Average Error: 1.3 → 1.2
Time: 51.2s
Precision: 64
\[x + y \cdot \frac{z - t}{z - a}\]
↓
\[x + \frac{y}{\frac{z - a}{z - t}}\]
x + y \cdot \frac{z - t}{z - a}
↓
x + \frac{y}{\frac{z - a}{z - t}}
double f(double x, double y, double z, double t, double a) {
        double r28305098 = x;
        double r28305099 = y;
        double r28305100 = z;
        double r28305101 = t;
        double r28305102 = r28305100 - r28305101;
        double r28305103 = a;
        double r28305104 = r28305100 - r28305103;
        double r28305105 = r28305102 / r28305104;
        double r28305106 = r28305099 * r28305105;
        double r28305107 = r28305098 + r28305106;
        return r28305107;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r28305108 = x;
        double r28305109 = y;
        double r28305110 = z;
        double r28305111 = a;
        double r28305112 = r28305110 - r28305111;
        double r28305113 = t;
        double r28305114 = r28305110 - r28305113;
        double r28305115 = r28305112 / r28305114;
        double r28305116 = r28305109 / r28305115;
        double r28305117 = r28305108 + r28305116;
        return r28305117;
}

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

Derivation

  1. Initial program 1.3

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

  3. Applied clear-num1.3

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

  5. Applied un-div-inv1.2

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

  6. Final simplification1.2

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

Reproduce

herbie shell --seed 2019165 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisLine from plot-0.2.3.4, A"

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

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