Average Error: 10.9 → 1.3
Time: 19.2s
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 r32213151 = x;
        double r32213152 = y;
        double r32213153 = z;
        double r32213154 = t;
        double r32213155 = r32213153 - r32213154;
        double r32213156 = r32213152 * r32213155;
        double r32213157 = a;
        double r32213158 = r32213153 - r32213157;
        double r32213159 = r32213156 / r32213158;
        double r32213160 = r32213151 + r32213159;
        return r32213160;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r32213161 = x;
        double r32213162 = y;
        double r32213163 = z;
        double r32213164 = a;
        double r32213165 = r32213163 - r32213164;
        double r32213166 = t;
        double r32213167 = r32213163 - r32213166;
        double r32213168 = r32213165 / r32213167;
        double r32213169 = r32213162 / r32213168;
        double r32213170 = r32213161 + r32213169;
        return r32213170;
}

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

Original10.9
Target1.3
Herbie1.3
\[x + \frac{y}{\frac{z - a}{z - t}}\]

Derivation

  1. Initial program 10.9

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

  3. Applied associate-/l*1.3

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

  4. Final simplification1.3

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

Reproduce

herbie shell --seed 2019171 
(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))))