Average Error: 10.6 → 1.3
Time: 12.4s
Precision: 64
\[x + \frac{y \cdot \left(z - t\right)}{z - a}\]
↓
\[x + y \cdot \frac{z - t}{z - a}\]
x + \frac{y \cdot \left(z - t\right)}{z - a}
↓
x + y \cdot \frac{z - t}{z - a}
double f(double x, double y, double z, double t, double a) {
        double r382909 = x;
        double r382910 = y;
        double r382911 = z;
        double r382912 = t;
        double r382913 = r382911 - r382912;
        double r382914 = r382910 * r382913;
        double r382915 = a;
        double r382916 = r382911 - r382915;
        double r382917 = r382914 / r382916;
        double r382918 = r382909 + r382917;
        return r382918;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r382919 = x;
        double r382920 = y;
        double r382921 = z;
        double r382922 = t;
        double r382923 = r382921 - r382922;
        double r382924 = a;
        double r382925 = r382921 - r382924;
        double r382926 = r382923 / r382925;
        double r382927 = r382920 * r382926;
        double r382928 = r382919 + r382927;
        return r382928;
}

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

Original10.6
Target1.2
Herbie1.3
\[x + \frac{y}{\frac{z - a}{z - t}}\]

Derivation

  1. Split input into 2 regimes

  2. if y < -6.366002923159597e-72 or 1.0253879521988147e-19 < y

    1. Initial program 19.6

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

    3. Applied *-un-lft-identity19.6

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

    4. Applied times-frac0.6

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

    5. Simplified0.6

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

    if -6.366002923159597e-72 < y < 1.0253879521988147e-19

    1. Initial program 0.4

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

    3. Applied div-inv0.4

      \[\leadsto x + \color{blue}{\left(y \cdot \left(z - t\right)\right) \cdot \frac{1}{z - a}}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification1.3

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

Reproduce

herbie shell --seed 2019291 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTicks from plot-0.2.3.4, A"
  :precision binary64

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

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