Average Error: 24.2 → 10.4
Time: 9.1s
Precision: 64
\[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\]
↓
\[\begin{array}{l} \mathbf{if}\;a \le -7.3388195415728562 \cdot 10^{-124} \lor \neg \left(a \le 7.6379556270684528 \cdot 10^{-187}\right):\\ \;\;\;\;x + \left(y - x\right) \cdot \left(\left(z - t\right) \cdot \frac{1}{a - t}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y + \frac{x \cdot z}{t}\right) - \frac{z \cdot y}{t}\\ \end{array}\]
x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}
↓
\begin{array}{l}
\mathbf{if}\;a \le -7.3388195415728562 \cdot 10^{-124} \lor \neg \left(a \le 7.6379556270684528 \cdot 10^{-187}\right):\\
\;\;\;\;x + \left(y - x\right) \cdot \left(\left(z - t\right) \cdot \frac{1}{a - t}\right)\\

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

\end{array}
double f(double x, double y, double z, double t, double a) {
        double r686257 = x;
        double r686258 = y;
        double r686259 = r686258 - r686257;
        double r686260 = z;
        double r686261 = t;
        double r686262 = r686260 - r686261;
        double r686263 = r686259 * r686262;
        double r686264 = a;
        double r686265 = r686264 - r686261;
        double r686266 = r686263 / r686265;
        double r686267 = r686257 + r686266;
        return r686267;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r686268 = a;
        double r686269 = -7.338819541572856e-124;
        bool r686270 = r686268 <= r686269;
        double r686271 = 7.637955627068453e-187;
        bool r686272 = r686268 <= r686271;
        double r686273 = !r686272;
        bool r686274 = r686270 || r686273;
        double r686275 = x;
        double r686276 = y;
        double r686277 = r686276 - r686275;
        double r686278 = z;
        double r686279 = t;
        double r686280 = r686278 - r686279;
        double r686281 = 1.0;
        double r686282 = r686268 - r686279;
        double r686283 = r686281 / r686282;
        double r686284 = r686280 * r686283;
        double r686285 = r686277 * r686284;
        double r686286 = r686275 + r686285;
        double r686287 = r686275 * r686278;
        double r686288 = r686287 / r686279;
        double r686289 = r686276 + r686288;
        double r686290 = r686278 * r686276;
        double r686291 = r686290 / r686279;
        double r686292 = r686289 - r686291;
        double r686293 = r686274 ? r686286 : r686292;
        return r686293;
}

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

Original24.2
Target9.2
Herbie10.4
\[\begin{array}{l} \mathbf{if}\;a \lt -1.6153062845442575 \cdot 10^{-142}:\\ \;\;\;\;x + \frac{y - x}{1} \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;a \lt 3.7744031700831742 \cdot 10^{-182}:\\ \;\;\;\;y - \frac{z}{t} \cdot \left(y - x\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{1} \cdot \frac{z - t}{a - t}\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if a < -7.338819541572856e-124 or 7.637955627068453e-187 < a

    1. Initial program 22.6

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

    3. Applied *-un-lft-identity22.6

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

    4. Applied times-frac9.4

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

    5. Simplified9.4

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

    7. Applied div-inv9.5

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

    if -7.338819541572856e-124 < a < 7.637955627068453e-187

    1. Initial program 30.1

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

    2. Taylor expanded around inf 13.8

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

  4. Final simplification10.4

    \[\leadsto \begin{array}{l} \mathbf{if}\;a \le -7.3388195415728562 \cdot 10^{-124} \lor \neg \left(a \le 7.6379556270684528 \cdot 10^{-187}\right):\\ \;\;\;\;x + \left(y - x\right) \cdot \left(\left(z - t\right) \cdot \frac{1}{a - t}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y + \frac{x \cdot z}{t}\right) - \frac{z \cdot y}{t}\\ \end{array}\]

Reproduce

herbie shell --seed 2020034 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Chart.Axis.Types:linMap from Chart-1.5.3"
  :precision binary64

  :herbie-target
  (if (< a -1.6153062845442575e-142) (+ x (* (/ (- y x) 1) (/ (- z t) (- a t)))) (if (< a 3.774403170083174e-182) (- y (* (/ z t) (- y x))) (+ x (* (/ (- y x) 1) (/ (- z t) (- a t))))))

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