Average Error: 10.6 → 1.3
Time: 16.8s
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 r29648995 = x;
        double r29648996 = y;
        double r29648997 = z;
        double r29648998 = t;
        double r29648999 = r29648997 - r29648998;
        double r29649000 = r29648996 * r29648999;
        double r29649001 = a;
        double r29649002 = r29648997 - r29649001;
        double r29649003 = r29649000 / r29649002;
        double r29649004 = r29648995 + r29649003;
        return r29649004;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r29649005 = x;
        double r29649006 = y;
        double r29649007 = z;
        double r29649008 = t;
        double r29649009 = r29649007 - r29649008;
        double r29649010 = a;
        double r29649011 = r29649007 - r29649010;
        double r29649012 = r29649009 / r29649011;
        double r29649013 = r29649006 * r29649012;
        double r29649014 = r29649005 + r29649013;
        return r29649014;
}

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
Target1.2
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 2019179 
(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))))