Average Error: 1.2 → 1.2
Time: 12.5s
Precision: 64
\[x + y \cdot \frac{z - t}{z - a}\]
↓
\[x + y \cdot \left(\frac{z}{z - a} - \frac{t}{z - a}\right)\]
x + y \cdot \frac{z - t}{z - a}
↓
x + y \cdot \left(\frac{z}{z - a} - \frac{t}{z - a}\right)
double f(double x, double y, double z, double t, double a) {
        double r473135 = x;
        double r473136 = y;
        double r473137 = z;
        double r473138 = t;
        double r473139 = r473137 - r473138;
        double r473140 = a;
        double r473141 = r473137 - r473140;
        double r473142 = r473139 / r473141;
        double r473143 = r473136 * r473142;
        double r473144 = r473135 + r473143;
        return r473144;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r473145 = x;
        double r473146 = y;
        double r473147 = z;
        double r473148 = a;
        double r473149 = r473147 - r473148;
        double r473150 = r473147 / r473149;
        double r473151 = t;
        double r473152 = r473151 / r473149;
        double r473153 = r473150 - r473152;
        double r473154 = r473146 * r473153;
        double r473155 = r473145 + r473154;
        return r473155;
}

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

Original1.2
Target1.1
Herbie1.2
\[x + \frac{y}{\frac{z - a}{z - t}}\]

Derivation

  1. Initial program 1.2

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

  3. Applied div-sub1.2

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

  4. Final simplification1.2

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

Reproduce

herbie shell --seed 2019212 
(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)))))