Average Error: 10.7 → 10.7
Time: 14.4s
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 r549873 = x;
        double r549874 = y;
        double r549875 = z;
        double r549876 = r549874 - r549875;
        double r549877 = t;
        double r549878 = r549876 * r549877;
        double r549879 = a;
        double r549880 = r549879 - r549875;
        double r549881 = r549878 / r549880;
        double r549882 = r549873 + r549881;
        return r549882;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r549883 = x;
        double r549884 = y;
        double r549885 = z;
        double r549886 = r549884 - r549885;
        double r549887 = t;
        double r549888 = r549886 * r549887;
        double r549889 = a;
        double r549890 = r549889 - r549885;
        double r549891 = r549888 / r549890;
        double r549892 = r549883 + r549891;
        return r549892;
}

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
Target0.7
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 3 regimes

  2. if (/ (* (- y z) t) (- a z)) < -3.6042496369238863e+224

    1. Initial program 50.1

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

    3. Applied associate-/l*3.3

      \[\leadsto x + \color{blue}{\frac{y - z}{\frac{a - z}{t}}}\]
    4. Using strategy rm

    5. Applied associate-/r/2.6

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

    if -3.6042496369238863e+224 < (/ (* (- y z) t) (- a z)) < 5.869543805125872e+296

    1. Initial program 0.3

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

    if 5.869543805125872e+296 < (/ (* (- y z) t) (- a z))

    1. Initial program 61.6

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

    3. Applied associate-/l*0.9

      \[\leadsto x + \color{blue}{\frac{y - z}{\frac{a - z}{t}}}\]
    4. Using strategy rm

    5. Applied clear-num1.0

      \[\leadsto x + \color{blue}{\frac{1}{\frac{\frac{a - z}{t}}{y - z}}}\]
  3. Recombined 3 regimes into one program.

  4. Final simplification10.7

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

Reproduce

herbie shell --seed 2019291 
(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))))