Average Error: 9.9 → 1.1
Time: 17.6s
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 r29302137 = x;
        double r29302138 = y;
        double r29302139 = z;
        double r29302140 = t;
        double r29302141 = r29302139 - r29302140;
        double r29302142 = r29302138 * r29302141;
        double r29302143 = a;
        double r29302144 = r29302139 - r29302143;
        double r29302145 = r29302142 / r29302144;
        double r29302146 = r29302137 + r29302145;
        return r29302146;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r29302147 = x;
        double r29302148 = y;
        double r29302149 = z;
        double r29302150 = a;
        double r29302151 = r29302149 - r29302150;
        double r29302152 = t;
        double r29302153 = r29302149 - r29302152;
        double r29302154 = r29302151 / r29302153;
        double r29302155 = r29302148 / r29302154;
        double r29302156 = r29302147 + r29302155;
        return r29302156;
}

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

Original9.9
Target1.1
Herbie1.1
\[x + \frac{y}{\frac{z - a}{z - t}}\]

Derivation

  1. Initial program 9.9

    \[x + \frac{y \cdot \left(z - t\right)}{z - a}\]
  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 2019158 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTicks from plot-0.2.3.4, A"

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

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