Average Error: 1.4 → 1.3
Time: 6.1s
Precision: 64
\[x + y \cdot \frac{z - t}{z - a}\]
↓
\[x + \frac{y}{\frac{z - a}{z - t}}\]
x + y \cdot \frac{z - t}{z - a}
↓
x + \frac{y}{\frac{z - a}{z - t}}
double f(double x, double y, double z, double t, double a) {
        double r547512 = x;
        double r547513 = y;
        double r547514 = z;
        double r547515 = t;
        double r547516 = r547514 - r547515;
        double r547517 = a;
        double r547518 = r547514 - r547517;
        double r547519 = r547516 / r547518;
        double r547520 = r547513 * r547519;
        double r547521 = r547512 + r547520;
        return r547521;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r547522 = x;
        double r547523 = y;
        double r547524 = z;
        double r547525 = a;
        double r547526 = r547524 - r547525;
        double r547527 = t;
        double r547528 = r547524 - r547527;
        double r547529 = r547526 / r547528;
        double r547530 = r547523 / r547529;
        double r547531 = r547522 + r547530;
        return r547531;
}

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

Original1.4
Target1.3
Herbie1.3
\[x + \frac{y}{\frac{z - a}{z - t}}\]

Derivation

  1. Initial program 1.4

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

  3. Applied clear-num1.4

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

  5. Applied un-div-inv1.3

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

  6. Final simplification1.3

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

Reproduce

herbie shell --seed 2020039 +o rules:numerics
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisLine from plot-0.2.3.4, A"
  :precision binary64

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

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