Average Error: 11.1 → 1.4
Time: 4.6s
Precision: binary64
\[x + \frac{y \cdot \left(z - t\right)}{z - a}\]
↓
\[x + y \cdot \frac{1}{\frac{z - a}{z - t}}\]
x + \frac{y \cdot \left(z - t\right)}{z - a}
↓
x + y \cdot \frac{1}{\frac{z - a}{z - t}}
(FPCore (x y z t a) :precision binary64 (+ x (/ (* y (- z t)) (- z a))))
↓
(FPCore (x y z t a)
 :precision binary64
 (+ x (* y (/ 1.0 (/ (- z a) (- z t))))))
double code(double x, double y, double z, double t, double a) {
	return ((double) (x + (((double) (y * ((double) (z - t)))) / ((double) (z - a)))));
}
↓
double code(double x, double y, double z, double t, double a) {
	return ((double) (x + ((double) (y * (1.0 / (((double) (z - a)) / ((double) (z - t))))))));
}

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

Original11.1
Target1.2
Herbie1.4
\[x + \frac{y}{\frac{z - a}{z - t}}\]

Derivation

  1. Initial program Error: 11.1 bits

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

  2. SimplifiedError: 1.3 bits

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

  4. Applied clear-numError: 1.4 bits

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

  5. Final simplificationError: 1.4 bits

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

Reproduce

herbie shell --seed 2020204 
(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))))