Average Error: 10.8 → 0.4
Time: 29.0s
Precision: 64
\[x + \frac{\left(y - z\right) \cdot t}{a - z}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{\left(y - z\right) \cdot t}{a - z} = -\infty:\\ \;\;\;\;x + \frac{y - z}{\frac{a - z}{t}}\\ \mathbf{elif}\;\frac{\left(y - z\right) \cdot t}{a - z} \le 6.22641692113179643 \cdot 10^{275}:\\ \;\;\;\;x + \frac{\left(y - z\right) \cdot t}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t}{a - z}\\ \end{array}\]
x + \frac{\left(y - z\right) \cdot t}{a - z}
↓
\begin{array}{l}
\mathbf{if}\;\frac{\left(y - z\right) \cdot t}{a - z} = -\infty:\\
\;\;\;\;x + \frac{y - z}{\frac{a - z}{t}}\\

\mathbf{elif}\;\frac{\left(y - z\right) \cdot t}{a - z} \le 6.22641692113179643 \cdot 10^{275}:\\
\;\;\;\;x + \frac{\left(y - z\right) \cdot t}{a - z}\\

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

\end{array}
double f(double x, double y, double z, double t, double a) {
        double r408411 = x;
        double r408412 = y;
        double r408413 = z;
        double r408414 = r408412 - r408413;
        double r408415 = t;
        double r408416 = r408414 * r408415;
        double r408417 = a;
        double r408418 = r408417 - r408413;
        double r408419 = r408416 / r408418;
        double r408420 = r408411 + r408419;
        return r408420;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r408421 = y;
        double r408422 = z;
        double r408423 = r408421 - r408422;
        double r408424 = t;
        double r408425 = r408423 * r408424;
        double r408426 = a;
        double r408427 = r408426 - r408422;
        double r408428 = r408425 / r408427;
        double r408429 = -inf.0;
        bool r408430 = r408428 <= r408429;
        double r408431 = x;
        double r408432 = r408427 / r408424;
        double r408433 = r408423 / r408432;
        double r408434 = r408431 + r408433;
        double r408435 = 6.226416921131796e+275;
        bool r408436 = r408428 <= r408435;
        double r408437 = r408431 + r408428;
        double r408438 = r408424 / r408427;
        double r408439 = r408423 * r408438;
        double r408440 = r408431 + r408439;
        double r408441 = r408436 ? r408437 : r408440;
        double r408442 = r408430 ? r408434 : r408441;
        return r408442;
}

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

Original10.8
Target0.6
Herbie0.4
\[\begin{array}{l} \mathbf{if}\;t \lt -1.0682974490174067 \cdot 10^{-39}:\\ \;\;\;\;x + \frac{y - z}{a - z} \cdot t\\ \mathbf{elif}\;t \lt 3.9110949887586375 \cdot 10^{-141}:\\ \;\;\;\;x + \frac{\left(y - z\right) \cdot t}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - z}{a - z} \cdot t\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if (/ (* (- y z) t) (- a z)) < -inf.0

    1. Initial program 64.0

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

    3. Applied associate-/l*0.2

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

    if -inf.0 < (/ (* (- y z) t) (- a z)) < 6.226416921131796e+275

    1. Initial program 0.2

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

    if 6.226416921131796e+275 < (/ (* (- y z) t) (- a z))

    1. Initial program 58.5

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

    3. Applied *-un-lft-identity58.5

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

    4. Applied times-frac1.8

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

    5. Simplified1.8

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

  4. Final simplification0.4

    \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(y - z\right) \cdot t}{a - z} = -\infty:\\ \;\;\;\;x + \frac{y - z}{\frac{a - z}{t}}\\ \mathbf{elif}\;\frac{\left(y - z\right) \cdot t}{a - z} \le 6.22641692113179643 \cdot 10^{275}:\\ \;\;\;\;x + \frac{\left(y - z\right) \cdot t}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t}{a - z}\\ \end{array}\]

Reproduce

herbie shell --seed 2019199 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTick from plot-0.2.3.4, A"

  :herbie-target
  (if (< t -1.0682974490174067e-39) (+ x (* (/ (- y z) (- a z)) t)) (if (< t 3.9110949887586375e-141) (+ x (/ (* (- y z) t) (- a z))) (+ x (* (/ (- y z) (- a z)) t))))

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