Average Error: 6.2 → 0.8
Time: 27.5s
Precision: 64
\[x + \frac{y \cdot \left(z - x\right)}{t}\]
↓
\[\begin{array}{l} \mathbf{if}\;x + \frac{y \cdot \left(z - x\right)}{t} \le -3.57164337169283755 \cdot 10^{297}:\\ \;\;\;\;\frac{z - x}{\frac{t}{y}} + x\\ \mathbf{elif}\;x + \frac{y \cdot \left(z - x\right)}{t} \le 1.83014942255142419 \cdot 10^{297}:\\ \;\;\;\;x + \frac{y \cdot \left(z - x\right)}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{t}{z - x}} + x\\ \end{array}\]
x + \frac{y \cdot \left(z - x\right)}{t}
↓
\begin{array}{l}
\mathbf{if}\;x + \frac{y \cdot \left(z - x\right)}{t} \le -3.57164337169283755 \cdot 10^{297}:\\
\;\;\;\;\frac{z - x}{\frac{t}{y}} + x\\

\mathbf{elif}\;x + \frac{y \cdot \left(z - x\right)}{t} \le 1.83014942255142419 \cdot 10^{297}:\\
\;\;\;\;x + \frac{y \cdot \left(z - x\right)}{t}\\

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

\end{array}
double f(double x, double y, double z, double t) {
        double r429271 = x;
        double r429272 = y;
        double r429273 = z;
        double r429274 = r429273 - r429271;
        double r429275 = r429272 * r429274;
        double r429276 = t;
        double r429277 = r429275 / r429276;
        double r429278 = r429271 + r429277;
        return r429278;
}
↓
double f(double x, double y, double z, double t) {
        double r429279 = x;
        double r429280 = y;
        double r429281 = z;
        double r429282 = r429281 - r429279;
        double r429283 = r429280 * r429282;
        double r429284 = t;
        double r429285 = r429283 / r429284;
        double r429286 = r429279 + r429285;
        double r429287 = -3.5716433716928375e+297;
        bool r429288 = r429286 <= r429287;
        double r429289 = r429284 / r429280;
        double r429290 = r429282 / r429289;
        double r429291 = r429290 + r429279;
        double r429292 = 1.8301494225514242e+297;
        bool r429293 = r429286 <= r429292;
        double r429294 = r429284 / r429282;
        double r429295 = r429280 / r429294;
        double r429296 = r429295 + r429279;
        double r429297 = r429293 ? r429286 : r429296;
        double r429298 = r429288 ? r429291 : r429297;
        return r429298;
}

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

Original6.2
Target2.0
Herbie0.8
\[x - \left(x \cdot \frac{y}{t} + \left(-z\right) \cdot \frac{y}{t}\right)\]

Derivation

  1. Split input into 3 regimes

  2. if (+ x (/ (* y (- z x)) t)) < -3.5716433716928375e+297

    1. Initial program 51.7

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

    2. Taylor expanded around 0 51.7

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

    3. Simplified1.4

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

    if -3.5716433716928375e+297 < (+ x (/ (* y (- z x)) t)) < 1.8301494225514242e+297

    1. Initial program 0.6

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

    if 1.8301494225514242e+297 < (+ x (/ (* y (- z x)) t))

    1. Initial program 53.1

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

    2. Simplified1.1

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y}{t}, z - x, x\right)}\]
    3. Using strategy rm

    4. Applied fma-udef1.1

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

    5. Simplified3.0

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

  4. Final simplification0.8

    \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{y \cdot \left(z - x\right)}{t} \le -3.57164337169283755 \cdot 10^{297}:\\ \;\;\;\;\frac{z - x}{\frac{t}{y}} + x\\ \mathbf{elif}\;x + \frac{y \cdot \left(z - x\right)}{t} \le 1.83014942255142419 \cdot 10^{297}:\\ \;\;\;\;x + \frac{y \cdot \left(z - x\right)}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{t}{z - x}} + x\\ \end{array}\]

Reproduce

herbie shell --seed 2020046 +o rules:numerics
(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)))