Average Error: 1.2 → 1.1
Time: 13.5s
Precision: 64
\[x + y \cdot \frac{z - t}{z - a}\]
↓
\[\frac{y}{\frac{z - a}{z - t}} + x\]
x + y \cdot \frac{z - t}{z - a}
↓
\frac{y}{\frac{z - a}{z - t}} + x
double f(double x, double y, double z, double t, double a) {
        double r514137 = x;
        double r514138 = y;
        double r514139 = z;
        double r514140 = t;
        double r514141 = r514139 - r514140;
        double r514142 = a;
        double r514143 = r514139 - r514142;
        double r514144 = r514141 / r514143;
        double r514145 = r514138 * r514144;
        double r514146 = r514137 + r514145;
        return r514146;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r514147 = y;
        double r514148 = z;
        double r514149 = a;
        double r514150 = r514148 - r514149;
        double r514151 = t;
        double r514152 = r514148 - r514151;
        double r514153 = r514150 / r514152;
        double r514154 = r514147 / r514153;
        double r514155 = x;
        double r514156 = r514154 + r514155;
        return r514156;
}

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

Derivation

  1. Initial program 1.2

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

  3. Applied clear-num1.2

    \[\leadsto x + y \cdot \color{blue}{\frac{1}{\frac{z - a}{z - t}}}\]
  4. Using strategy rm

  5. Applied *-un-lft-identity1.2

    \[\leadsto x + \color{blue}{\left(1 \cdot y\right)} \cdot \frac{1}{\frac{z - a}{z - t}}\]

  6. Applied associate-*l*1.2

    \[\leadsto x + \color{blue}{1 \cdot \left(y \cdot \frac{1}{\frac{z - a}{z - t}}\right)}\]

  7. Simplified1.1

    \[\leadsto x + 1 \cdot \color{blue}{\frac{y}{\frac{z - a}{z - t}}}\]

  8. Final simplification1.1

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

Reproduce

herbie shell --seed 2019294 
(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)))))