Average Error: 1.2 → 1.1
Time: 5.0s
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 r557303 = x;
        double r557304 = y;
        double r557305 = z;
        double r557306 = t;
        double r557307 = r557305 - r557306;
        double r557308 = a;
        double r557309 = r557305 - r557308;
        double r557310 = r557307 / r557309;
        double r557311 = r557304 * r557310;
        double r557312 = r557303 + r557311;
        return r557312;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r557313 = y;
        double r557314 = z;
        double r557315 = a;
        double r557316 = r557314 - r557315;
        double r557317 = t;
        double r557318 = r557314 - r557317;
        double r557319 = r557316 / r557318;
        double r557320 = r557313 / r557319;
        double r557321 = x;
        double r557322 = r557320 + r557321;
        return r557322;
}

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 2020081 +o rules:numerics
(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)))))