Average Error: 10.9 → 1.1
Time: 11.6s
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 r451530 = x;
        double r451531 = y;
        double r451532 = z;
        double r451533 = t;
        double r451534 = r451532 - r451533;
        double r451535 = r451531 * r451534;
        double r451536 = a;
        double r451537 = r451532 - r451536;
        double r451538 = r451535 / r451537;
        double r451539 = r451530 + r451538;
        return r451539;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r451540 = x;
        double r451541 = y;
        double r451542 = z;
        double r451543 = a;
        double r451544 = r451542 - r451543;
        double r451545 = t;
        double r451546 = r451542 - r451545;
        double r451547 = r451544 / r451546;
        double r451548 = r451541 / r451547;
        double r451549 = r451540 + r451548;
        return r451549;
}

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

Original10.9
Target1.1
Herbie1.1
\[x + \frac{y}{\frac{z - a}{z - t}}\]

Derivation

  1. Initial program 10.9

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

  3. Applied associate-/l*1.1

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

  4. Final simplification1.1

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

Reproduce

herbie shell --seed 2020046 
(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))))