Average Error: 10.5 → 1.5
Time: 3.8s
Precision: 64
\[x + \frac{y \cdot \left(z - t\right)}{a - t}\]
↓
\[x + \frac{y}{\left(a - t\right) \cdot \frac{1}{z - t}}\]
x + \frac{y \cdot \left(z - t\right)}{a - t}
↓
x + \frac{y}{\left(a - t\right) \cdot \frac{1}{z - t}}
double f(double x, double y, double z, double t, double a) {
        double r607697 = x;
        double r607698 = y;
        double r607699 = z;
        double r607700 = t;
        double r607701 = r607699 - r607700;
        double r607702 = r607698 * r607701;
        double r607703 = a;
        double r607704 = r607703 - r607700;
        double r607705 = r607702 / r607704;
        double r607706 = r607697 + r607705;
        return r607706;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r607707 = x;
        double r607708 = y;
        double r607709 = a;
        double r607710 = t;
        double r607711 = r607709 - r607710;
        double r607712 = 1.0;
        double r607713 = z;
        double r607714 = r607713 - r607710;
        double r607715 = r607712 / r607714;
        double r607716 = r607711 * r607715;
        double r607717 = r607708 / r607716;
        double r607718 = r607707 + r607717;
        return r607718;
}

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

Original10.5
Target1.4
Herbie1.5
\[x + \frac{y}{\frac{a - t}{z - t}}\]

Derivation

  1. Initial program 10.5

    \[x + \frac{y \cdot \left(z - t\right)}{a - t}\]
  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-inv1.5

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

  6. Final simplification1.5

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

Reproduce

herbie shell --seed 2019356 
(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))))