Average Error: 1.5 → 1.3
Time: 15.8s
Precision: 64
\[x + y \cdot \frac{z - t}{a - t}\]
↓
\[x + \frac{y}{\frac{a - t}{z - t}}\]
x + y \cdot \frac{z - t}{a - t}
↓
x + \frac{y}{\frac{a - t}{z - t}}
double f(double x, double y, double z, double t, double a) {
        double r41259029 = x;
        double r41259030 = y;
        double r41259031 = z;
        double r41259032 = t;
        double r41259033 = r41259031 - r41259032;
        double r41259034 = a;
        double r41259035 = r41259034 - r41259032;
        double r41259036 = r41259033 / r41259035;
        double r41259037 = r41259030 * r41259036;
        double r41259038 = r41259029 + r41259037;
        return r41259038;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r41259039 = x;
        double r41259040 = y;
        double r41259041 = a;
        double r41259042 = t;
        double r41259043 = r41259041 - r41259042;
        double r41259044 = z;
        double r41259045 = r41259044 - r41259042;
        double r41259046 = r41259043 / r41259045;
        double r41259047 = r41259040 / r41259046;
        double r41259048 = r41259039 + r41259047;
        return r41259048;
}

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

Original1.5
Target0.4
Herbie1.3
\[\begin{array}{l} \mathbf{if}\;y \lt -8.508084860551241069024247453646278348229 \cdot 10^{-17}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;y \lt 2.894426862792089097262541964056085749132 \cdot 10^{-49}:\\ \;\;\;\;x + \left(y \cdot \left(z - t\right)\right) \cdot \frac{1}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a - t}\\ \end{array}\]

Derivation

  1. Initial program 1.5

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

  3. Applied clear-num1.5

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

  5. Applied un-div-inv1.3

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

  6. Final simplification1.3

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

Reproduce

herbie shell --seed 2019174 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisLine from plot-0.2.3.4, B"

  :herbie-target
  (if (< y -8.508084860551241e-17) (+ x (* y (/ (- z t) (- a t)))) (if (< y 2.894426862792089e-49) (+ x (* (* y (- z t)) (/ 1.0 (- a t)))) (+ x (* y (/ (- z t) (- a t))))))

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