Average Error: 10.9 → 0.7
Time: 17.9s
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 r487536 = x;
        double r487537 = y;
        double r487538 = z;
        double r487539 = t;
        double r487540 = r487538 - r487539;
        double r487541 = r487537 * r487540;
        double r487542 = a;
        double r487543 = r487542 - r487539;
        double r487544 = r487541 / r487543;
        double r487545 = r487536 + r487544;
        return r487545;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r487546 = y;
        double r487547 = z;
        double r487548 = t;
        double r487549 = r487547 - r487548;
        double r487550 = r487546 * r487549;
        double r487551 = a;
        double r487552 = r487551 - r487548;
        double r487553 = r487550 / r487552;
        double r487554 = -1.611599144545035e-25;
        bool r487555 = r487553 <= r487554;
        double r487556 = 1.0542580607462433e+299;
        bool r487557 = r487553 <= r487556;
        double r487558 = !r487557;
        bool r487559 = r487555 || r487558;
        double r487560 = r487552 / r487546;
        double r487561 = r487549 / r487560;
        double r487562 = x;
        double r487563 = r487561 + r487562;
        double r487564 = r487562 + r487553;
        double r487565 = r487559 ? r487563 : r487564;
        return r487565;
}

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))))