Average Error: 11.0 → 1.3
Time: 3.7s
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 r704648 = x;
        double r704649 = y;
        double r704650 = z;
        double r704651 = t;
        double r704652 = r704650 - r704651;
        double r704653 = r704649 * r704652;
        double r704654 = a;
        double r704655 = r704654 - r704651;
        double r704656 = r704653 / r704655;
        double r704657 = r704648 + r704656;
        return r704657;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r704658 = x;
        double r704659 = y;
        double r704660 = a;
        double r704661 = t;
        double r704662 = r704660 - r704661;
        double r704663 = z;
        double r704664 = r704663 - r704661;
        double r704665 = r704662 / r704664;
        double r704666 = r704659 / r704665;
        double r704667 = r704658 + r704666;
        return r704667;
}

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

Original11.0
Target1.3
Herbie1.3
\[x + \frac{y}{\frac{a - t}{z - t}}\]

Derivation

  1. Initial program 11.0

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

  3. Applied associate-/l*1.3

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

  4. Final simplification1.3

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

Reproduce

herbie shell --seed 2020036 
(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))))