Average Error: 10.7 → 10.7
Time: 16.3s
Precision: 64
\[x + \frac{\left(y - z\right) \cdot t}{a - z}\]
↓
\[x + \frac{\left(y - z\right) \cdot t}{a - z}\]
x + \frac{\left(y - z\right) \cdot t}{a - z}
↓
x + \frac{\left(y - z\right) \cdot t}{a - z}
double f(double x, double y, double z, double t, double a) {
        double r518434 = x;
        double r518435 = y;
        double r518436 = z;
        double r518437 = r518435 - r518436;
        double r518438 = t;
        double r518439 = r518437 * r518438;
        double r518440 = a;
        double r518441 = r518440 - r518436;
        double r518442 = r518439 / r518441;
        double r518443 = r518434 + r518442;
        return r518443;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r518444 = x;
        double r518445 = y;
        double r518446 = z;
        double r518447 = r518445 - r518446;
        double r518448 = t;
        double r518449 = r518447 * r518448;
        double r518450 = a;
        double r518451 = r518450 - r518446;
        double r518452 = r518449 / r518451;
        double r518453 = r518444 + r518452;
        return r518453;
}

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

Original10.7
Target0.6
Herbie10.7
\[\begin{array}{l} \mathbf{if}\;t \lt -1.068297449017406694366747246993994850729 \cdot 10^{-39}:\\ \;\;\;\;x + \frac{y - z}{a - z} \cdot t\\ \mathbf{elif}\;t \lt 3.911094988758637497591020599238553861375 \cdot 10^{-141}:\\ \;\;\;\;x + \frac{\left(y - z\right) \cdot t}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - z}{a - z} \cdot t\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if (/ (* (- y z) t) (- a z)) < -1.8956587618098694e+185 or 1.120015169911997e+307 < (/ (* (- y z) t) (- a z))

    1. Initial program 52.4

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

    3. Applied *-un-lft-identity52.4

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

    4. Applied times-frac2.1

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

    5. Simplified2.1

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

    if -1.8956587618098694e+185 < (/ (* (- y z) t) (- a z)) < 1.120015169911997e+307

    1. Initial program 0.3

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

  4. Final simplification10.7

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

Reproduce

herbie shell --seed 2019297 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTick from plot-0.2.3.4, A"
  :precision binary64

  :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))))