411702;
        double r13411704 = t;
        double r13411705 = r13411703 / r13411704;
        double r13411706 = r13411699 + r13411705;
        return r13411706;
}
↓
double f(double x, double y, double z, double t) {
        double r13411707 = x;
        double r13411708 = z;
        double r13411709 = r13411708 - r13411707;
        double r13411710 = y;
        double r13411711 = r13411709 * r13411710;
        double r13411712 = t;
        double r13411713 = r13411711 / r13411712;
        double r13411714 = r13411707 + r13411713;
        double r13411715 = -4.01524276071732e+305;
        bool r13411716 = r13411714 <= r13411715;
        double r13411717 = r13411712 / r13411709;
        double r13411718 = r13411710 / r13411717;
        double r13411719 = r13411707 + r13411718;
        double r13411720 = 2.0380978479863463e+304;
        bool r13411721 = r13411714 <= r13411720;
        double r13411722 = r13411721 ? r13411714 : r13411719;
        double r13411723 = r13411716 ? r13411719 : r13411722;
        return r13411723;
}

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
Target2.1
Herbie0.9
\[x - \left(x \cdot \frac{y}{t} + \left(-z\right) \cdot \frac{y}{t}\right)\]

Derivation

  1. Split input into 2 regimes

  2. if (+ x (/ (* y (- z x)) t)) < -4.01524276071732e+305 or 2.0380978479863463e+304 < (+ x (/ (* y (- z x)) t))

    1. Initial program 60.1

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

    3. Applied associate-/l*1.3

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

    if -4.01524276071732e+305 < (+ x (/ (* y (- z x)) t)) < 2.0380978479863463e+304

    1. Initial program 0.8

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

  4. Final simplification0.9

    \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{\left(z - x\right) \cdot y}{t} \le -4.015242760717319860347263184406053785305 \cdot 10^{305}:\\ \;\;\;\;x + \frac{y}{\frac{t}{z - x}}\\ \mathbf{elif}\;x + \frac{\left(z - x\right) \cdot y}{t} \le 2.038097847986346269413799617144504707187 \cdot 10^{304}:\\ \;\;\;\;x + \frac{\left(z - x\right) \cdot y}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{t}{z - x}}\\ \end{array}\]

Reproduce

herbie shell --seed 2019172 +o rules:numerics
(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)))