Average Error: 1.3 → 1.3
Time: 4.1s
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 r566127 = x;
        double r566128 = y;
        double r566129 = z;
        double r566130 = t;
        double r566131 = r566129 - r566130;
        double r566132 = a;
        double r566133 = r566129 - r566132;
        double r566134 = r566131 / r566133;
        double r566135 = r566128 * r566134;
        double r566136 = r566127 + r566135;
        return r566136;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r566137 = x;
        double r566138 = y;
        double r566139 = z;
        double r566140 = a;
        double r566141 = r566139 - r566140;
        double r566142 = r566139 / r566141;
        double r566143 = t;
        double r566144 = r566143 / r566141;
        double r566145 = r566142 - r566144;
        double r566146 = r566138 * r566145;
        double r566147 = r566137 + r566146;
        return r566147;
}

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

Original1.3
Target1.2
Herbie1.3
\[x + \frac{y}{\frac{z - a}{z - t}}\]

Derivation

  1. Initial program 1.3

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

  3. Applied div-sub1.3

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

  4. Final simplification1.3

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

Reproduce

herbie shell --seed 2020047 
(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)))))