Average Error: 24.4 → 10.4
Time: 8.2s
Precision: 64
\[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\]
↓
\[\begin{array}{l} \mathbf{if}\;a \le -2.766011212036650170966031009633619175096 \cdot 10^{-223} \lor \neg \left(a \le 2.631683075691333687052658508933688075174 \cdot 10^{-195}\right):\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;\left(y + \frac{x \cdot z}{t}\right) - \frac{z \cdot y}{t}\\ \end{array}\]
x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}
↓
\begin{array}{l}
\mathbf{if}\;a \le -2.766011212036650170966031009633619175096 \cdot 10^{-223} \lor \neg \left(a \le 2.631683075691333687052658508933688075174 \cdot 10^{-195}\right):\\
\;\;\;\;x + \left(y - x\right) \cdot \frac{z - t}{a - t}\\

\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 r700827 = x;
        double r700828 = y;
        double r700829 = r700828 - r700827;
        double r700830 = z;
        double r700831 = t;
        double r700832 = r700830 - r700831;
        double r700833 = r700829 * r700832;
        double r700834 = a;
        double r700835 = r700834 - r700831;
        double r700836 = r700833 / r700835;
        double r700837 = r700827 + r700836;
        return r700837;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r700838 = a;
        double r700839 = -2.76601121203665e-223;
        bool r700840 = r700838 <= r700839;
        double r700841 = 2.6316830756913337e-195;
        bool r700842 = r700838 <= r700841;
        double r700843 = !r700842;
        bool r700844 = r700840 || r700843;
        double r700845 = x;
        double r700846 = y;
        double r700847 = r700846 - r700845;
        double r700848 = z;
        double r700849 = t;
        double r700850 = r700848 - r700849;
        double r700851 = r700838 - r700849;
        double r700852 = r700850 / r700851;
        double r700853 = r700847 * r700852;
        double r700854 = r700845 + r700853;
        double r700855 = r700845 * r700848;
        double r700856 = r700855 / r700849;
        double r700857 = r700846 + r700856;
        double r700858 = r700848 * r700846;
        double r700859 = r700858 / r700849;
        double r700860 = r700857 - r700859;
        double r700861 = r700844 ? r700854 : r700860;
        return r700861;
}

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

Original24.4
Target9.1
Herbie10.4
\[\begin{array}{l} \mathbf{if}\;a \lt -1.615306284544257464183904494091872805513 \cdot 10^{-142}:\\ \;\;\;\;x + \frac{y - x}{1} \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;a \lt 3.774403170083174201868024161554637965035 \cdot 10^{-182}:\\ \;\;\;\;y - \frac{z}{t} \cdot \left(y - x\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{1} \cdot \frac{z - t}{a - t}\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if a < -2.76601121203665e-223 or 2.6316830756913337e-195 < a

    1. Initial program 23.6

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

    3. Applied *-un-lft-identity23.6

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

    4. Applied times-frac10.5

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

    5. Simplified10.5

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

    if -2.76601121203665e-223 < a < 2.6316830756913337e-195

    1. Initial program 29.5

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

    2. Taylor expanded around inf 10.0

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

  4. Final simplification10.4

    \[\leadsto \begin{array}{l} \mathbf{if}\;a \le -2.766011212036650170966031009633619175096 \cdot 10^{-223} \lor \neg \left(a \le 2.631683075691333687052658508933688075174 \cdot 10^{-195}\right):\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;\left(y + \frac{x \cdot z}{t}\right) - \frac{z \cdot y}{t}\\ \end{array}\]

Reproduce

herbie shell --seed 2019354 
(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))))