Average Error: 10.6 → 1.4
Time: 3.5s
Precision: binary64
\[x + \frac{y \cdot \left(z - t\right)}{a - t}\]
↓
\[x + \frac{1}{\frac{\frac{a - t}{z - t}}{y}}\]
x + \frac{y \cdot \left(z - t\right)}{a - t}
↓
x + \frac{1}{\frac{\frac{a - t}{z - t}}{y}}
double code(double x, double y, double z, double t, double a) {
	return ((double) (x + ((double) (((double) (y * ((double) (z - t)))) / ((double) (a - t))))));
}
↓
double code(double x, double y, double z, double t, double a) {
	return ((double) (x + ((double) (1.0 / ((double) (((double) (((double) (a - t)) / ((double) (z - t)))) / y))))));
}

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

Original10.6
Target1.3
Herbie1.4
\[x + \frac{y}{\frac{a - t}{z - t}}\]

Derivation

  1. Initial program 10.6

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

  3. Applied associate-/l*1.3

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

  5. Applied clear-num1.4

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

  6. Final simplification1.4

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

Reproduce

herbie shell --seed 2020161 
(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))))