Average Error: 10.7 → 1.1
Time: 3.6s
Precision: 64
\[x + \frac{y \cdot \left(z - t\right)}{a - t}\]
↓
\[x + \frac{y}{\frac{a - t}{z - t}}\]
x + \frac{y \cdot \left(z - t\right)}{a - t}
↓
x + \frac{y}{\frac{a - t}{z - t}}
double f(double x, double y, double z, double t, double a) {
        double r518020 = x;
        double r518021 = y;
        double r518022 = z;
        double r518023 = t;
        double r518024 = r518022 - r518023;
        double r518025 = r518021 * r518024;
        double r518026 = a;
        double r518027 = r518026 - r518023;
        double r518028 = r518025 / r518027;
        double r518029 = r518020 + r518028;
        return r518029;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r518030 = x;
        double r518031 = y;
        double r518032 = a;
        double r518033 = t;
        double r518034 = r518032 - r518033;
        double r518035 = z;
        double r518036 = r518035 - r518033;
        double r518037 = r518034 / r518036;
        double r518038 = r518031 / r518037;
        double r518039 = r518030 + r518038;
        return r518039;
}

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

Derivation

  1. Initial program 10.7

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

  3. Applied associate-/l*1.1

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

  4. Final simplification1.1

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

Reproduce

herbie shell --seed 2020064 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTicks from plot-0.2.3.4, B"
  :precision binary64

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

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