Average Error: 9.8 → 0.2
Time: 18.8s
Precision: 64
\[x + \frac{y \cdot \left(z - t\right)}{a - t}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{\left(z - t\right) \cdot y}{a - t} = -\infty:\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{a - t} + x\\ \mathbf{elif}\;\frac{\left(z - t\right) \cdot y}{a - t} \le 3.5979176886514064 \cdot 10^{+307}:\\ \;\;\;\;\frac{\left(z - t\right) \cdot y}{a - t} + x\\ \mathbf{else}:\\ \;\;\;\;\frac{z - t}{\frac{a - t}{y}} + x\\ \end{array}\]
x + \frac{y \cdot \left(z - t\right)}{a - t}
↓
\begin{array}{l}
\mathbf{if}\;\frac{\left(z - t\right) \cdot y}{a - t} = -\infty:\\
\;\;\;\;\left(z - t\right) \cdot \frac{y}{a - t} + x\\

\mathbf{elif}\;\frac{\left(z - t\right) \cdot y}{a - t} \le 3.5979176886514064 \cdot 10^{+307}:\\
\;\;\;\;\frac{\left(z - t\right) \cdot y}{a - t} + x\\

\mathbf{else}:\\
\;\;\;\;\frac{z - t}{\frac{a - t}{y}} + x\\

\end{array}
double f(double x, double y, double z, double t, double a) {
        double r29847353 = x;
        double r29847354 = y;
        double r29847355 = z;
        double r29847356 = t;
        double r29847357 = r29847355 - r29847356;
        double r29847358 = r29847354 * r29847357;
        double r29847359 = a;
        double r29847360 = r29847359 - r29847356;
        double r29847361 = r29847358 / r29847360;
        double r29847362 = r29847353 + r29847361;
        return r29847362;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r29847363 = z;
        double r29847364 = t;
        double r29847365 = r29847363 - r29847364;
        double r29847366 = y;
        double r29847367 = r29847365 * r29847366;
        double r29847368 = a;
        double r29847369 = r29847368 - r29847364;
        double r29847370 = r29847367 / r29847369;
        double r29847371 = -inf.0;
        bool r29847372 = r29847370 <= r29847371;
        double r29847373 = r29847366 / r29847369;
        double r29847374 = r29847365 * r29847373;
        double r29847375 = x;
        double r29847376 = r29847374 + r29847375;
        double r29847377 = 3.5979176886514064e+307;
        bool r29847378 = r29847370 <= r29847377;
        double r29847379 = r29847370 + r29847375;
        double r29847380 = r29847369 / r29847366;
        double r29847381 = r29847365 / r29847380;
        double r29847382 = r29847381 + r29847375;
        double r29847383 = r29847378 ? r29847379 : r29847382;
        double r29847384 = r29847372 ? r29847376 : r29847383;
        return r29847384;
}

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

Original9.8
Target1.2
Herbie0.2
\[x + \frac{y}{\frac{a - t}{z - t}}\]

Derivation

  1. Split input into 3 regimes

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

    1. Initial program 60.2

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

    3. Applied *-un-lft-identity60.2

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

    4. Applied *-commutative60.2

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

    5. Applied times-frac0.1

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

    6. Simplified0.1

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

    if -inf.0 < (/ (* y (- z t)) (- a t)) < 3.5979176886514064e+307

    1. Initial program 0.2

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

    if 3.5979176886514064e+307 < (/ (* y (- z t)) (- a t))

    1. Initial program 60.2

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

    3. Applied *-commutative60.2

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

    4. Applied associate-/l*0.2

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

  4. Final simplification0.2

    \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(z - t\right) \cdot y}{a - t} = -\infty:\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{a - t} + x\\ \mathbf{elif}\;\frac{\left(z - t\right) \cdot y}{a - t} \le 3.5979176886514064 \cdot 10^{+307}:\\ \;\;\;\;\frac{\left(z - t\right) \cdot y}{a - t} + x\\ \mathbf{else}:\\ \;\;\;\;\frac{z - t}{\frac{a - t}{y}} + x\\ \end{array}\]

Reproduce

herbie shell --seed 2019158 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTicks from plot-0.2.3.4, B"

  :herbie-target
  (+ x (/ y (/ (- a t) (- z t))))

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