Average Error: 10.7 → 1.2
Time: 18.8s
Precision: 64
\[x + \frac{y \cdot \left(z - t\right)}{a - t}\]
↓
\[x + \frac{y}{\frac{a - t}{z - t}}\]
x + \frac{y \cdot \left(z - t\right)}{a - t}
↓
x + \frac{y}{\frac{a - t}{z - t}}
double f(double x, double y, double z, double t, double a) {
        double r40958629 = x;
        double r40958630 = y;
        double r40958631 = z;
        double r40958632 = t;
        double r40958633 = r40958631 - r40958632;
        double r40958634 = r40958630 * r40958633;
        double r40958635 = a;
        double r40958636 = r40958635 - r40958632;
        double r40958637 = r40958634 / r40958636;
        double r40958638 = r40958629 + r40958637;
        return r40958638;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r40958639 = x;
        double r40958640 = y;
        double r40958641 = a;
        double r40958642 = t;
        double r40958643 = r40958641 - r40958642;
        double r40958644 = z;
        double r40958645 = r40958644 - r40958642;
        double r40958646 = r40958643 / r40958645;
        double r40958647 = r40958640 / r40958646;
        double r40958648 = r40958639 + r40958647;
        return r40958648;
}

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
Target1.2
Herbie1.2
\[x + \frac{y}{\frac{a - t}{z - t}}\]

Derivation

  1. Initial program 10.7

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

  3. Applied associate-/l*1.2

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

  4. Final simplification1.2

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

Reproduce

herbie shell --seed 2019171 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTicks from plot-0.2.3.4, B"

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

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