Average Error: 10.8 → 1.3
Time: 10.8s
Precision: 64
\[x + \frac{y \cdot \left(z - t\right)}{z - a}\]
↓
\[x + \frac{y}{\frac{z - a}{z - t}}\]
x + \frac{y \cdot \left(z - t\right)}{z - a}
↓
x + \frac{y}{\frac{z - a}{z - t}}
double f(double x, double y, double z, double t, double a) {
        double r474607 = x;
        double r474608 = y;
        double r474609 = z;
        double r474610 = t;
        double r474611 = r474609 - r474610;
        double r474612 = r474608 * r474611;
        double r474613 = a;
        double r474614 = r474609 - r474613;
        double r474615 = r474612 / r474614;
        double r474616 = r474607 + r474615;
        return r474616;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r474617 = x;
        double r474618 = y;
        double r474619 = z;
        double r474620 = a;
        double r474621 = r474619 - r474620;
        double r474622 = t;
        double r474623 = r474619 - r474622;
        double r474624 = r474621 / r474623;
        double r474625 = r474618 / r474624;
        double r474626 = r474617 + r474625;
        return r474626;
}

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

Original10.8
Target1.3
Herbie1.3
\[x + \frac{y}{\frac{z - a}{z - t}}\]

Derivation

  1. Split input into 2 regimes

  2. if z < -5.1181462442232664e-138 or 2.632670860847324e-173 < z

    1. Initial program 12.8

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

    3. Applied associate-/l*0.6

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

    if -5.1181462442232664e-138 < z < 2.632670860847324e-173

    1. Initial program 3.8

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

    3. Applied associate-/l*3.5

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

    5. Applied clear-num3.6

      \[\leadsto x + \color{blue}{\frac{1}{\frac{\frac{z - a}{z - t}}{y}}}\]
    6. Using strategy rm

    7. Applied *-un-lft-identity3.6

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

    8. Applied div-inv3.6

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

    9. Applied times-frac3.5

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

    10. Applied associate-/r*3.5

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

    11. Simplified3.5

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

  4. Final simplification1.3

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

Reproduce

herbie shell --seed 2019308 
(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))))