Average Error: 10.7 → 1.4
Time: 8.7s
Precision: 64
\[x + \frac{y \cdot \left(z - t\right)}{a - t}\]
↓
\[x + \frac{y}{\frac{a}{z - t} - \frac{t}{z - t}}\]
x + \frac{y \cdot \left(z - t\right)}{a - t}
↓
x + \frac{y}{\frac{a}{z - t} - \frac{t}{z - t}}
double f(double x, double y, double z, double t, double a) {
        double r434993 = x;
        double r434994 = y;
        double r434995 = z;
        double r434996 = t;
        double r434997 = r434995 - r434996;
        double r434998 = r434994 * r434997;
        double r434999 = a;
        double r435000 = r434999 - r434996;
        double r435001 = r434998 / r435000;
        double r435002 = r434993 + r435001;
        return r435002;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r435003 = x;
        double r435004 = y;
        double r435005 = a;
        double r435006 = z;
        double r435007 = t;
        double r435008 = r435006 - r435007;
        double r435009 = r435005 / r435008;
        double r435010 = r435007 / r435008;
        double r435011 = r435009 - r435010;
        double r435012 = r435004 / r435011;
        double r435013 = r435003 + r435012;
        return r435013;
}

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

Original10.7
Target1.4
Herbie1.4
\[x + \frac{y}{\frac{a - t}{z - t}}\]

Derivation

  1. Initial program 10.7

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

  3. Applied associate-/l*1.4

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

  5. Applied div-sub1.4

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

  6. Final simplification1.4

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

Reproduce

herbie shell --seed 2019308 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTicks from plot-0.2.3.4, B"
  :precision binary64

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

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