Average Error: 10.9 → 0.7
Time: 16.2s
Precision: 64
\[x + \frac{y \cdot \left(z - t\right)}{a - t}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(z - t\right)}{a - t} \le -1.611599144545034992288746807936135012432 \cdot 10^{-25} \lor \neg \left(\frac{y \cdot \left(z - t\right)}{a - t} \le 1.054258060746243275263708971660933948259 \cdot 10^{299}\right):\\ \;\;\;\;\frac{z - t}{\frac{a - t}{y}} + x\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{a - t}\\ \end{array}\]
x + \frac{y \cdot \left(z - t\right)}{a - t}
↓
\begin{array}{l}
\mathbf{if}\;\frac{y \cdot \left(z - t\right)}{a - t} \le -1.611599144545034992288746807936135012432 \cdot 10^{-25} \lor \neg \left(\frac{y \cdot \left(z - t\right)}{a - t} \le 1.054258060746243275263708971660933948259 \cdot 10^{299}\right):\\
\;\;\;\;\frac{z - t}{\frac{a - t}{y}} + x\\

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

\end{array}
double f(double x, double y, double z, double t, double a) {
        double r384265 = x;
        double r384266 = y;
        double r384267 = z;
        double r384268 = t;
        double r384269 = r384267 - r384268;
        double r384270 = r384266 * r384269;
        double r384271 = a;
        double r384272 = r384271 - r384268;
        double r384273 = r384270 / r384272;
        double r384274 = r384265 + r384273;
        return r384274;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r384275 = y;
        double r384276 = z;
        double r384277 = t;
        double r384278 = r384276 - r384277;
        double r384279 = r384275 * r384278;
        double r384280 = a;
        double r384281 = r384280 - r384277;
        double r384282 = r384279 / r384281;
        double r384283 = -1.611599144545035e-25;
        bool r384284 = r384282 <= r384283;
        double r384285 = 1.0542580607462433e+299;
        bool r384286 = r384282 <= r384285;
        double r384287 = !r384286;
        bool r384288 = r384284 || r384287;
        double r384289 = r384281 / r384275;
        double r384290 = r384278 / r384289;
        double r384291 = x;
        double r384292 = r384290 + r384291;
        double r384293 = r384291 + r384282;
        double r384294 = r384288 ? r384292 : r384293;
        return r384294;
}

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

Original10.9
Target1.3
Herbie0.7
\[x + \frac{y}{\frac{a - t}{z - t}}\]

Derivation

  1. Split input into 2 regimes

  2. if (/ (* y (- z t)) (- a t)) < -1.611599144545035e-25 or 1.0542580607462433e+299 < (/ (* y (- z t)) (- a t))

    1. Initial program 32.2

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

    2. Simplified1.8

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

    4. Applied clear-num1.9

      \[\leadsto \mathsf{fma}\left(\color{blue}{\frac{1}{\frac{a - t}{y}}}, z - t, x\right)\]
    5. Using strategy rm

    6. Applied fma-udef1.9

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

    7. Simplified1.7

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

    if -1.611599144545035e-25 < (/ (* y (- z t)) (- a t)) < 1.0542580607462433e+299

    1. Initial program 0.2

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

  4. Final simplification0.7

    \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(z - t\right)}{a - t} \le -1.611599144545034992288746807936135012432 \cdot 10^{-25} \lor \neg \left(\frac{y \cdot \left(z - t\right)}{a - t} \le 1.054258060746243275263708971660933948259 \cdot 10^{299}\right):\\ \;\;\;\;\frac{z - t}{\frac{a - t}{y}} + x\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{a - t}\\ \end{array}\]

Reproduce

herbie shell --seed 2019323 +o rules:numerics
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTicks from plot-0.2.3.4, B"
  :precision binary64

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

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