Average Error: 6.3 → 0.3
Time: 18.9s
Precision: 64
\[x + \frac{y \cdot \left(z - t\right)}{a}\]
↓
\[\begin{array}{l} \mathbf{if}\;y \cdot \left(z - t\right) = -\infty \lor \neg \left(y \cdot \left(z - t\right) \le 1.647266620191553049675054543994090310004 \cdot 10^{211}\right):\\ \;\;\;\;\frac{z - t}{\frac{a}{y}} + x\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{a}\\ \end{array}\]
x + \frac{y \cdot \left(z - t\right)}{a}
↓
\begin{array}{l}
\mathbf{if}\;y \cdot \left(z - t\right) = -\infty \lor \neg \left(y \cdot \left(z - t\right) \le 1.647266620191553049675054543994090310004 \cdot 10^{211}\right):\\
\;\;\;\;\frac{z - t}{\frac{a}{y}} + x\\

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

\end{array}
double f(double x, double y, double z, double t, double a) {
        double r174293 = x;
        double r174294 = y;
        double r174295 = z;
        double r174296 = t;
        double r174297 = r174295 - r174296;
        double r174298 = r174294 * r174297;
        double r174299 = a;
        double r174300 = r174298 / r174299;
        double r174301 = r174293 + r174300;
        return r174301;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r174302 = y;
        double r174303 = z;
        double r174304 = t;
        double r174305 = r174303 - r174304;
        double r174306 = r174302 * r174305;
        double r174307 = -inf.0;
        bool r174308 = r174306 <= r174307;
        double r174309 = 1.647266620191553e+211;
        bool r174310 = r174306 <= r174309;
        double r174311 = !r174310;
        bool r174312 = r174308 || r174311;
        double r174313 = a;
        double r174314 = r174313 / r174302;
        double r174315 = r174305 / r174314;
        double r174316 = x;
        double r174317 = r174315 + r174316;
        double r174318 = r174306 / r174313;
        double r174319 = r174316 + r174318;
        double r174320 = r174312 ? r174317 : r174319;
        return r174320;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original6.3
Target0.6
Herbie0.3
\[\begin{array}{l} \mathbf{if}\;y \lt -1.07612662163899753216593153715602325729 \cdot 10^{-10}:\\ \;\;\;\;x + \frac{1}{\frac{\frac{a}{z - t}}{y}}\\ \mathbf{elif}\;y \lt 2.894426862792089097262541964056085749132 \cdot 10^{-49}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z - t}}\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if (* y (- z t)) < -inf.0 or 1.647266620191553e+211 < (* y (- z t))

    1. Initial program 41.7

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

    2. Simplified0.3

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

    4. Applied fma-udef0.3

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

    5. Simplified0.3

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

    if -inf.0 < (* y (- z t)) < 1.647266620191553e+211

    1. Initial program 0.3

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

  4. Final simplification0.3

    \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot \left(z - t\right) = -\infty \lor \neg \left(y \cdot \left(z - t\right) \le 1.647266620191553049675054543994090310004 \cdot 10^{211}\right):\\ \;\;\;\;\frac{z - t}{\frac{a}{y}} + x\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{a}\\ \end{array}\]

Reproduce

herbie shell --seed 2019322 +o rules:numerics
(FPCore (x y z t a)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, E"
  :precision binary64

  :herbie-target
  (if (< y -1.0761266216389975e-10) (+ x (/ 1 (/ (/ a (- z t)) y))) (if (< y 2.894426862792089e-49) (+ x (/ (* y (- z t)) a)) (+ x (/ y (/ a (- z t))))))

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