Average Error: 1.4 → 0.6
Time: 5.0s
Precision: 64
\[x + y \cdot \frac{z - t}{a - t}\]
↓
\[\begin{array}{l} \mathbf{if}\;y \le -7.0414149412589552 \cdot 10^{-65} \lor \neg \left(y \le 3.45403338259661 \cdot 10^{-167}\right):\\ \;\;\;\;x + \frac{y}{\frac{a - t}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;x + \left(y \cdot \left(z - t\right)\right) \cdot \frac{1}{a - t}\\ \end{array}\]
x + y \cdot \frac{z - t}{a - t}
↓
\begin{array}{l}
\mathbf{if}\;y \le -7.0414149412589552 \cdot 10^{-65} \lor \neg \left(y \le 3.45403338259661 \cdot 10^{-167}\right):\\
\;\;\;\;x + \frac{y}{\frac{a - t}{z - t}}\\

\mathbf{else}:\\
\;\;\;\;x + \left(y \cdot \left(z - t\right)\right) \cdot \frac{1}{a - t}\\

\end{array}
double f(double x, double y, double z, double t, double a) {
        double r699250 = x;
        double r699251 = y;
        double r699252 = z;
        double r699253 = t;
        double r699254 = r699252 - r699253;
        double r699255 = a;
        double r699256 = r699255 - r699253;
        double r699257 = r699254 / r699256;
        double r699258 = r699251 * r699257;
        double r699259 = r699250 + r699258;
        return r699259;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r699260 = y;
        double r699261 = -7.041414941258955e-65;
        bool r699262 = r699260 <= r699261;
        double r699263 = 3.45403338259661e-167;
        bool r699264 = r699260 <= r699263;
        double r699265 = !r699264;
        bool r699266 = r699262 || r699265;
        double r699267 = x;
        double r699268 = a;
        double r699269 = t;
        double r699270 = r699268 - r699269;
        double r699271 = z;
        double r699272 = r699271 - r699269;
        double r699273 = r699270 / r699272;
        double r699274 = r699260 / r699273;
        double r699275 = r699267 + r699274;
        double r699276 = r699260 * r699272;
        double r699277 = 1.0;
        double r699278 = r699277 / r699270;
        double r699279 = r699276 * r699278;
        double r699280 = r699267 + r699279;
        double r699281 = r699266 ? r699275 : r699280;
        return r699281;
}

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

Original1.4
Target0.4
Herbie0.6
\[\begin{array}{l} \mathbf{if}\;y \lt -8.50808486055124107 \cdot 10^{-17}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;y \lt 2.8944268627920891 \cdot 10^{-49}:\\ \;\;\;\;x + \left(y \cdot \left(z - t\right)\right) \cdot \frac{1}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a - t}\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if y < -7.041414941258955e-65 or 3.45403338259661e-167 < y

    1. Initial program 0.8

      \[x + y \cdot \frac{z - t}{a - t}\]
    2. Using strategy rm

    3. Applied clear-num0.8

      \[\leadsto x + y \cdot \color{blue}{\frac{1}{\frac{a - t}{z - t}}}\]
    4. Using strategy rm

    5. Applied un-div-inv0.7

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

    if -7.041414941258955e-65 < y < 3.45403338259661e-167

    1. Initial program 2.7

      \[x + y \cdot \frac{z - t}{a - t}\]
    2. Using strategy rm

    3. Applied div-inv2.7

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

    4. Applied associate-*r*0.3

      \[\leadsto x + \color{blue}{\left(y \cdot \left(z - t\right)\right) \cdot \frac{1}{a - t}}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification0.6

    \[\leadsto \begin{array}{l} \mathbf{if}\;y \le -7.0414149412589552 \cdot 10^{-65} \lor \neg \left(y \le 3.45403338259661 \cdot 10^{-167}\right):\\ \;\;\;\;x + \frac{y}{\frac{a - t}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;x + \left(y \cdot \left(z - t\right)\right) \cdot \frac{1}{a - t}\\ \end{array}\]

Reproduce

herbie shell --seed 2020027 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisLine from plot-0.2.3.4, B"
  :precision binary64

  :herbie-target
  (if (< y -8.508084860551241e-17) (+ x (* y (/ (- z t) (- a t)))) (if (< y 2.894426862792089e-49) (+ x (* (* y (- z t)) (/ 1 (- a t)))) (+ x (* y (/ (- z t) (- a t))))))

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