Average Error: 11.2 → 0.4
Time: 45.7s
Precision: 64
\[x + \frac{\left(y - z\right) \cdot t}{a - z}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{\left(y - z\right) \cdot t}{a - z} = -\infty:\\ \;\;\;\;x + \frac{y - z}{a - z} \cdot t\\ \mathbf{elif}\;\frac{\left(y - z\right) \cdot t}{a - z} \le 8.192139118797283256652162858391000098475 \cdot 10^{276}:\\ \;\;\;\;\frac{\left(y - z\right) \cdot t}{a - z} + x\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - z}{a - z} \cdot t\\ \end{array}\]
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}{a - z} \cdot t\\

\mathbf{elif}\;\frac{\left(y - z\right) \cdot t}{a - z} \le 8.192139118797283256652162858391000098475 \cdot 10^{276}:\\
\;\;\;\;\frac{\left(y - z\right) \cdot t}{a - z} + x\\

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

\end{array}
double f(double x, double y, double z, double t, double a) {
        double r22528431 = x;
        double r22528432 = y;
        double r22528433 = z;
        double r22528434 = r22528432 - r22528433;
        double r22528435 = t;
        double r22528436 = r22528434 * r22528435;
        double r22528437 = a;
        double r22528438 = r22528437 - r22528433;
        double r22528439 = r22528436 / r22528438;
        double r22528440 = r22528431 + r22528439;
        return r22528440;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r22528441 = y;
        double r22528442 = z;
        double r22528443 = r22528441 - r22528442;
        double r22528444 = t;
        double r22528445 = r22528443 * r22528444;
        double r22528446 = a;
        double r22528447 = r22528446 - r22528442;
        double r22528448 = r22528445 / r22528447;
        double r22528449 = -inf.0;
        bool r22528450 = r22528448 <= r22528449;
        double r22528451 = x;
        double r22528452 = r22528443 / r22528447;
        double r22528453 = r22528452 * r22528444;
        double r22528454 = r22528451 + r22528453;
        double r22528455 = 8.192139118797283e+276;
        bool r22528456 = r22528448 <= r22528455;
        double r22528457 = r22528448 + r22528451;
        double r22528458 = r22528456 ? r22528457 : r22528454;
        double r22528459 = r22528450 ? r22528454 : r22528458;
        return r22528459;
}

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

Original11.2
Target0.6
Herbie0.4
\[\begin{array}{l} \mathbf{if}\;t \lt -1.068297449017406694366747246993994850729 \cdot 10^{-39}:\\ \;\;\;\;x + \frac{y - z}{a - z} \cdot t\\ \mathbf{elif}\;t \lt 3.911094988758637497591020599238553861375 \cdot 10^{-141}:\\ \;\;\;\;x + \frac{\left(y - z\right) \cdot t}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - z}{a - z} \cdot t\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if (/ (* (- y z) t) (- a z)) < -inf.0 or 8.192139118797283e+276 < (/ (* (- y z) t) (- a z))

    1. Initial program 61.4

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

    2. Simplified0.6

      \[\leadsto \color{blue}{\mathsf{fma}\left(t, \frac{y - z}{a - z}, x\right)}\]
    3. Using strategy rm

    4. Applied fma-udef0.6

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

    if -inf.0 < (/ (* (- y z) t) (- a z)) < 8.192139118797283e+276

    1. Initial program 0.3

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

  4. Final simplification0.4

    \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(y - z\right) \cdot t}{a - z} = -\infty:\\ \;\;\;\;x + \frac{y - z}{a - z} \cdot t\\ \mathbf{elif}\;\frac{\left(y - z\right) \cdot t}{a - z} \le 8.192139118797283256652162858391000098475 \cdot 10^{276}:\\ \;\;\;\;\frac{\left(y - z\right) \cdot t}{a - z} + x\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - z}{a - z} \cdot t\\ \end{array}\]

Reproduce

herbie shell --seed 2019168 +o rules:numerics
(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))))