Average Error: 11.1 → 1.1
Time: 15.7s
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 r804085 = x;
        double r804086 = y;
        double r804087 = z;
        double r804088 = t;
        double r804089 = r804087 - r804088;
        double r804090 = r804086 * r804089;
        double r804091 = a;
        double r804092 = r804087 - r804091;
        double r804093 = r804090 / r804092;
        double r804094 = r804085 + r804093;
        return r804094;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r804095 = x;
        double r804096 = y;
        double r804097 = z;
        double r804098 = a;
        double r804099 = r804097 - r804098;
        double r804100 = t;
        double r804101 = r804097 - r804100;
        double r804102 = r804099 / r804101;
        double r804103 = r804096 / r804102;
        double r804104 = r804095 + r804103;
        return r804104;
}

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

Original11.1
Target1.1
Herbie1.1
\[x + \frac{y}{\frac{z - a}{z - t}}\]

Derivation

  1. Initial program 11.1

    \[x + \frac{y \cdot \left(z - t\right)}{z - a}\]
  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 2019305 +o rules:numerics
(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))))