Average Error: 10.6 → 1.3
Time: 19.0s
Precision: 64
\[x + \frac{y \cdot \left(z - t\right)}{z - a}\]
↓
\[x + y \cdot \frac{z - t}{z - a}\]
x + \frac{y \cdot \left(z - t\right)}{z - a}
↓
x + y \cdot \frac{z - t}{z - a}
double f(double x, double y, double z, double t, double a) {
        double r27356702 = x;
        double r27356703 = y;
        double r27356704 = z;
        double r27356705 = t;
        double r27356706 = r27356704 - r27356705;
        double r27356707 = r27356703 * r27356706;
        double r27356708 = a;
        double r27356709 = r27356704 - r27356708;
        double r27356710 = r27356707 / r27356709;
        double r27356711 = r27356702 + r27356710;
        return r27356711;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r27356712 = x;
        double r27356713 = y;
        double r27356714 = z;
        double r27356715 = t;
        double r27356716 = r27356714 - r27356715;
        double r27356717 = a;
        double r27356718 = r27356714 - r27356717;
        double r27356719 = r27356716 / r27356718;
        double r27356720 = r27356713 * r27356719;
        double r27356721 = r27356712 + r27356720;
        return r27356721;
}

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

Original10.6
Target1.3
Herbie1.3
\[x + \frac{y}{\frac{z - a}{z - t}}\]

Derivation

  1. Initial program 10.6

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

  3. Applied *-un-lft-identity10.6

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

  4. Applied times-frac1.3

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

  5. Simplified1.3

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

  6. Final simplification1.3

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

Reproduce

herbie shell --seed 2019172 
(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))))