Average Error: 10.4 → 1.1
Time: 14.1s
Precision: 64
\[x + \frac{y \cdot \left(z - t\right)}{z - a}\]
↓
\[x + \frac{y}{\frac{z - a}{z - t}}\]
x + \frac{y \cdot \left(z - t\right)}{z - a}
↓
x + \frac{y}{\frac{z - a}{z - t}}
double f(double x, double y, double z, double t, double a) {
        double r29510020 = x;
        double r29510021 = y;
        double r29510022 = z;
        double r29510023 = t;
        double r29510024 = r29510022 - r29510023;
        double r29510025 = r29510021 * r29510024;
        double r29510026 = a;
        double r29510027 = r29510022 - r29510026;
        double r29510028 = r29510025 / r29510027;
        double r29510029 = r29510020 + r29510028;
        return r29510029;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r29510030 = x;
        double r29510031 = y;
        double r29510032 = z;
        double r29510033 = a;
        double r29510034 = r29510032 - r29510033;
        double r29510035 = t;
        double r29510036 = r29510032 - r29510035;
        double r29510037 = r29510034 / r29510036;
        double r29510038 = r29510031 / r29510037;
        double r29510039 = r29510030 + r29510038;
        return r29510039;
}

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

Original10.4
Target1.1
Herbie1.1
\[x + \frac{y}{\frac{z - a}{z - t}}\]

Derivation

  1. Initial program 10.4

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

  3. Applied associate-/l*1.1

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

  4. Final simplification1.1

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

Reproduce

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

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

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