Average Error: 10.4 → 1.3
Time: 15.8s
Precision: 64
\[x + \frac{y \cdot \left(z - t\right)}{z - a}\]
↓
\[x + \frac{y}{\frac{z - a}{z - t}}\]
x + \frac{y \cdot \left(z - t\right)}{z - a}
↓
x + \frac{y}{\frac{z - a}{z - t}}
double f(double x, double y, double z, double t, double a) {
        double r419648 = x;
        double r419649 = y;
        double r419650 = z;
        double r419651 = t;
        double r419652 = r419650 - r419651;
        double r419653 = r419649 * r419652;
        double r419654 = a;
        double r419655 = r419650 - r419654;
        double r419656 = r419653 / r419655;
        double r419657 = r419648 + r419656;
        return r419657;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r419658 = x;
        double r419659 = y;
        double r419660 = z;
        double r419661 = a;
        double r419662 = r419660 - r419661;
        double r419663 = t;
        double r419664 = r419660 - r419663;
        double r419665 = r419662 / r419664;
        double r419666 = r419659 / r419665;
        double r419667 = r419658 + r419666;
        return r419667;
}

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

Original10.4
Target1.3
Herbie1.3
\[x + \frac{y}{\frac{z - a}{z - t}}\]

Derivation

  1. Initial program 10.4

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

  3. Applied associate-/l*1.3

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

  4. Final simplification1.3

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

Reproduce

herbie shell --seed 2019304 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTicks from plot-0.2.3.4, A"
  :precision binary64

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

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